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Sim3DMax User Manual

1. The File Format can be one of ascii fortran_binary c_binary The choice ascii is used for files in a text for mat as produced by FORTRAN for type COMPLEX Diffractsource Wavelength micron 0 65 Filename diffract_output dat File Format ascii Grid Type staggered z location micron 0 1 The fortran_binary format corresponds to unformatted output produced by FORTRAN and is the same as the binary format used in DIFFRACT The option c_binary is for the binary output produced for by C programs The later is different from FORTRAN in that it does not have data tags and elements of the arrays are written in the row major order Binary format allows smaller file size and faster data input or output than does ASCII 4 PARAMETER FILE DESCRIPTION 25 Az 2 H x y Figure 6 In Diffract source file E fields must be sampled on an xry plane at some position z with H fields sampled on an xy plane at position z Az 2 The Grid Type can be specified as staggered or collocated to indicate the logical location on the computation mesh of the E and H fields The staggered corresponds to a staggered positioning of E and H fields as defined in the FDTD method The collocated option corresponds to all field components defined at the cell center The grid type should be set to be the same as the grid type used when creating the source file with FDTD Export option in DIFFRACT The last line is optional and specifies position a
2. 0 707000E 03 Figure 33 Imaged sample comprised of three randomly placed marks Center round sphero cylindrical cap bump with length 1000nm width 800nm height 60nm Top left flat elliptical stadium pit with length 1200nm width 1000nm depth 60nm Bottom right round sphero cylindrical cap pit with length 1500nm width 700nm depth 60nm The imaged sample consists of three marks pits and bumps placed arbi trarily in a layer of material with high reflection coefficient ny n ki 9 APPLICATION EXAMPLES 89 0 4 4 52 r 1 n1 1 n 0 9633 similar to the Optical Disk surface The input geometry Figure 33 AddLayer material Z min Z max AddBump bump_type material substrate x_O y_O Z_O width height length thickness angle AddBump bump_type material substrate x_QO y_O Z_O a b height length thickness wall_angle angle string micron micron Aluminum 260e 3 100e 3 L sphero cylindrical cap string string micron micron micron micron micron micron micron Aluminum Vacuum 0 0 0 0 260e 3 800e 3 60e 3 200e 3 160e 3 degrees 45 Lelliptical stadium string string micron micron micron micron micron micron micron degrees degrees Aluminum Vacuum 1 0 1 0 260e 3 1200e 3 1000e 3 60e 3 0e 3 160e 3 60 45 9 APPLICATION EXAMPLES 90 AddBump bump_type sphero cylind
3. 4A tmaz where Azjop is the grid spacing used near the PML region at the top of the computational domain There can be only one ExportReflected entry in the input file and its position on the grid is always at the top of the domain as specified above regardless of the position along the z axis of any of the sources When used with DiffractSource or PlanewaveSource at their default locations the ExportReflected plane will be just above the source plane and will sample only the reflected fields 4 22 2 Export of the transmitted field If ExportReflected entry described above is specified it must also be followed by at least one ExportTransmitted entry This entry is similar to the entry for the reflected field but its plane has a user defined rather than default position If an ExportTransmitted entry is not necessary in the computation its position can be set to be outside of the computational domain and it will be ignored The ExportTransmitted entry sets the filename of the export file into which to write complex valued amplitude distribution of the Ez Ey and H H H fields computed at the specified plane The file content and pa rameters are the same as for the reflected field described above ExportTransmitted Filename fdtd export transmitted File Format fortran_binary Grid Type collocated z location micron 50e 3 NX NY 512 512 In addition z location specifies the position of the pla
4. Similar problems occur when computationally expensive monitors e g Fourier Transform or volume energy monitors have locations such that with some choice of the processor grid all monitors end up in one or two CPUs instead of being distributed evenly among all processors When possible proper processor grid should be selected to produce a better apriori load balancing The actual measured load balance may still vary due to the size of PML layers which are more compute intensive than other equation updates and per processor problem size that together with processor cache utilization can have an impact on parallel computation efficiency Appendix C Staggered positioning of the field components in user defined sources Since the E and H fields in the FDTD method are not collocated in space and time the user defined sources in 2D computations section 4 18 must properly take into account the staggering of the fields The field locations for the 2D TM Ex Hy_Hz and TE Hx_Ey_Ez modes are shown in Figure 38 When complex field amplitude distribution is specified in the user file ITM TE x Jk 1 E jk 1 H j 1k 1 Figure 38 E and H field staggering in 2D Ex Hy Hz and Hx_Ey_Ez modes for a source defined along the y axis i e zmin zmax in the UserSource definition the E H fields for the Ex Hy Hz mode and H Ey fields for the Hx Ey Ez mode must be defined at positions separated by a half cell size in the z direct
5. where f z yWworwoy lwz z wy z2 and b z atan Z we z w 1 n z Da l Da Dx R z zlit Z 2 lp Tw4 A and similar definitions apply to functions with y label In 2D OF Ox 0 the corresponding formulas are Ely 2 f z e 2c eik AR 3 f z ywo w z p y or p 2 and p z atan w z wg 1 T 2 D lp Riz z 1 ae a 4 and lp mw A In the equations k is the wavenumber in the incidence medium and A is the wavelength in the incidence medium The unit vector E V m E V m y um i y um Figure 10 and E components of a 2D Gaussian beam sourced along the y axis at Zmin Zmaz 3 5m with beam amplitude FWHM 0 5um Ao 0 65um Nref 1 3 and direction set to 1 The z parameter is 4um resulting for a beam that propagates in the z direction in initial focusing along the linear polarization direction is denoted by s Formulas 1 3 4 PARAMETER FILE DESCRIPTION o gt D D Figure 11 Ey and S components of a 3D Gaussian beam 33 assume that z axis is the direction of propagation and are an exact solution to the Schrodinger equation OE x Oz V7E x 2ik 0 E x derived from Maxwell s equations assuming that 3 is small In the case of multiple beam sources GaussianBeamSource the parameter file must be specified one after another 4 18 2D source specification from t
6. 6 1 6 2 6 3 6 4 6 9 Dielectric materials 0 00 eee ee en Debye model 2 a a a a Lorentz model aooaa a a a a a a a a Drude model oaoa aa 2 0000 002 2 ee Magnetic material model a a a a a a a 7 Geometry File Description fl ee 1 3 1 4 9 1 9 2 9 3 9 4 9 5 Geometry specification from an input file o oo aaa Basic Geometric primitives sooo a e e e 2 08 7 2 1 Sphere oaa 00000 eee O a eee eae ee eee 7 2 8 Ellpsoid 0 0 0 020000222 oe 1 2 4 AA og ow ewe bee eee eee teeee EERTE te ee Ee Ee Po oe ee eS Pees POI ea ewe ee eee ee BE eet Blips 454564408 tReet aH EH Ee eae ees tet I ee we ee eRe S tage FOCI se mew wee whee ERR Des Geometric objects for optical data storage media modeling 7 3 1 Bumps pits acne eee bene tee eae ears 1 3 2 Grooves 2 nwa we ee ORO wee EO ees 7 3 3 Conformal layer 04 7 3 4 Sine layer 2 0 a a Dielectric Material Interfaces 0 0 Comments in the input files Application Examples Order of convergence 2 a a a Reflection from abi layer 08 Scattering of a planewave from a sphere Laser beam scattering from a mark Imaging problem 0 00000 ee een 46 48 49 50 54 59 59 57 57 58 58 59 59 59 60 60 60 62 63 66 66 10 i 13 14 T4 Appendices 96 A Computational domain decomposition for parallel processing 96 B Pa
7. 0 5 x_min max micron 450e 3 70e 3 AddQuadrilateral material string GaAs elie zal micron 0 5 O 5 M22 micron 25 O 5 X3 Z3 micron 0 0 0 0 x4 z4 micron 0 25 0 0 y_min max micron 0 25 0 25 AddTriangle material string Vacuum xi yl imicronki OTIO X2 y2 micron 1 0 1 0 X3 Whe micron 0 0 1 0 Zz min max micron 450e 3 70e 3 The lengths sizes and coordinates in three space dimensions are always spec ified in the order x y z The lengths sizes and coordinates in the plane are always specified in the order x y or x z or y z For all objects specified with the min max entries the minimum and maximum coordinate values determine the thickness of the object max min These objects such as a layer cone triangle etc can be specified to have an extent thickness along one of the axis e g x y or z Corresponding axis labels for other parameters must be specified accordingly For example if the Cylinder object is set to have a y_min max extent then its center position should be set to be in the X Z plane by using x z center For AddEllipsoid and AddEllips the a b and c parameters are semi major axis values The angle option for the AddEllips object specifies the angle of rotation counter clockwise for positive values of the ellipse with respect to the positive direction of the x axis The AddCappedRectangle 7 GEOMETRY FILE DESCRIPTION 62 type represents an object of finite thickn
8. Floquet or PML can be used The selected boundary condition applies to both top and bottom boundaries of the specified axis e The Perfect Electric Conductor PEC boundary condition sets the tangential electric field components to zero on the boundary e The periodic boundary condition allows simulation of the periodic systems in 2D or 3D e The Floquet boundary condition is used with the planewave source sec 4 16 to model periodic systems in 2D or 3D with arbitrary planewave incidence angles e The Perfectly Matched Layer PML option sets up an absorbing layer that simulates an open boundary condition An example of the content of the boundary conditions file that sets the x axis to a 15 point PML with default PML parameters for o and k y axis to periodic and z axis to PEC BoundaryConditions x axis PML nz_pml 15 Sigma kappa 0 0 0 0 y axis periodic z axis PEC If the desired boundary type is PML for any of the axes the next line after axis PML must specify for that axis the number of points in the absorbing layer followed by sigma kappa the values of Cmax and Kmaz at the end of the absorbing layer A polynomial of order Mypm 3 is used in computing the grading of the PML layers If Omar Or Kmaz are set to zero they will assume their respective default values of Kmar 1 0 and Omax 8 X Mpml 1 Npm Ay Lo o where A is the cell size in the PML region Inside the PML layers the material refr
9. The material Aluminum is assumed to be defined in the material definition file The values 2min Zmaz are arbitrary and don t have to be inside the com putational domain boundaries Values that lie outside the bounds of the computational domain are truncated to the edges of the computational do main Each geometric primitive overwrites any pre existing definition at the points where it is defined so if two layers or any other objects physically overlap in space the one defined latest in the file will take precedence at the points of overlap To change the background material of the entire compu tational domain a layer of the desired material can be added with Zin Zmaz of the layer correspondingly less than and greater than the computational domain boundaries Zmin Zmar Figure 1 7 2 1 Sphere AddSphere material string Gold center micron 0 0 0 0 0 0 radius micron dash Figure 15 Definition of parameters for sphere center o yo Zo radius r 7 GEOMETRY FILE DESCRIPTION 59 7 2 2 Cube AddCube material string Aluminum center micron 0 0 0 0 0 0 Lx Ly LZ micron 1 0 1 5 0 8 Figure 16 Definition of parameters for cube center o Yo zo size Lz Ly Lz 7 2 3 Ellipsoid AddEllipsoid material string Cobalt 7 center micron 0 0 0 0 0 0 a b c micron 1 0 1 5 0 8 X y Figure 17 Definition of parameters for ellipsoid center o yo zo semi major axis a b c 7 2 4 Cone AddCone ma
10. or side lengths Example definitions for unit element 7 GEOMETRY FILE DESCRIPTION unit element Lcircle radius micron unit element ellips a b micron unit element rectangle Ex Ey micron unit element triangle side micron 63 0 15 Ole ihe 0 0 3 0 2 0 3 The last line is optional It specifies rotation angle of the lattice in the E oe a a La its ie revi greriaytt rig rrirryd fice 2 foro ie r4ri ey 4 I eeoeoeoeeeo 3 YYYY YYYYY oeese eee LILIT IKII eeoeseeeesee e PeSeeeeoeeeao G eeeee88 TYyryrryrrryyny ee8e600808 806 a Mia iim Me tin ae am 4 aa ae p 2 1 1 2 x um y um y um x um 3 l N TT T MA azAAA AA LA SA bhAAAA AAAA Adl RAAAAAAAA ASA hAAAAA AAA AA LAA A A bh 4sAAa AbAbAASA bALAAA ALALAASA LbALAAA AAAAd hAAAA AAAA S a A A A A Pr wae Gar 1 2 Figure 22 Triangular lattice of circular rods with a point defect Rectangular lattice of triangular rods with line defects Honeycomb lattice of circular holes plane selected by the plane entry 7 2 9 Pattern A periodic pattern that has a unit element consisting of a number of other geometric objects can be setup using an AddPattern object 7 GEOMETRY FILE DESCRIPTION AddPattern pattern center micron 0 0 0 0 0 0 pattern size micron 1 4 1 4 0 5 M N P number 4 4 1 ConvexPolygon material str
11. x y H x y fields are sampled on a plane located along the z axis a distance of 6 2 behind the plane on which E x y E 2 y fields are sampled Figure 6 while positive 6 corresponds to H fields sampled on a plane 6 2 ahead of the E field plane The 6 and domain sizes L L are in units of A n The E and H fields are in normal ized units defined in the DIFFRACT manual For a beam propagating in DIFFRACT along the positive direction of the z axis the H fields must be sampled half a cell behind E fields hence negative 0 Az must be specified in the FDTD Export option of DIFFRACT when creating a file for DIFFRACT source option described in section 4 14 For DIFFRACT versions 8 2 and 8 3 the file contains on the first line the refractive index n the wavelength in the vacuum A the units of the wavelength cm mm um nm followed on the second line by Nz Ny Lz Ly and the field distributions with intervening as above The domain sizes Ly and L and are in units of the wavelength A in the vacuum For DIFFRACT versions 8 4 and above default the same as the format of versions 8 2 and 8 3 but the E and H fields are in physical units of V m and A m 4 21 Coordinate system transformation In Diffract the beam nominally propagates along the positive z axis In Sim3D_Max the incident Diffractsource beam cross section is intended for propagation along the negative z axis Figure 13 Hence a coordinate
12. 22 end of simulation CheckpointFile RestartFromCheckpointFile no WriteCheckpointFile yes Each processor creates one checkpoint file in the working directory under filename chkpLxMxN where L M N are integers identifying the processor If the checkpoint file already exists it is overwritten When simulation is restarted from the checkpoint file the program as sumes that the material and geometry definition files are the same as those used in the run that created the checkpoint file Also start time tmin is reset to the simulation time read from the checkpoint file and tmaz is set to the new tmin plus the difference between tmax and tmin appearing in the input parameters file All other time dependent entries in the parameter file are used as specified When monitors or ExportReflected Transmitted planes are used with the checkpoint option the Fourier transforms and monitored fields are not saved to the checkpoint files and hence they do not persist from one checkpoint to another Instead they are computed anew in every run Therefore for example the data in the Export plane files from any run is valid only if the simulation time tmax tmin of that particular run is large enough to sample the minimum required number of periods of the source otherwise a warning message is issued by the program 4 12 Source time profile The TimeProfile block is optional in the input file When present it spec ifies the mod
13. It must be an ASCII text file and is expected to contain on the first line the number of points nz ny nz which should match the number of points specified in the input parameters file The rest of the input file should contain the logical enumeration value m of the material for each cell 2 7 k of the computational grid This logical value is simply an integer number m gt 0 corresponding to the order in which materials are defined one after another in the material definition file Materials are counted in the material definition file starting from 1 The value 0 corresponds to the predefined material Vacuum The order of the cell input is one in which k changes from 1 to n first then 7 from 1 to ny then ti from 1 to ng The material assignment for each cell read from the file overwrites any geometry defined by entries specified before the ReadGeometryFile Other geometry entries basic objects or another ReadGeometryFile can follow ReadGeometryFile 7 GEOMETRY FILE DESCRIPTION 08 entry and will modify the setup accordingly 7 2 Basic Geometric primitives Each geometric primitive is associated with a particular material via user defined material labels as they appear in the material definition file e g the following adds a layer uniform in x and y of aluminum 50nm in thickness from z 10nm to z 60nm to the default background of Vacuum AddLayer material string Aluminum Z_min micron 10e 3 Z_max micron 60e 3
14. Re E Im E Field3 Field4 are Re H Im H Field5 Field6 are Re H lm H Field7 is real lt S gt Field8 is real lt S gt The complex valued amplitudes of the E and H fields are computed via time Discrete Fourier Transform of the real valued E and H FDTD vari ables The DFT is evaluated at the source frequency if bandwidth option is set to Lsource frequency The real valued components of the time av eraged Poynting vector are computed from complex valued E and H fields as lt lt S gt gt Re E x H This formula assumes a continuous wave time harmonic dependence of fields 5 BOUNDARY CONDITIONS FILE DESCRIPTION 46 4 24 2 Monitors for computations in 3D For 3D computations parameter Mode is set to 3D and xmin xmax ymin ymax or zmin zmax can be used to specify a line segment or a plane section along which the monitor is applied For a line segment only one of the min max coordinate pairs can have distinct values so that the line segment is aligned with one of the x y or z coordinate directions For a plane section only two of the min max coordinate pairs can have distinct values so that the section is in the XY YZ or XZ plane In 3D for a monitor type time history the first line specifies the 3D computation mode monitor type number of monitor points in space and number of points sampled in time e g 3D time history Nx Ny Nz Ntime The output file contains one line for each point in space
15. distribution in the export plane In such cases magnitude and phase distributions of the ex ported fields are not suitable for propagation in the DIFFRACT software since it requires constant refractive index in the export plane However the data can be visualized or processed otherwise 4 23 Monitor header comment A sequence of characters can be added at the beginning of the first line of the Monitor files described in section 4 24 For example MonitorFileComment string will put as the first character on the first line which describes the monitor type number of points etc in all Monitor files This entry is optional in the input file 4 24 Monitor specification Monitors are optional in the input file They can be used to sample fields at specified points and within a specified time interval Parameter Mode can be either 3D Hx_Ey_Ez for a Hz Ey E 2D mode or Ex_Hy_Hz for Ez H H 2D mode The Type can be either fourier transform or time history The output file specified under Filename is an ASCII text file Monitor Mode Hx_Ey_Ez Type Lfourier transform Filename string monitori out xmin xmax micron 0 0 0 0 ymin ymax micron TROR RO zmin zmax micron 0 0 0 0 t_on t_off periods 8 bandwidth frequency interval fmin fmax THz 285 0 315 0 Another monitor example 4 PARAMETER FILE DESCRIPTION 43 Monitor Mode Ex_Hy_Hz Type time history Filename string monitor2 out xm
16. done with 5 6 x 10 grid points per processor show that the run time stays almost constant when the problem size increases proportionally to the number of processors The tests done on Linux cluster with fixed 1GB total problem size show linear decrease of the run time with number of CPUs Similar scaling was measured on the SGI Origin system with fixed total problem size 4 x 10 grid points distributed to 4 8 and 16 processors A number of factors can contribute to reducing the load balance and hence parallel computation efficiency When material distribution in the compu tational domain and choice of the processor grid are such that one of the processors ends up with most of its sub domain occupied by the material that requires more CPU intensive update of the constitutive equations than materials present on other processors e g Lorentz or MPM material models vs dielectric Figure 37 then the overall run time may be dominated by the processor with the highest load reducing parallel efficiency M dielectric EE Lorentz a b M M 1 1 M M Z X Y Figure 37 a Example of computational domain decomposition along the z axis and resulting uneven load assignment processor P updates in its sub domain computationally more expensive Lorentz material model and also has to process monitors M and M in the XY plane b Load balance in this example can be achieved by partitioning the computational domain along the y axis
17. embedded in a glass substrate The Floquet boundary condition allows simulation of a planewave incident at an arbitrary angle on a structure that is periodic along the z and or y axis With this boundary condition the L and Ly can be arbitrary and do not have to be integer multiples of 27 k 27 k Therefore a single unit cell of the periodic structure can be modeled 4 PARAMETER FILE DESCRIPTION 30 PML PML Pa Periodic Periodic lt Periodic gt eS J PLL D TFSF area a Periodic PlaneWave source TFSF top z plane or DIFFRACT source plane Z i S PML cattering Scattering a Object PML object gt X Figure 9 Left computational domain with PML boundaries along all axis and Total Field Scattered Field TFSF formulation for the planewave source The scattering object is enclosed by the TFSF surface the refractive index must be the same at all sides of the TFSF boundary Right computational domain with PML boundaries along the z axis and periodic or Floquet boundary conditions along the z and y axis It is assumed in this plot that the TFSF boundary top option is in effect for the planewave source 4 17 Gaussian beam source specification One or more gaussian beams can be specified for 2D or 3D computations by using a GaussianBeamSource GaussianBeamSource Wavelength micron 0 633 Mode LHx_Ey_Ez Exyz component Ly FWHM micron 2 0 2 0 beam waist offset micron 0 0 dir
18. field component entry are E field followed by one of the x Ly or z for computations in 3D For 2D Hx_Ey_Ez mode E field components Ly or z or H field component x can be speci fied For 2D Ex_Hy_Hz mode H field components Ly or z or E field component x can be specified At each time step of the computation the value of the specified field component at the source location single grid point rps 0 Yo 20 is set to a time harmonic sin wt dependence with specified TimeProfile This results in a non transparent hard point source Instead of the electric field component a polarization vector component can be specified For example P field x can beset for 3D or 2D Ex_Hy_Hz computation mode In this case the point source is transparent and is im plemented by adding at a single grid point a time derivative of the polar ization vector Pps of the point source to the time derivative of the rest of the displacement field aD aP ag at O Ips On the computational grid the point source is representative of a volume of the single grid cell and hence the amplitude of the point source will depend on the grid resolution In the case of multiple point sources PointSource entries in the parameter file must be specified one after another 4 16 Planewave source specification A planewave source is set by the following input 4 PARAMETER FILE DESCRIPTION 27 PlaneWavesource Wavelength micron 0 65 Mod
19. name of a text file containing simulation parameters e g 5im3D Max parameters input If parameter filename is not specified the program will prompt the user to enter it To do many runs in sequence batch files in Windows or shell script files in Unix can be used For example in Windows a text file called e g simulate bat containing lines 4 PARAMETER FILE DESCRIPTION 9 5im3D_Max parametersil input b 5im3D_Max parameters2 input b 5im3D_Max parametersN input can be executed to perform unattended N simulations with different param eters The switch b at the end of the command lines prevents the batch job from stopping at the end of each run or in case error conditions are encountered For parallel runs the program is invoked using MPI launcher and takes in addition to the input parameter file name an optional list of three integer numbers These numbers specify the desired number of processing elements CPUs or threads per x y z dimension of the computational domain see Appendix A Figure 35 for details For example to start a run on six pro cessors and default distribution of processing elements use mpiexec exe np 6 Sim3D_Max exe parameters input To assign one processor along the x axis three along the y axis and two along the z axis use mpiexec exe np 6 Sim3D_Max exe parameters input 1 3 2 The choice of processor grid load balancing issues and parallel performance on different platforms are dis
20. number 8 x1 y1 micron 0 25 0 5 x2 y2 micron 0 25 0 5 x3 y3 micron 0 4 0 2 x4 y4 micron 0 4 0 2 x4 y4 micron 0 25 0 5 X54 y5 micron 0 25 0 5 x7 y7 micron 0 4 0 2 x8 y8 micron 0 4 0 2 z_min max micron 0 25 0 25 AddLayer material string Si02 y_min micron 750e 3 9 APPLICATION EXAMPLES 19 y_max micron 1000e 3 are commented out and will have no effect on the geometry setup Successive commented out blocks must be separated by at least one space or newline character 9 Application Examples This section works through simple validation cases and example input files set to simulate scattering of a laser beam from a mark similar to those found on the optical disk surface and an imaging problem with a partially coherent light source References 4 8 and articles listed in Appendix E illustrate more application examples dependence of the reflected signal on beam center position with respect to the sub wavelength marks modeling of push pull tracking signal from a grooved optical disk surface and light transmission through small elliptical apertures in a thin metal film E V m A A Transmitted Reflected ct is exa 1 8 8 Error Figure 28 Rate of convergence for a problem of a planewave scattering from a a dielectric interface The error in the numerical solution decreases as O Az with increasing number of points per wa
21. nx 2nzpyyr non PML points over the length L nz pmL dZtop dXp4 inside of the domain where d top dpo 18 the cell size in the PML regions Inside the PML layers the nonuniform grid should not have any variation of the cell size in the direction normal to the PML layer To change the boundary conditions or modify the default number of PML points see section 5 Large cell size ratio r A A in neighboring regions of the non uniform erid along any axis can have a negative impact on the accuracy of the solu 4 PARAMETER FILE DESCRIPTION 15 tion Gradual change of the cell size must be used when a ratio of cell size r gt 2 is used for grid refinement Additionally large cell size aspect ratios A A u v x y z must be avoided to maintain accuracy The grid cell size along any axis and within a region of material with refractive index nef can be estimated as A lt A NppwunNref where A is the free space wavelength of interest and Nppw is the number of cells per wavelength in the medium Typically for errors in the solution to be less than a few percent Nppw gt 20 30 must be used The computation time step is proportional to the smallest cell size found in the computational domain Convergence of the solutions can be verified by decreasing the cell sizes typically by a factor of 2 with all other problem parameters unchanged and repeating the simulation 4 4 Computations in 2D The default computation mode is 3
22. operating systems ABI7OS NT 2000 XP Pro XP Pro with Accoleware Compute Cluster Server 2003 x64_ cx if xe if An Intel Pentium 4 AMD Opteron or equivalent 1GHz or better pro cessor and 1Gbyte or more of random access memory are recommended The lower bound on the memory in bytes required by any given problem can be estimated with the following formula M N x Ny x N x Ny x Nf 2 INSTALLING THE FDTD PROGRAM TO HARD DISK 7 where Nz Ny N are the number of points along the x y z axis and N is the number of variables stored at each point The value of N is 6 for E and H vector fields if only dielectric material model is used and N 6 3p E and H plus polarization vectors if a dispersive Debye material model with p poles is used or N 9 6p for the dispersive materials described by the Lorenz or Drude model with p poles see section 6 The number of variables doubles when the Floquet boundary conditions are used The factor Ny in the formula equals 4 bytes per float number for single precision and Ny 8 for double precision For example an application that uses only a dielectric material model boundary conditions other than Floquet and 200 x 200 x 100 grid points will require about 200Mbytes of memory Binary executables of the program for parallel computations take advantage of the many CPUs in the multiple processor workstations or a cluster of workstations connected by a high speed com
23. plus a interpN extension where N is the rank of the 6 processor that created the file The content of the interpN file is the same as that of the input source file with two exceptions the first line specifying the number of points is omitted and there is an additional field last entry on each line identifying material logical index along the source line The E and H fields are sourced in time with time harmonic ansatz e as RelH y z e Re E y z e etc Appendix C Figure 38 gives a detailed description of the required staggered E and H field positioning of the user defined source for the 2D Hx_Ey_Ez and Ex_Hy_Hz computations In the case of multiple user defined sources UserSource entries in the parameter file must be specified one after another 4 PARAMETER FILE DESCRIPTION 35 0 6 Y nax max 0 4 0 2 waveguide center 2 z um T l l 0 2 source line segment 0 4 1 0 8 06 04 02 0 0 2 0 4 0 6 0 8 1 y um Figure 12 Example of a waveguide running along the y axis with the source applied on a line segment along the z axis at Ymin Ymax 0 8um The refractive index distribution waveguide width and center line position are specified as part of the WaveguideSource definition and should correspond to the geometry and material properties specified in the geometry and material definition files 4 19 2D planar waveguide source specification A plana
24. there is one input parameter the name of the file with the distribution of the optical constants e g Material Label string GST model dielectric x y filename string GST input The data file is an ASCII file containing on the first line a single word e g Dielectric x y followed on the second line by Ll iin Line LYmin LYmax Nx Ny Nog bq 6 MATERIAL FILE DESCRIPTION 50 where Lamin LEmaz specify the domain size in nanometers in which the data is defined Nx Ny are the number of rows columns in the file and Nag Cog are the background refractive index and conductivity Subsequent lines must contain entries nij dij for each point i j of the grid defined on the first line The units of n and o must be the same as in the material model dielectric described above The data in the file is read in the order indicated by the following pseudo code segment for i 1 to Nx for j l to Ny read nli j sigmali Lj Then the data is interpolated to the FDTD computational grid The grid points that are outside of the range specified by L min L amp mar LYmin LYmaz are assigned background optical constant values Nag Obg A more general distribution of the refractive index and conductivity de pendent on all of the coordinates can be realized with the material model dielectric x y z Material Label string GST T model dielectric x y z filename string epsxyz dat The input data file is an ASCII file c
25. trans formation z gt z y y is applied to the E z y and H z y fields read from the Diffract source file Similarly the transmitted field obtained with 4 PARAMETER FILE DESCRIPTION 38 the Export Transmitted entry in Sim3D_Max nominally propagates along the negative z axis in the FDTD grid and coordinate system rotation z z y y is applied to it upon export so that the data can be imported into Diffract for propagation along the positive z axis The reflected field obtained with ExportReflected entry in Sim3D_Max propagates along the positive z axis and no coordinate system rotation is applied to it upon ex port Its direction coincides with that obtained in DIFFRACT for the re flected beam that propagates in the z direction Figure 13 1 DIFFRACT Z T Sim3D_Max Z 0 5 d 0 5 a Tey 7 0 5 0 5 Figure 13 In DIFFRACT the incident and transmitted beams solid blue lines propagate along the z direction hence the reflected beam dashed blue line propagates along the z Upon reflection in DIFFRACT a coordinate system rotation is applied in order for the reflected beam to propagate along the z as well dashed red line In Sim3D Max the coordinate system is rotated so that the incident and transmitted beams propagate along the z direction and reflected beam along the z When the CoordinateSystem Diffract option is used in Sim3D_Max the coordinate system rotation is applied
26. 00K and nzngs_sio 400K Zils nast 400K 1 3 4i at T 400K Reo o Ro Tan Bon Aor air by a focal lens with NA 0 85 and focal length f 4346o After focusing the beam is transferred into a medium with n 1 55 and exported into a file for use as a source in the FDTD simulations The source distri bution is read and placed into the FDTD grid on an X Y plane positioned 35nm above the surface of the stack with incident beam propagating in the negative z direction The reflected beam in FDTD propagates in a positive z direction and is computed just above the source plane To have a com parable computation performed in DIFFRACT alone without FDTD first the beam is propagated in DIFFRACT 35nm to the surfce of the stack then the field reflected from the stack is computed and propagated 35nm back to where the incident focused beam started inside the n 1 55 medium 0 200000E 07 0 200000E 07 0 200000E 07 0 200000E 07 Y Lambda Y Lambda Y Lambda Y Lambda 0 200000E 07 0 200000E 07 0 200000E 07 0 200000E 07 0 200000E 07 X Lambda 0 200000E 07 0 200000E 07 X Lambda 0 200000E 07 0 200000E 07 X Lambda 0 200000E 07 0 200000E 07 X Lambda 0 200000E 07 Figure 29 Left two log_intensity_3 scale plots Iz399 and Iy309 of the reflected wave computed with DIFFRACT alone Right two I 300 and Iy300 computed with DIFFRACT FDTD The results of computations for mat
27. 5e 3 length micron 0 5 thickness micron 50e 3 wall_angle degrees 45 0 angle degrees 60 0 The bump types sphero cylindrical stadium and elliptical stadium have a constant thickness t of the layer when the thickness is measured along the local normal to the surface whereas sphero cylindrical cap bumps have constant thickness of the layer when the thickness is measured along the z axis 7 GEOMETRY FILE DESCRIPTION TO 7 3 2 Grooves The AddGrooves option allows user to set up grooves with a trapezoidal shape In the following example first a layer of i02 is created and then grooves are added to it AddLayer material string Si02 Z_min micron 250e 3 Z_max micron 70e 3 AddGrooves substrate string 102 A B C D zeta micron 300e 3 800e 3 1100e 3 1800e 3 70e 3 angle degrees 60 0 x0 y0 micron 0e 3 0e 3 where substrate specifies material of the layer in which grooves are to 2 0 1 2 x um Figure 26 X Z plane cross section of the multilayer grooved stack with definitions of the input parameters for the groove geometry be made A B C D zeta set groove parameters Figure 26 and angle speci fies angle measured counter clockwise from the x axis of the grooves in the 7 GEOMETRY FILE DESCRIPTION 71 XY plane The x0 y0 specify the shift of the position of the center line of a groove with respect to the center of the computational domain This can be used for example to direct eith
28. 6 6121 10 M Mansuripur A R Zakharian Y Xie and J V Moloney Light transmission through subwavelength slits and apertures invited pa per 4th Asia Pacific Data Storage Conference Taiwan September 2004 IEEE Trans Magnetics 41 2 2005 1012 1015 11 T Liu A R Zakharian R Rathnakumar M Fallahi J V Moloney and M Mansuripur Applications of photonic crystals in optical data REFERENCES 95 storage Proceedings of SPIE Optical Data Storage Conference 5380 430 438 2004 12 T Liu A R Zakharian M Fallahi and M Mansuripur Multimode Interference Based Photonic Crystal Waveguide Power Splitter Jour nal of Lightwave Technology 22 12 2004 2842 2846 13 T Liu A R Zakharian M Fallahi and M Mansuripur Design of a Compact Photonic crystal based Polarizing Beam splitter Journal of Lightwave Technology to appear 2005 14 Y Xie A R Zakharian M Mansuripur and J V Moloney Transmis sion of ight through a periodic array of slits in a thick metallic film Optics Express 13 12 2005 4485 15 A R Zakharian M Mansuripur and J V Moloney 1 Surface plasmon polaritons on metallic surfaces Optics Express 15 1 2007 183 197 16 A R Zakharian M Mansuripur and J V Moloney 2 Surface plasmon polaritons on metallic surfaces IEEE Tran on Magnetics 43 2 2007 845 890 Appendix A Computational domain decomposition for parallel processin
29. 8 0e15 mu_inf relative 1 0 delta_m rad s 2 5e14 omega_m rad s 6 0e15 Debye x y dielectric x y dielectric x y z and magnetic mate rial models currently can be used only in 3D computation mode and should not extend into PML layers 7 GEOMETRY FILE DESCRIPTION ov 7 Geometry File Description The file specified under the Geometry Definition Filename entry of the parameter file see 4 contains definitions of the structures to be set up in the computational domain The default i e empty geometry definition file is a free space computational domain occupied by the predefined ma terial Vacuum see section 6 More complex structures may be simulated by adding any number of geometric objects to this free space computational domain Currently defined basic geometric primitives are layer cube ellip soid sphere triangular rectangular circular elliptical capped rectangular apertures or marks of finite thickness and different lattice types Also pre defined are geometric objects commonly used in optical data storage research bumps and pits grooves conformal layers 7 1 Geometry specification from an input file An arbitrary distribution in the computational domain of a finite number of materials can be imported from a file using the following entry in the geometry definition file ReadGeometryFile Filename string user_geom dat The specified file has the same structure as the mindex output file described in 4 9
30. AWN WA KIN W AWA j 4 a A il a I1 User s Manual Version 2 17 Contents 1 System requirements 2 Installing the FDTD program to hard disk 3 Command line arguments 4 Parameter File Description A l 4 2 4 3 4 4 4 5 4 6 Aut 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 A 17 4 18 4 19 4 20 4 21 4 22 A29 4 24 Simulation name aoaaa a a a a a a a ke Time control a a a a a a Spatial grid specification Computations in 2D aoaaa 0 0084 Working Directory Material Definition File 0a a a a Geometry Definition File Boundary Conditions File Material index output Field output Checkpoint files Source time profile POMS cathe bee daye eee betes durnas DIFFRACT source specification Point source specification 2 aoa a a ee el Planewave source specification Gaussian beam source specification 2D source specification from the fle 2D planar waveguide source specification File format version compatibility with DIFFRACT Coordinate system transformation Export file specification 0 0 00 00 0048 4 22 1 Export of the reflected field 4 22 2 Export of the transmitted field Monitor header comment 2 2 048 Monitor specification 4 24 1 Monitors for computations in 2D 4 24 2 Monitors for computations in 3D 5 Boundary Conditions File Description 6 Material File Description
31. D In order to switch to two dimensional computations either uniform grid or second approach to the non uniform grid specification must be used to set the number of points in the x direction to nx 1 and the boundary condition for the xaxis must be defined as periodic in the boundary conditions file described in section 5 One of the 2D sources must be specified for Hx_Ey_Ez or Ex_Hy_Hz mode computation sources are described in subsection 4 13 With nx set to 1 the 2D computational domain is the Y Z plane and the 2D modes are the transverse electric TE Hz Ey Ez and transverse magnetic TM Ez H Hz modes with field components depending on time and y z coordinates E E t y z and H H t y z Hence this manual uses the convention in which TE or TMz signifies the mode with electric or magnetic field transverse to the x axis For 2D computations the domain in the x direction is just one cell long and can have arbitrary coordinates min Lmar Of the computational domain A convenient choice of min mar usually iS min O and Zmar equal to the largest cell size along the y or z axis All source monitor geometry etc objects that require input of an x coordinate must use values within the min lt lt Zmar range if positioning in the Y Z plane of the computational domain is desired 4 PARAMETER FILE DESCRIPTION 16 4 5 Working Directory The working directory is a full pathname specifying a directo
32. ES plus twelve pairs of C o 87 Ct 5 0 3 5 1 5 i 1 2 3 6 1 x 30 j 1 2 3 4 with 0 90 180 270 Each of the input source files is used in the Diffract source option of the FDTD input parameter file setup to compute the reflected fields FDTD INPUT VALUES Start stop and timestep tmin tmax delta_t Uniform Grid nx ny nz xmin xmax ymin ymax zmin zmax Working directory Material Definition Filename Geometry Definition Filename Boundary Conditions Filename Material index Write to file Filename Fields NumberOfOutputs WriteEx Ey Ez WriteHx Hy Hz CheckpointFile nanoseconds nanoseconds automatic with CFL cells cells cells micron micron micron micron micron micron imag material input geometry input boundaries input No mindex out O no no no no no no O 30E 006 0 4 800 800 200 NO H OF CO OC OM CO 9 APPLICATION EXAMPLES RestartFromCheckpointFile WriteCheckpointFile DiffractSource Wavelength Filename File Format Grid Type ExportReflected Filename File Format Grid Type NX NY ExportTransmitted Filename File Format Grid Type x location NY NZ f um 0 707000E 03 0 400000E 07 0 700000E 07 Xfurn 88 no no micron 0 25 SPO1 DAT fortran_binary collocated sr01 dat fortran_binary collocated 256 256 st01 dat fortran_binary collocated micron 10e3 256 100
33. LE DESCRIPTION 18 Z um p a SS Figure 2 Sample geometry set up for a near field antenna over a bump The transmitter consists of a bow tie aperture in a metal layer cross section and a sphero cylindrical bump in another layer bottom cross section view Fields NumberOfOutputs 2 WriteEx Ey Ez no yes yes WriteHx Hy Hz yes no no These lines can be followed by an optional line requesting output of the Poynting vector field as well e g WriteSx Sy Sz no yes no Field out put can be disabled by setting Number of outputs to 0 If Number of outputs is N gt 0 then fields are written into files N times at t tinar N tmas N tmar 4 PARAMETER FILE DESCRIPTION 19 Figure 3 Sample geometry set up of a multi layer stack with an array of elliptic and capped rectangle marks similar to those used in the optical data storage media Arbitrary times for output can be set as follows NumberOfOutputs 4 OutputTimes Luser_defined Time_1 nanoseconds 0 8e 6 Time_2 nanoseconds 1 07e 6 Time_3 nanoseconds 1 35e 6 Time_4 nanoseconds 1 8e 6 WriteEx Ey Ez yes yes yes WriteHx Hy Hz no no no The number of Time_i lines must be equal to NumberOfOutputs When 4 PARAMETER FILE DESCRIPTION 20 requested the E fields are written into files Ex bin out Ey bin out and Ez bin out The H fields are written into files Hx bin out Hy bin out Hz bin out During the
34. ON 59 Material Label string M1 model multipole Debye poles integer 2 eps_inf relative conductivity L1 Cohm m taud femtosec delta_epsO relative taui femtosec delta_epsi relative Similarly to the dielectric material model arbitrary continuous variation of the single pole Debye model parameters in the XY plane can be realized with material type Debye x y This model may be used for example to simulate optical disk data storage components in which material parame ters are continuous functions of the temperature in the plane of the disk T T a y For the material type Debye x y there is one input parame ter the name of the file with the distribution of Debye model parameters e g Material Label string PtOx model Debye x y filename string PtOx input The data file is an ASCII file containing on the first line a single word e g Debye followed on the second line by LXmin LI max LY min LY max Na Ny Tbe Coo bg A p Obg where L min LEmaz specify the domain size in nanometers in which the data is defined Nx Ny are the number of rows columns in the file and the rest specify background Debye model parameters Subsequent lines must contain entries Tij E ij Ae Gij for each point i j of the grid defined on the first line The units of parameters must be the same as in the material model Debye described above The data is read from the file in the same order as for the dielectric x y mater
35. T software for further processing and propagation through various optical ele ments 9 APPLICATION EXAMPLES 89 9 5 Imaging problem We consider an imaging problem with the following setup of the numerical experiment a partially coherent source with wavelength Ag 250nm illu minates a sample and the reflected light is propagated a total distance of 5000um to the entrance pupil of a collimating lens focal length equal to 5 0mm NA 0 8 then focused to the final image plane by a focusing lens having f 40mm NA 0 1 The magnification M of this system is the ratio of the two focal lengths namely M 40 5 8 The simulation is done in four steps 1 Data sets representing partially coherent source are created in DIFFRACT and stored in the files to be used as input source in FDTD computations 2 For each of the source files an FDTD simulation is performed to obtain the light distribution reflected from the sample and the reflected fields are stored for import back into DIFFRACT software 3 Each reflected field distribution is imported into DIFFRACT and prop agated through the collimating and focusing lenses to the image plane where intensity of the light distribution is recorded 4 The intensities from each computation in step 3 are added to obtain the total image The partially coherent illumination is modeled by creating in DIFFRACT uniform beams and using C11 and options of the beam Distortion entry to ass
36. Y 250 000000 25 000 Propagate in environment PROP Length_Units um Propagation distance 4999 562 Multiply curvature Y N N Reposition beam Y N N Propagation regime FRNHF omax 0 010000 Scalar Quasi vector SC Lens LENS Length_Units um Type COLL LOX EGY 0 000000 0 0000 NA FL 0 800000 5000 0 Aberrations None Scalar Quasi vector QV Lens LENS Length_Units mm Type PFOC LCX LCY 0 000000 0 0000 NA FL 0 100000 40 000 9 APPLICATION EXAMPLES Aberrations Scalar Quasi vector Calculation method Propagation distance 92 Plot distribution Type Logarithmic SCALE Xmin Xmax Ymin Ymax Color or Gray scale Z component Y N Save data files Y N File identifier Length_Units um 30 000 30 000 File management Graphics Action Data file loaded to TEMP Action Data file added to TEMP Weight Factor Action Color or Gray scale Action saving TEMP in data file Action None QV APRX 40 00000 PLOT Intensity 4 000000 30 00000 30 00000 C N Y O FMAN L ITOT DAT A IX0O0 DAT 1 000000 D C F ITOT DAT Q Following import of the reflected field file a square mask is applied to the distribution to cancel the fields induced by the FDTD absorbing boundary conditions near the edges of the domain Then a DFT filter is applied to remove non propagating evanescent fields S gt 1 and to re sample the dis tribution into a larger 25um x 25um mesh requ
37. active index and grid cell sizes should not have any variation in the direction normal to the PML layer If the boundary specification file is empty the default boundary condition is PML absorbing boundary for all axes with a default number of points in the PML layers set to nz pmr 10 and n pmr 15 This results in 6 MATERIAL FILE DESCRIPTION 48 approximately 40 db reflection for dielectric media The default settings can be modified using a specification of the boundary type for each axis The Floquet boundary condition used with the planewave source can be set with an entry x axis Floquet or y axis Floquet for the x or y axis 6 Material File Description The file specified under the Material Definition Filename entry of the parameter file see 4 contains a definition of the material properties used in the simulation The file can contain an arbitrary number of material def initions Each material can be of one of the predefined types dielectric dielectric x y Debye Lorentz etc Each material declaration starts with two lines Material Label string YourLabel model MaterialType where YourLabel is a unique arbitrary word except for the reserved word Vacuum chosen by the user to identify each material The material label Vacuum is predefined as a dielectric with permittivity 9 and permeability uo Material Type is one of the available types dielectric Debye Lorentz etc For example Material Labe
38. aist offset sets an initial shift of the beam waist plane from the source plane and corresponds to the variable z in equations 1 3 The parameter direction is optional It sets the direc tion of propagation along 1 or against 1 the positive direction of the y or z axis in 2D Figure 10 and along or against the positive direction of the z axis in 3D The default propagation direction is 1 in 2D computations GaussianBeamSource Wavelength micron 0 633 Mode 3D Exyz component Ly FWHM micron ee bes beam waist offset micron 0 0 x0 y0 z0 micron 0 0 0 0 0 0 xmin xmax micron 7 0 7 0 ymin ymax micron 7 0 7 0 zmin zmax micron 0 4 0 4 In 3D computations the beam propagates by default along the z axis in the negative direction similar to the DiffractSource The phase parameter is also optional It specifies the constant phase shift Qo to be added to the time harmonic dependence of the beam source wt o The default value of the phase shift is zero The default propagation direction can be changed as discussed above In 3D only x0 y0 is used to set beam center and zmin zmax must both be equal and set to the desired location of the source plane along the z axis 4 PARAMETER FILE DESCRIPTION 32 The source is computed according to the following formula E x y z t sexp i kz wt E with complex valued envelope given in 3D by AN E z y z f z e teer wsl2 y 2 x eF B 2R R 1
39. and time with the following 13 columns time in nanoseconds x y z coordinates of the point in microns Ex Ey Ez Hx Hy Hz Sx Sy Sz For a 3D fourier transform monitor the output file contains one line for each point in space with the following 19 columns frequency value in THz x y z coordinates of the point in microns Re Ex Im Ex Re Ey Im Ey Re Ez Im Ez Re Hx Im Ha Re Hy Im Hy Re H z Im Hz Sx Sy Sz For a plane monitor in 3D an additional file is generated containing the area integral of the Poynting vector component normal to the plane as a function of time or frequency The filename of this file is the same as that of 6 the monitor file but with extension is added before the processor rank An integral of the electromagnetic energy E D H B 2 over a specified volume containing only dielectric materials can be monitored as a function of time with an energy monitor A volume is specified with all min max coordinate pairs having distinct values Detailed summary of the monitor file formats is given in Appendix D There can be multiple Monitor entries in the parameter file specified one after another 5 Boundary Conditions File Description The file specified under the Boundary Conditions Filename entry of the parameter file see 4 contains a definition of the BCs used in the simulation 5 BOUNDARY CONDITIONS FILE DESCRIPTION A7 Currently boundary types PEC periodic
40. arameters for the Lorentz model are set to result in n ki Je 2 Ti at the wavelength Ay 650nm of the incident light Material Label string Si02 model dielectric refractive index dimensionless 1 5 conductivity 1 ohm m 0 0 9 APPLICATION EXAMPLES 83 Material Label string Aluminum model Lorentz omegaQ Hz 23 536118e14 delta Hz 2 9504974e14 eps_inf relative 1 81 delta_eps relative 32 802 conductivity L1 Cohm m 0 0 In the input geometry definition file first a substrate layer is set to extend from the bottom of the computational domain to z 70nm then a 50nm thick layer of aluminum is added on top of the substrate A pit bump with a negative height in the aluminum layer is placed in the center of the computational domain xp yo 0 AddLayer material string Si02 Z_min micron 450e 3 Z_max micron 70e 3 AddLayer material string Aluminum z_min micron 70e 3 Z_max micron 20e 3 AddBump bump_type sphero cylindrical cap material string Aluminum substrate string Vacuum x_0 micron 0 0 y_0 micron 0 0 z_0 micron 70e 3 width micron 400e 3 height micron 60e 3 length micron 200e 3 thickness micron 50e 3 Figures 32 31 show the grid and material layout corresponding to the above example input files and the computed reflected transverse E field amplitude 9 APPLICATION EXAMPLES 84 The reflected light field distribution can be imported back into DIFFRAC
41. ase shift between the envelope function f t and the carrier wave sin wt ceo is zero dceo 0 The carrier envelope offset ceo can be changed with an optional entry carrier envelope offset degrees 90 0 4 13 Sources One of the following sources must be specified in the input parameters file e source from the input DIFFRACT file point source 4 PARAMETER FILE DESCRIPTION 24 e planewave source e Gaussian beam source e source from the input file in 2D e planar waveguide source in 2D Sub sections 4 14 4 19 describe input required for each of these sources 4 14 DIFFRACT source specification To use a DIFFRACT source the user must set the wavelength in mi crons the filename see 4 5 for input filename rules of a complex valued source amplitude distribution for E and H fields the format of the file and the grid type For a beam propagating in DIFFRACT along the positive direction of the z axis H fields must be sampled on a plane positioned a distance A 2 half of a FDTD grid cell behind the plane where E fields are sampled Figure 6 Therefore negative value of A not A 2 must be specified when the source file is produced by the FDTD export option of DIFFRACT The content and format of the file are described in detail in section 4 20 and in the manual for the DIFFRACT software 3 Either Source or DiffractSource may be used to specify a source distribu tion created with DIFFRACT
42. ation mode monitor type number of monitor points in space and number of points sampled in time e g LEx_Hy_Hz time history Ny Nz Ntime The rest of the file consists of one line for each point in space and time with the following 8 columns time in nanoseconds y z coordinates of the point in microns Fieldl Field2 Field3 Field4 Field5 The fields Field through Field5 are defined as for Hx_Ey_Ez mode Field1 is Hz Field2 is amp Field3 is Field4 is S Field5 is S for LEx_Hy_Hz mode 4 PARAMETER FILE DESCRIPTION 45 Field1 is Field2 is H Field3 is H Field4 is S Field5 is S For a L fourier transform monitor the file contains on the first line the computation mode monitor type number of monitor points in space and number of points sampled in frequency e g LEx_Hy_Hz fourier transform Ny Nz Nfreq If bandwidth source frequency option was selected the Nfreq will be equal to 1 The rest of the file consists of one line for each point in space and frequency with the following 11 columns frequency value in THz y z coordinates of the point in microns Field1 Field2 Field3 Field4 Field5 Field6 Field Field8 The fields Field1 through Field8 are defined as for Hx_Ey_Ez mode Field1 Field2 are Re H Im Hz Field3 Field4 are Re E 1m E Field5 Field6 are Re E Im E Field7 is real lt S gt Field8 is real lt S gt for Ex_Hy_Hz mode Field1 Field2 are
43. cies or wave lengths specified on the next line with an entry fmin fmax or lmin 1max 4 PARAMETER FILE DESCRIPTION 44 for example fmin fmax THz 285 0 315 0 or lmin lmax nm 850 0 920 0 The sampling factor specification is optional It can be used to set the decimation factor for sampling fields in time For example sampling factor Linteger 5 sets monitor data processing to occur only every 5th time step The default sampling factor is 1 The output of the monitor of time history of fields on a specified area which also generates time history of the area integral of the Poynting vector component S normal to the plane can be controlled by specifying on the last line of the monitor entry whether to create files with time history of E H and S output distribution or only time history of the integral of Sa output Lintegral or both output all When output type is not specified the default is output all 4 24 1 Monitors for computations in 2D For TE TM computations in 2D the xmin xmax values are ignored and only one of the ymin ymax or zmin zmax pairs must have distinct min max values The monitor then specifies a line segment aligned with the y or z axis Along this line either the time history or Discrete Fourier Transform of the E H fields and the Poynting vector S E x H are sampled and written to the specified file For a time history monitor the output file contains on the first line the comput
44. combined for different axis as described below The Floquet boundary condition is appro priate for simulating periodic structures and always implies PML boundaries along the z axis and Floquet boundary conditions along the x and y axis The planewave source is implemented using the Total Field Scattered Field TFSF formulation with the TFSF boundaries defined two points away from the PML absorbing boundary The TFSF boundary consists of 6 planes 4 line segments in 2D that make up a surface of a cube in 3D a 4 PARAMETER FILE DESCRIPTION 28 Figure 7 Definition of the parameters for the planewave source Incidence direction k is specified by the angles 0 and while the polarization angle can be set to the one of the two orthogonal directions in the plane or orthogonal to the plane defined by the k and k vectors rectangle in 2D Figures 8 9 and provide the means to truncate in space the infinitely extended planewave Figure 8 shows the Y Z cross section of the computational domain with an example of a planewave that propagates in the negative z and positive y direction When a periodic boundary condition is specified for any of the axis then there will be no TFSF boundary plane normal to that axis Figure 9 For example if periodic boundary conditions are used for the x and y axis the only relevant TFSF boundaries are the top and bottom X Y planes When a periodic boundary condition is set for some axis w x y z th
45. computation each time snapshot of the spatial dis Figure 4 left and E right components of a y polarized 3D Gaussian beam sourced in the xy plane with periodic boundary conditions at Zmin Zmax 0 7m with z parameter set to 0 beam amplitude FWHM 1 2um Ao 0 8m Nnref 1 0 and direction set to 1 tribution of the fields is appended to the end of the corresponding file When Poynting vector output is requested the last output to the Sx bin out Sy bin out and Sz bin out files is the time average of S over one period of the source frequency instead of a time snapshot The files can be read and visualized Figures 4 5 after each output while the computation is in progress When new simulation is started the output files are overwritten The fields are written into files as binary unformatted data The order of output of the fields is one in which index k along the z axis changes first then index 7 along the y axis and last index 2 along the z axis Each point k j i is written as a 4 byte floating point number Hence if N outputs are requested and the number of points in the computational domain is nz ny nz the size of each output file will be 4N x nz X ny X n bytes If any of the fields are requested to be written the material layout binary file Ml bin out and ASCII text files coords and coordx coordy co ordz are also created The material layout file Ml bin ou
46. cussed in Appendix B The Acceleware hardware accelerated runs can be launched by specify ing on the command line the option acceleware auto e g Sim3D_Max exe C somedir parameters input b acceleware auto This executes computations using Acceleware hardware that speeds up the computations with automatic selection of the processing option for optimal performance 4 Parameter File Description The input parameter file parameters input in the above example has a predefined structure The order in which parameters appear in the file and the number of entries on each line should conform to the description given below The number of white space characters before after or between the 4 PARAMETER FILE DESCRIPTION 10 entries on each line and the number of newline characters between lines can be arbitrary The entry here means a sequence of characters not separated by a white space tab newline or carriage return character For example if the manual shows x0 y0 z0 then DO NOT use x0 y0 zO instead 4 1 Simulation name The first line should be a line consisting of three arbitrary words It can be used to describe the file or simulation Example FDTD Input Parameters 4 2 Time control Time control specifies the start and finish times for the simulation in nanosec onds and sets the time step e g Start stop and timestep tmin nanoseconds 0 0 tmax nanoseconds 20 0e 6 delta_t automatic wi
47. d Np specify number of processors per coordinate direction see Figure 35 so the product NprNpyNpz must be equal to Np If the total number of grid points along each coordinate axis is nz n and n the number of points per processor in the parallel computation will be Ne NoxsNy Npy and nz Npz The ratios of nz to Npr must be integer numbers If the number of grid points along any of the axis is not integer divisible by the number of the processors specified for that axis the number of grid points is increased to the closest integer such that nz Npz is an integer number The new grid points are added to the corresponding axis and the computational domain size is updated as follows for the Uniform Grid the zmax ymax or zmaz is increased for the Non Uniform Gridi the extent of the wl region for x and y axis is increased or A3 region for the z axis is increased for the Non Uniform Grid2 the number of cells is increased in the last grid specifying region for the x y or z axis The number of processors used in the computation has no effect on the number and structure of the input or output files with the following excep tions 1 The output files defined in the Monitor entries section 4 24 of the parameter file are created by each processor separately The rank of the processor that creates the file is appended to the filename Each processor writes into the monitor file the data for the set of monitor spatial points that c
48. data can be re quested as follows magnitude phase Ex Ey Ez yes yes yes magnitude phase Hx Hy Hz yes yes yes Poynting vector S8x Sy 5zZ yes yes yes current density Jx Jy Jz yes yes yes All of the above lines are optional and when omitted or when set to no the corresponding output files are not generated When specified a folder is created in the working directory into which the files are written under the names mEx dat mEy dat etc for the magnitude data and pEx dat pEy dat etc for the phase data in radians For the real valued Poynt ing vector only amplitude data sx dat etc is generated The files are written in a text ASCII format and in the same xy order as the data in the export file The magnitude and phase folder has the same name as the export file but without the filename extension If the export filename does not have an extension a suffix mp is added to it to create the folder name There can be multiple Export lransmitted entries specified one after another for sampling the computational domain with different planes and at various locations Note however that when an export plane is at a location such that it samples a region with refractive index variation in that plane then the refractive index value stored in the export file is not well defined 4 PARAMETER FILE DESCRIPTION 42 since it will represent only one value of the refractive index
49. e 3D theta degrees 30 0 phi degrees 45 0 polarization degrees 90 0 TFSF boundary top The Mode can be either 3D or one of the Ex_Hy_Hz or Hx Ey Ez for computations in 2D The propagation direction of the planewave is along the wavevector k kz ky kz specified by the angles 0 and Figure 7 The angle theta 0 0 180 is defined with respect to the negative k component for the planewave propagating along the negative z direction The angle 0 360 is measured with respect to the positive direction of the x axis Specification of the angle is optional when omitted its value defaults to my 2 Two orthogonal polarizations of the planewave can be specified by setting the polarization angle to 0 E field in the plane defined by the k and kz or 90 E field normal to the plane defined by the k and k vectors Specifica tion of the polarization angle is optional when omitted its value defaults to 0 In 2D computations only the angle 0 90 90 has an effect since the wavevector is in the Y Z plane k 0 k kz and hence 7 2 while the polarization angle is determined by the Mode parameter Hx_Ey_Ez mode corresponds to 0 polarization angle and LEx_Hy_Hz mode to the 90 The planewave source can be used together with the PML periodic or Floquet boundary conditions also known as Bloch periodic boundary con ditions The PML and periodic boundary conditions can be
50. eam of light with wavelength Ay 650nm The focusing lens has a numer ical aperture NA 0 6 and focal length 5000p To adequately resolve the pit a non uniform grid is used with resolution of 5nm in the z direction and 10nm in the x and y directions at the position of the pit The input parameter file PIT SIMULATION PARAMETERS otart stop and timestep tmin nanoseconds 0 0 tmax nanoseconds 20 0e 6 delta_t automatic with CFL 0 4 Non Uniform Gridi wi micron 500e 3 9 APPLICATION EXAMPLES 80 w2 micron 200e 3 w3 micron 2040e 3 delta_1 micron 10e 3 delta_2 micron 20e 3 delta_3 micron 30e 3 hi micron 160e 3 h2 micron 140e 3 h3 micron 300e 3 deltaz_1 micron 10e 3 deltaz_2 micron 5 0e 3 deltaz_3 micron 10e 3 Working directory Material Definition Filename Geometry Definition Filename C username Maxwel1l FDTD pit_materials input pit_geometry input Boundary Conditions Filename boundaries input Material index Write to file no Filename mindex out Fields NumberOfOutputs 0 WriteEx Ey Ez no no no WriteHx Hy Hz no no no CheckpointFile RestartFromCheckpointFile no WriteCheckpointFile no DiffractSource Wavelength micron 0 65 Filename diffract_source dat File Format ascii Grid Type staggered ExportReflected 9 APPLICATION EXAMPLES Sl Filename fdtd export r File Format ascil Grid Type collocated ExportTransmitted Filename fdtd export t File Forma
51. ection plus minus 1 phase degrees 90 0 x0 y0 z0 micron 0 0 0 1 0 0 xmin xmax micron 0 0 0 0 ymin ymax micron Soa zmin zmax micron 0 2 0 2 The Mode can be Hx_Ey_Ez LEx_Hy_Hz or 3D For the Hx_Ey_Ez mode the polarization component can be set to y for propagation along z or z for propagation along y For the Ex_Hy_Hz mode polarization is x and for 3D computations it can be x or y In 2D computations in the Y Z plane the beam propagates by default along the positive direction of the y or z axis In 2D the line segment along which the source is ap 4 PARAMETER FILE DESCRIPTION l plied is specified by the ymin ymax and zmin zmax options and xmin xmax is ignored Only one of the ymin ymax or zmin zmax pairs can have distinct values hence specifying a line segment aligned with the y or z axis In the example above the source is applied from y 5um to y 4um along the y axis at z 0 2 as specified by zmin zmax The x0 y0 z0 specifies the beam center In 2D only yO or zO is used to set the beam center position The FWHM specifies two numbers in micron for the amplitude full width half max of the beam width at z 0 For the 3D case the amplitude FWHM values are related to woz and wo by FWHM wo jy2V In 2 In 2D case wor and wo must be set to the same number and represent an amplitude FWHM equal to wo2VIn2 The Wo Wor Woy correspond to the formulas described below The parameter beam w
52. en in order for the planewave to be a valid solution the domain size L along the w axis and the planewave wavevector k 0 must satisfy the condition Lu n x 2n ky where n 1 2 The TFSF boundary entry in the planewave specification is optional It can be used in conjunction with the periodic boundary conditions for the x and y axes to specify that only the top TFSF boundary X Y plane should be used for a planewave source as is the case in Figure 9 right In the TFSF formulation the planewave source is applied at the TFSF boundary and the planewave propagates only in the Total Field region Out side of the TFSF boundary only the Scattered Field is present Simulations that use TFSF formulation for the planewave source must have a refractive 4 PARAMETER FILE DESCRIPTION 29 Total Field Incident planewave Scattered Field Scattered Field ymin ymax Figure 8 YZ cross section of the computational domain with Total Field Scattered Field TFSF formu lation for the planewave source The refractive index must be the same at all sides of the TFSF boundary index distribution in the computational domain such that the refractive in dex nres is same at all TFSF boundaries Hence the TFSF planewave source is appropriate for problems that involve interaction of a planewave with iso lated or periodic objects embedded in a uniform medium for example scattering of a planewave from a chain of metallic nanospheres
53. er groove or land or edge through the center of the computational domain In the above example if there is more than one i02 layer already setup the grooves are applied to the layer with largest z_max Figure 27 Wobbled grooves on an Optical Disk Surface using parameters from the example in the text with Q 0 left and Q 180 right Groove width modulation groove radial position modulation and similar effects can be modeled using the AddWobbledGrooves geometry object AddWobbledGrooves substrate string Aluminum A B C D zeta micron 100e 3 660e 3 760e 3 1100e 3 80e 3 angle degrees 30 0 x0 y0 micron 860e 3 500e 3 AO PO micron 50e 3 2000e 3 A1 P1 micron 50e 3 2000e 3 Q1 degrees 0 0 The AddWobbledGrooves object specifies grooved structure in the same way as the AddGrooves object The additional parameters AO PO and A1 P1 Q1 set the wobble amplitude period and relative phase of the opposite groove edges as shown in Figure 27 The groove edges have variation of the form Ao sin 27rz P and A sin 2mrx P Q1 The groove edge variation defined 7 GEOMETRY FILE DESCRIPTION 12 by the Ap Py parameters has 0 phase with respect to the o yo point 7 3 3 Conformal layer Once some structures are specified in the computational domain a confor mal layer can be added on top of the existing structures using AddConformal Layer definition AddConformalLayer mat
54. erial string Aluminum add on top of string Si02 thickness micron 50e 3 where in this example a layer of Aluminum 50nm thick is added on top of the structures made of i02 If there are i02 structures at more than one z coordinate for example two layers of i02 separated by some other material then the conformal layer will be added on top of the i02 layer with largest z_max The following sequence of structure definitions will produce a multilayer erooved stack shown in Figure 26 AddLayer material string Si02 z_min micron 250e 3 z_max micron 70e 3 AddGrooves substrate string Si02 A B C D zeta micron 300e 3 800e 3 1100e 3 1800e 3 70e 3 angle degrees 60 0 x0 y0 micron 0e 3 0e 3 7 GEOMETRY FILE DESCRIPTION 13 AddConformalLayer material string Aluminum add on top of string Si02 thickness micron 50e 3 AddConformalLayer material string Gold add on top of string Aluminum thickness micron 50e 3 7 3 4 Sine layer The AddSinLayer option allows user to set up a sinusoidally modulated layer The direction entry can take values X LY or Z and sets the axis w x y z along which hsin 27w p variation is applied AddSinLayer material string Gold direction Z x0 y0 z0 micron 0 0 50e 3 1000e 3 pitch height thickness micron 0 36 50e 3 50e 3 The pitch of the variation is p the amplitude of the sine A corresponds to the height parameter and the thickness of the layer is give
55. erial parameters corresponding to tem peratures of T 3004 and T 400K are shown in Table 4 for the intensities I and l of the x and y components of the reflected field indicating good agreement between intensities and phase difference Agr Q400 300 from computations performed with DIFFRACT FDTD and DIFFRACT alone 9 APPLICATION EXAMPLES 18 Table 4 Comparison of numerical solutions using DIFFRACT and DIFFRACT FDTD for a focused beam incident on a bi layer with parameters specified in the caption of Table 3 w iwo eoo aoo Agr 9 3 Scattering of a planewave from a sphere In this test case example we compute in three space dimensions the prob lem of scattering of a planewave from small dielectric and metal spheres Figure 30 shows exact solutions computed using Mie scattering theory and corresponding numerical solutions The incident planewave propagates along the negative direction of the z axis A uniform grid cell size of A 10nm exact o FDTD 3 Exact Al 650 nh Debye model o ns1 5 n 2 7i Exact Ag 850 nm Lorentz model 25 1 1 5 n 0 269 5 96i o FDTD A 5nm pi o FDTD A A 10nm if FDTD A _ 5nm k 0 ma aooga o a o 0 a gt g a ae ae z micron z micron Figure 30 Comparison of exact lines and FDTD symbols solutions in terms of total electric field magnitude variation along the light incidence axis passing through the center of the s
56. ess and the same shape as the X Y cross section shown in Figure 25b with radius w 2 Triangular objects are specified by three points in the XY plane The quadrilateral and polygon objects are specified by the coordinates of their vertices in a plane listed in clockwise or counter clockwise order 7 2 8 Lattice A two dimensional lattice of rectangular circular elliptic and triangular rods of finite thickness can be added using AddLattice option The fol lowing example creates a honeycomb lattice of Aluminum rodes with elliptic cross sections in xy plane and with rod lengths along the z axis from 70nm to 20nm AddLattice material string Aluminum plane XY lattice type Lhoneycomb lattice constant micron 0 85 lattice center micron 0 0 0 0 M N number 11 11 vertical_min max micron 70e 3 20e 3 unit element ellips a b micron 0 2 0 15 angle degrees 0 0 The plane option can take values XY XZ YZ to set the plane of the lattice Then vertical min max extent option will then apply corre spondingly in z y and x axis The lattice type can be of types square triangular and honeycomb with a corresponding lattice constant Figure 22 The lattice is centered at lattice center in the specified plane and consists of M by N unit elements unit element can be a circle ellips rectangle or equilateral triangle The next lines specify the properties of the unit element radius semi major axes
57. g LS ea aaa aaa weeT Mine ae ae tea eas REE ae ae ee E LETTE SE EGE LE EGE AD Te ag E KR A a ea eae A NR e M A OME AEE AA cl i Nm a Ta NAD es eee Ri Ea nn El eee OL AAA AAAAAAVAAAY ASS ea aS an a ea a D oa BSS ae ene ee eee WW ae Wy a LEAK es a ae SS ILL Meee Sea AES SS O DZIALAL ELA AA A L f OEA ee Jl a ay ea E E a CLE TELLS aa 4 eee ee i ENNEN OT IT a NNT NA WAZ Z A NR VLLA AAAA XN a E Witte wea V OOO tts te Ei eee N BLE Dt AN SEE E A S E ET S A a S E ESEE Wi FFF Fe 1 SEET AEN E a SF SH SLD LEG LG ET TT fT IT GE GID ECT LE D BAR I R R JE A SJ E SE SG POIA EL A A AA A A A J N LEAD LD LO LOD I A SIFTS SO LS E ae LST LE EE IT I A J I BD SES IS LG LEAT 2 Noy 2 Non uniform grid computational domain decomposition with Np 8 Noz Npz 2 Processor rank changes first along the z axis then along the y and x axis Figure 35 This appendix describes conventions used for the computational domain decomposition in simulations with multiple processors The number of pro cessors and the desired decomposition of the computational domain are spec ified through the command line arguments mpiexec exe np Np Sim38D_Max exe parameters input Npx Npy Npz Each processor is assigned an integer number its rank in the range from 0 to Np 1 where N is the total number of CPUs used in the computa tion The Npr Npy an
58. he file 5 entries 1n One or more arbitrary source distributions can be specified as a file input for two dimensional computations Example Usersource Wavelength micron 0 9 Mode L LHx_Ey_Ez Filename string usersource dat ymin ymax micron Soles zmin zmax micron 1 0 1 0 Parameter Mode can be either Hx_Ey_Ez for a H Ey Ez 2D mode or 4 PARAMETER FILE DESCRIPTION 34 Ex_Hy_Hz for Ez H H mode The ymin ymax zmin zmax specify the extent of the source The source is applied along the y or z aligned coordinate lines so either ymin ymax or zmin zmax must be equal The ASCII text file is expected to contain on the first line the number of points present in the file The following lines must contain 5 columns coordinate of the point in microns real part of Fieldl imaginary part of Field1 real part of Field2 imaginary part of Field2 The fields Field and Field2 are defined as for Hx_Ey_Ez mode Field1 is A Field2 is if ymin equals ymax or Field2 is if zmin equals zmax for LEx_Hy_Hz mode Field1 is Ez Field2 is H if ymin equals ymax or Field2 is H if zmin equals zmax The range of coordinates of the source points in the file may be a subset or superset of the range specified by ymin ymax or zmin zmax The complex valued field amplitudes are read and interpolated into the FDTD grid The interpolated values are written to an output file with the same name as the input source file
59. i relative 6 4 Drude model The parameters for a dispersive medium based on the single pole Drude model correspond to a complex valued frequency domain susceptibility func tion n W p oe E t W Ko zp le t xlo where wp is the plasma frequency the relative permittivity at infinite frequency 0 is the damping coefficient Example input parameters for Drude model Material Label string Metal model Drude delta rad s 1e13 eps_inf relative 1 0 omega_p rad s 5e12 6 5 Magnetic material model The magnetic material type allows specification of magnetic permeabil ity and electric permittivity for materials with constant u po or with magnetic dispersion Example input parameters for constant and u 6 MATERIAL FILE DESCRIPTION 56 Material Label string MagMat model magnetic1 permittivity relative 2 25 permeability relative 2 0 Drude model is used to model electric and magnetic dispersion of magnetic materials Drude model parameters 0 Wp can be specified instead of the constant permittivity resulting in e w frequency dependence given in sub section 6 4 Similarly U m Wm can be specified instead of the constant permeability with frequency dependent u w given by 2 Hw Hoo 55 ae Example input parameters for dispersive magnetic material Material Label string MetaMat model magnetic2 eps_inf relative 1 0 delta rad s 1 25e14 omega_p rad s
60. ial substrate material hi EEIT ASTREE Z x0 y0 z0 E Figure 24 Definitions of parameters for bump type sphero cylindrical cap The edges of the bump are defined by two spherical shells matched to a cylindrical shell of length l with the cylinder axis directed along the x axis The shells have a constant thickness t when measured along the z axis bump position is specified by a central point o yo of the bump in the z y plane and the coordinate z of the bottom of the layer on which the bump is put zo of the bump is equal to the Zmin of the layer A pit can be set up by specifying a negative value for the height For the pit zo still signifies Zmin of the layer in which the pit is made while substrate specifies the material inside the pit The width w height h length l and layer thickness t for the L sphero cylindrical cap type are defined on Figure 24 The length is applied only in x coordinate so the bump pit is elongated only along x If the length is zero the bump is circular in the xy plane Example AddBump bump_type l sphero cylindrical cap material string Aluminum substrate string Vacuum x_0 micron 0 0 y_0 micron 0 0 z_0 micron 140e 3 width micron 400e 3 height micron 60e 3 length micron 200e 3 thickness micron 50e 3 For the bump types Lsphero cylindrical stadium 7 GEOMETRY FILE DESCRIPTION 68 layer material substrate material Fig
61. ial described above and interpolated to the FDTD computational grid The grid points that are outside of the range specified by Lamin LEmaz Lymin LYmaz are assigned background values Teg Eoo bg A bg Obg 6 MATERIAL FILE DESCRIPTION 54 6 3 Lorentz model The parameters for a dispersive medium based on the single pole Lorentz model correspond to a complex valued frequency domain susceptibility func tion Acwg Xe RF jw oP where w is the pole frequency the relative permittivity at infinite fre Oo lw co x w ITE quency A s E Es 18 the static or zero frequency relative permittivity is the damping coefficient Example parameters for aluminum n 2 Ti at A 690nm Material Label string Aluminum model Lorentz omega0 rad s 23 536118e14 delta rad s 2 9504974e14 eps_inf relative 1 81 delta_eps relative 32 802 conductivity Li Cohm m 0 0 Multi pole Lorentz model corresponding to the relative permittivity p5 Aew re ES ee es en Ws 27Wdy Ww tise can be set by specifying the number of poles N followed by and and the list of parameters for each pole in the format shown below Material Label string M2 model multipole Lorentz poles integer 2 eps_inf relative conductivity 1 Cohm m 6 MATERIAL FILE DESCRIPTION 59 omega0 rad s delta0 rad s delta_eps0 relative omega1 rad s deltal rad s delta_eps
62. ign a tilt to the beam via polar 0 6 C and azimuthal 1 angles A um x Sum square mask is applied to the beam and the distribution is exported to a file To reduce diffraction at the edges of the beam the top hat shape of the square beam is smoothed using shape softening option Alpha of the Mask entry Example of DIFFRACT commands used to create square beam with C11 5 and 1 0 Remarks Vacuum wavelength nm 250 0000 NVIRON 1 000000 9 APPLICATION EXAMPLES 86 Initial distribution BEAM Length_Units um Type UB SG GG LG HG LD UB BCX BCY 0 000000 0 0000 Radius of aperture 4 000000 Aberrations Seidel Spherical C40 O 000000 Coma C31 Phi31 0 000000 0 0000 Astigmatism C22 Phi22 0 000000 0 0000 Curvature C20 O 000000 Distortion Ci1 Philt 5 000000 0 0000 Polarization RHO ETA 0 000000 0 0000 NMAX NMAY 512 512 LMAX LMAY 25 00000 25 000 Amplitude phase mask MASK Length_Units um Shape Rectangle MCX MCY 0 000000 0 0000 Length Width Alpha 5 000000 5 0000 0 2000000 Orientation angle Theta O 000000 Inside amplitude phase 1 000000 0 0000 Outside amplitude phase 0 000000 0 0000 FDTD Interface FDTD Length_Units um Export Import Export NX NY 256 256 LX LY 6 000000 6 0000 Deltaz 0 004000 Staggered mesh Y N N Filename SPO1 DAT ASCII or Binary Binary In the computations described below the following sampling of angles was used CY 0 0 9 0 0 9 APPLICATION EXAMPL
63. in xmax micron 0 0 0 0 ymin ymax micron arlene len zmin zmax micron 0 0 0 0 t_on t_off nanoseconds 10e 6 20e 6 sampling factor integer 5 During parallel computation with N CPUs each processor writes to its own output file so processor rank an integer number between 0 and N 1 is appended to the output filename e g monitor1 out3 The content of the output file depends on the Mode entry and is described below With each new simulation the existing monitor files with the same name as specified under the Filename with appended processor numbers are removed The xmin xmax ymin ymax zmin zmax specify the extent of the mon itor The t_on t_off sets the monitor switch on and switch off times and can be specified either as t_on t_off nanoseconds 10e 6 20e 6 or t_on t_off periods 10 In the case when number of periods P is specified the sampling in time is done from ting P x T to tmax where T A c is the period of the source For the fourier transform monitor the bandwidth entry must be present with one of the options bandwidth Lsource frequency bandwidth frequency interval or bandwidth wavelength interval The first option Lsource frequency specifies that Fourier Transform should be evaluated at a single point in the frequency space the input source frequency The frequency interval or wavelength interval option allows Fourier Transform to be computed for a range of frequen
64. ing GaAs vertices number 8 x1 y1 micron 0 25 0 5 X2 y2 micron 0 25 0 5 XIN lmicroni 0 5 0 25 x4 y4 micron 0 5 0 25 X5 y6 micron 0 25 x6 y6 micron 0 25 0 5 2s Wi micron 0 5 0 25 x8 y8 lmicroni 0 6025 z_min max micron 0 25 0 25 ConvexPolygon material string GaAs vertices number 4 XE y1 microni 0257 0 5 x2 y2 micron 0 25 0 75 ome micron 0 25 0 75 x4 y4 micron 0 25 0 75 z_min max micron 0 25 0 125 ConvexPolygon material string Vacuum vertices number 8 x1 y1 micron 0 125 0 25 x2 y2 micron 0 125 0 25 X3 y gt iwiceroni T0257 70125 x4 y4 micron 0 25 0 125 X5 y9 micron 0 125 0 25 x6 y6 micron 0 125 0 25 KNT micron 0 25 0 125 x8 y8 micron 0 25 0 125 64 7 GEOMETRY FILE DESCRIPTION 65 z_min max micron 0 125 0 125 ConvexPolygon material string Vacuum vertices number 4 xl WL micron 0 125 0 75 x2 y2 micron 0 125 0 75 KO We micron 0 125 0 75 x4 y4 micron 0 125 0 75 z_min max micron 0 125 0 125 Disk material string GaAs x y center micron 0 7 0 7 radius micron 0 15 z_min max micron 0 125 0 125 This object allows a set of other basic geometric objects four convex poly 1 0 1 x um Figure 23 X Y cross section of an example periodic pattern from the text setup with four ConvexPolygons and one Cylinder object 7 GEOMETRY FILE DESCRIPTION 66 gons and a disk in the above example to be repeated in s
65. ion Specifically for the Ex_Hy_Hz mode when the complex amplitude of the E field is specified along a line parallel to the y axis index j with some constant zmin zmax index k of the source the corresponding Hf complex fields must be defined for the same position along the y axis but with z positions shifted by Az 2 For the Hx_Ey_Ez mode when the complex amplitude of the EF field is specified along a line parallel to the y axis index 7 with some constant zmin zmax index k of the source the corresponding H complex fields must also be defined for the same position along the y axis but with z positions shifted by Az 2 For example if a user defined Ex_Hy_Hz source has electric and magnetic field dependence on the space coordinates in the form Ely z E y e and H y z H y e then the input source file may contain complex amplitudes E y and H y e 4 Similar definitions apply to a source defined along the z axis with the ymin ymax in the UserSource definition for Ez H fields for the Ex _Hy_Hz mode and H E fields for the Hx_Ey_Ez mode In this case the corre sponding shifts of the field positions are along the y axis l l P usrc interp2 1 5 usrc interp5 l on es l go N k l pr N 3 y s S A KI monitor out2 monitor out 1 monitor outO ymin ymax Figure 39 Example of monitor and user defined source output for the 2D computational domain dec
66. ired for better sampling in the ky ky wavevector space The beam is propagated 4999 562um the differ ence between the focal length of 5mm and the 0 438um already propagated 9 APPLICATION EXAMPLES 93 in the FDTD grid to the collimating lens then through the focusing lens to the image plane The computed intensity distribution at the image plane is added to the file ITOT DAT After all reflected fields are propagated to the image plane this file will contain the total sum of intensities The images of a flat unmarked layer and two sets of three randomly placed marks are shown in Fig 34 The images have different relative inten sity scales As expected the image from a flat layer has uniform intensity distribution The low intensity region in the middle of the central image is contributed by the central bump which scatters the light while the two pits on each side have higher intensity due to reflection of the light from pit walls toward the pit center Similar effect is evident in the image of three circular pits Figure 34 Left image of a flat unmarked layer obtained using five beams with C11 0 1 0 and Ci 1 5 11 60 150 240 330 Center image of three randomly placed marks with geometry shown in Fig 33 and source sampling described in the text Right image of three circular pits with the following parameters top left to bottom right width 700nm 800nm 1000nm depth 50nm 60nm 60nm The i
67. l string Si02 model dielectric Material Label string Gold model Debye Material Label string AluminumOxide model Lorentz These two lines are followed by a set of parameters specific to the mate rial type 6 MATERIAL FILE DESCRIPTION 49 6 1 Dielectric materials For the type dielectric the material properties can be entered in any one of the following equivalent formats Material Label string GaAs750nm model dielectric sqrt Re eps dimensionless 3 6986 conductivity L1 Cohm m 16455 9 Material Label string GaAs750nm model dielectric n ki dimensionless 3 7 0 1i Material Label string GaAs750nm model dielectric eps relative 13 68 0 74i When used with a monochromatic source materials with a complex refractive index n ki can be modeled by the material type dielectric if n k gt 1 in the case of arbitrary n and k refer to the Debye material model The refractive index n ki permittivity and conductivity o are related by e ic n ki Re e vn k and o 2nkeqw where w is the frequency of the source Arbitrary continuous variation of the refractive index and conductivity in the X Y plane can be realized with material model dielectric x y This model is useful for simulating optical disk data storage components in which optical constants are continuous functions of the temperature in the plane of the disk T T x y For the material type dielectric x y
68. larly for y and z axis Alternatively a non uniform grid can be set up in one of the two ways In the first approach appropriate for grids symmetric in the XY plane the user specifies the sizes in micron of three regions w1 w2 w3 along the x or y axis followed by the cell sizes in each of these regions A1 A2 A3 see Figure la The x and y axis are treated identically and the generated grid is symmetric with respect to the center of the x and y axis The cell sizes are interpolated at the boundaries of the regions with dif ferent cell sizes to provide a grid with gradually changing cell size Unlike the uniform grid case for a non uniform grid the resulting computational domain size and number of cells are computed by the program and the co ordinate origin is positioned at the center of the computational domain The Tmaz Emin ANd Ymaz Ymin Values are set by the program to L 2 L 2 re spectively where L Ly are the total domain size computed from wy w2 w3 Similarly three regions h1 h2 h3 along the z axis are specified followed by the cell sizes in each of these regions Az Azo Az3 Figure la The Zin Zmax 4 PARAMETER FILE DESCRIPTION 12 I I I I l I l I X O l l L l Z oy I 4 4 l X l Z aa l I coe _ l wee I Pe l tee lier pe panar Z AARS 4 nee so l I gen l 7 l l l l N pregons Figure 1 a Computational domain and non uniform grid definition for the Non U
69. lls of a given size separately for each axis Non Uniform Grid2 N_xregions integer 2 deltax_i micron 10e 3 nx_1l cells 50 deltax_2 micron 10e 3 nx_2 cells 50 N_yregions integer 5 deltay_1 micron 10e 3 ny_1 cells 185 4 PARAMETER FILE DESCRIPTION 14 deltay_2 micron 5e 3 ny_2 cells 10 deltay_3 micron 2e 3 ny_3 cells 5 deltay_4 micron 1e 3 ny_4 cells 150 deltay_5 micron 2e 3 ny_5 cells 5 N_zregions integer 1 deltaz_1 micron 10e 3 nz_1 cellis 400 In the above example the grid consists of 2 regions along the z axis of 5 regions along the y axis and along the z axis the grid has just 1 re gion uniform For any of the axes the total number of cells is a sum of the specified number of cells for each region The in max are com puted as min Lyz 2 Umax Lr 2 where Ly eae NzriAzri Figure 1 Similarly for Ymin Ymars2mins mar Unlike the non uniform grid option Non Uniform Gridit no grid smoothing is used in the case of the grid set with Non Uniform Grid2 entry Some general considerations for setting up the grid When the PML boundary condition is set for any of the axes the com putational domain size input by the user will include a Perfectly Matched Layer PML region at the boundaries of that axis For example if there are n cells set for an z axis with total length Lz and nxzpyyz cells set for the PML region at each end of the domain then there will be
70. long the z axis of the X Y plane in which the source is excited When this line is not present the source plane position defaults to the top of the computational domain just before the PML layer at z Zmar nz put 3 AZtop where Azo is the erid spacing used in the PML region at the top of the computational domain The sourced field distribution imported from DIFFRACT creates a beam propagating in the FDTD grid along the negative direction of the z axis Due to the numerical approximation of the source distribution small amplitude about 30 db residual waves propagating in the opposite direc tion will be generated at the source plane The magnitude of these waves can be evaluated by launching the beam into a uniform medium and monitoring fields behind the source plane The magnitude of the residual waves can be reduced by refining the computation grid 4 15 Point source specification One or more point sources can be specified by their position x0 y0 z0 single field component to be sourced and the switch on off times 4 PARAMETER FILE DESCRIPTION 26 Pointsource Wavelength micron 0 65 x0 y0 z0 micron 0 0 0 0 100e 3 E field x t_on t_off nanoseconds 1 0e 6 6 0e 6 phase degrees 90 The phase parameter is optional It specifies the constant phase shift Qo to be added to the time harmonic dependence of the point source wt o When not specified the phase shift defaults to zero The valid options for the
71. mage on the bottom is that of a flat elliptical stadium pit the other two of round sphero cylindrical cap pits REFERENCES 94 References 1 K S Yee IEEE Trans Antennas and Prop vol 14 1966 pp 302 307 2 MPICH A Portable Implementation of MPI http www uniz mcs anl gov mpi mpich 3 DIFFRACT software MM Research Inc http www mmresearch com 4 M Mansuripur A R Zakharian and J V Moloney Interaction of Light with Subwavelength Structures Optics and Photonics News 13 3 2003 56 61 5 A R Zakharian J V Moloney and M Mansuripur Computer simula tions of the near field effects in high density optical disk data storage Computing in Optics a special issue of Computing in Science and En gineering 5 6 2003 15 21 6 M Mansuripur A R Zakharian and J V Moloney Transmission of Light through Small Elliptical Apertures Part I Optics and Pho tonics News 15 3 38 43 2004 7 M Mansuripur A R Zakharian and J V Moloney Transmission of Light through Small Elliptical Apertures Part II Optics and Pho tonics News 15 4 44 48 2004 8 A R Zakharian M Mansuripur and J V Moloney Transmission of Light Through Small Elliptical Apertures Optics Express 12 12 2004 2631 48 9 Y Xie A R Zakharian M Mansuripur and J V Moloney Transmis sion of Light Through Slit Apertures in Metallic Films Optics Express 12 25 2004 610
72. munication network The exe cution time and memory requirements per node are reduced by distributing the computation across many nodes For both serial and parallel execution of the program the MPI libraries must be installed on the system Support for the Microsoft MPI based High Performance Compute Cluster sys tems Compute Cluster Server 2003 x64 as well as for the freely available MPICH2 based systems is included A freely available implementation of the MPI standard for Windows NT4 2000 XP Professional XP Professional x64 or Server can be found on the installation disk or can be downloaded from the Argonne National Laboratory web site 2 2 Installing the FDTD program to hard disk To install the Finite Difference Time Domain FDTD program Sim3 D Max on hard disk load the distribution CD ROM Double click on Setup to start the installation requires administrator priviledges In addition to the setup of the Sim3D_Max package the Setup utility will also invoke the installers for the following packages e Message Passing Interface MPICH2 system e Acceleware drivers if applicable Tnstallation of the Message Passing Interface system is required for single as well as multi processor systems 3 COMMAND LINE ARGUMENTS 8 e SafeNet Sentinel USB license key drivers Choose Reboot later option during installation of each of the above components and reboot only once after the Setup finishes Upon s
73. n by the thickness entry Depending on the direction the x0 y0 z0 are used as follows When w x the sine runs along x with layer modulated in z uniform along y and the layer has one of its minima in the X Z plane at x0 z0 When w y the sine runs along y with layer modulated in z uniform along x and the layer has one of its minima in the Y Z plane at y0 z0 When w z the sine runs along z with layer modulated in y uniform along x and the layer has one of its minima in the Y Z plane at y0 z0 8 COMMENTS IN THE INPUT FILES 14 7 4 Dielectric Material Interfaces The interfaces between different dielectric media by default are treated as discontinuous step function transitions of the permittivity e g from to An entry in the geometry definition file AverageDielectricInterfaces can be used to create a distribution of in which the permittivity at the interfaces between two dielectric materials is replaced by 2 2 The averaging applies to all dielectric material interfaces found in the com putational domain separately along each of the coordinate directions and is valid only for materials with real valued e 8 Comments in the input files In the material and geometry input files C style comments but no nested comments can be used to comment out one or more material or geometry definition blocks For example the following blocks AddConvexPolygon material string Si02 vertices
74. nd the Export Transmitted sampling planes the meaning of reflected or transmitted may be lost depending on the relative location of the sampling plane posi tions and the source plane location 4 22 1 Export of the reflected field This item is optional in the input file It can be used to obtain complex valued distribution of the fields in the X Y plane The specified output file conforms to the file structure used in the FDTD import export option of DIFFRACT ExportReflected Filename fdtd export reflected File Format ascil Grid Type collocated NX NY 256 256 The File Format can be one of ascii fortran_binary c_binary and Grid Type can be staggered or collocated as described in sub section 4 14 A collocated grid and ASCII or Fortran binary format must be used when generating files intended for input into DIFFRACT via FDTD Im port option The NX NY option specifies the desired number of points along the x and y axis The line specifying NX NY can be omitted In that case the number of points will be set to the Nz N of the DIFFRACT input source 4 PARAMETER FILE DESCRIPTION 40 file 4 14 or if another source is used Nz Ny are set to the number of points in the XY plane of the FDTD grid The scattered field complex valued am plitude is computed in the xy plane at z Zmar nz PML 2 AZtop via the Discrete Fourier Transform of the time dependent solution applied in the time interval tmar
75. ne along the z axis in micrometers If this position is outside of the computational domain bounds no output file will be produced The line z location corresponds to fields sampled in the XY plane Similarly y location or x location 2Note that changing zmaz will change the Diffract source and export reflected field plane positions Also tmaz is set independently of Zmaz and should be chosen large enough to get time harmonic converged solution 4 PARAMETER FILE DESCRIPTION Al can be used to sample fields in the X Z or Y Z planes The line specifying the number of points in the sampling plane NX NY for the XY plane NX NZ for the X Z plane or NY NZ for the Y Z plane can be omitted in which case the number of points will default to the values from the DIFFRACT source file 4 14 or if DIFFRACT source is not used to the number of points in the corresponding plane of the FDTD grid After the line specifying the number of points an optional specification of the sampling region can follow For example in the Y Z plane one can specify an area centered on the point 0 0 as LY LZ micron 2 4 1 0 When not specified the sampling region will be set to the computational domain size for the corresponding cross section One exception is when DIFFRACT source is used then the sampling region in the X Y plane is set to Ly Ly values read from the DIFFRACT source file The reflected or transmitted field magnitude and phase
76. niform Grid1 input The grid is symmetric in the XY plane and consists of three regions with different cell sizes along either x y or z axis b Computational domain and non uniform grid definition for the Non Uniform Grid2 input The grid consists of arbitrary number of regions with different cell sizes along the z y and z axis In the example shown Neregions 2 Nyregions 3 Nezregions 4 The total number of cells along any axis is equal to the sum of the specified number of cells in each region of that axis When absorbing BCs are set PML regions are always counted as part of the total length of the domain 4 PARAMETER FILE DESCRIPTION 13 are computed and set by the program in the same way as Zmin mar AN example of non uniform grid specification is given below Non Uniform Gridi wi micron 500e 3 w2 micron 200e 3 w3 micron 2040e 3 delta_1 micron 10e 3 delta_2 micron 20e 3 delta_3 micron 30e 3 hi micron 160e 3 h2 micron 140e 3 h3 micron 300e 3 deltaz_1 micron 10e 3 deltaz 2 micron 5 0e 3 deltaz_3 micron 10e 3 Note that due to the smoothing of the cell size done by the program at the interfaces between regions with different resolution the resulting do main will have a total length larger by a few cells than the sum of lengths of individual grid regions A second way of setting up a non uniform grid allows direct specification of an arbitrary number of regions with a certain number of ce
77. of Ay 405nm and is incident normally onto the surface of the stack The computational grid has Az 5nm in the region occupied by the two layers and Az 10nm elsewhere Two sets of material refractive index values corresponding to tem peratures of T 300K and T 4004 are used and Debye material model is employed to represent the GST layer The exact and computed reflection and transmission characteristics are shown in Table 3 Both amplitude co efficients R and T and phase difference Ad 309 400 of the reflected and transmitted waves converge to the exact solution when grid cell size Az is reduced by a factor of two throughout the domain Only the phase differ ences and not absolute value of the phase can be used for comparison to the analytic results since the phases computed in FDTD have initial phase shifts due to start time of the the source and offset time of the field sampling for Fourier Transform For the same materials geometry wavelength and FDTD grid parame ters we also compute reflected fields for the case of an incident laser beam In DIFFRACT a circularly polarized Gaussian beam is brought to focus in 9 APPLICATION EXAMPLES 7 Table 3 Comparison of exact and numerical solutions for a planewave incident on a bi layer in a medium with refractive index n 1 55 layer thicknesses lzns sio gt lasr 50nm and layer refractive indecies NZnS SiO gt r 300K 2 52 nest 300K 1 753 3 2487 at T 3
78. om position with N 6 processors Appendix D Monitor file formats The content of various monitor files is described below by specifying the first line containing monitor mode type number of points in space and time or frequency domain followed by specification of the fields columns of the subsequent lines Time is output in units of ns frequency in units of THz and spatial coordinates in units of wm E H S and integrals are in MKS units TIME HISTORY MONITORS line monitor of fields in 2D mode time history Ny Nz Ntime time coordy coordz F1 F2 F3 sy 5z where F1i Ex F2 Hy F3 Hz for mode Ex_Hy_Hz F1 Hx F2 Ey F3 Ez for mode Hx_Ey_Ez line or plane monitor of fields in 3D 3D time history Nx Ny Nz Ntime time coordx coordy coordz Ex Ey Ez Hx Hy Hz Sx sy 5z plane monitor of energy flux integral in 3D 3D Lintegral Sn time history Ntime time integral_over_area_of_5Sn volume monitor of energy in 3D 3D Lenergy time history Ntime time integral_over_volume_ E D H B 2 FOURIER TRANSFORM MONITORS r and i after field component names stand for real and imaginary parts of complex valued data line monitor of fields in 2D mode fourier transform Ny Nz Nfreq frequency coordy coordz Fir Fii Far F2i F3r F831 sy 5z where F1i Ex F2 Hy F3 Hz for mode Ex_Hy_Hz or F1 Hx F2 Ey F3 Ez for mode Hx_Ey_Ez line or plane monitor of fields in 3D 3D fourier transform Nx Ny Nz Nfreg frequency coordx coo
79. on compatibility with DIFFRACT This entry is optional in the input file It specifies the version of DIFFRACT software with which the DiffractSource and export files should be compatible ExportFileFormat version 8 2 The export files are produced by the ExportReflected and Export Trans mitted entries described in subsections 4 22 1 4 22 2 If the file format version is not specified the default is compatibility with DIFFRACT versions 8 4 and up When using source files subsection 4 14 created with DIFFRACT versions 8 3 and lower it is mandatory to explicitly specify the file format version otherwise the source distribution will be incorrect When DIFFRACT source file is used the ExportFile Format is set to the same format as the source The different file formats are as follows For DIFFRACT versions less than 8 2 4 PARAMETER FILE DESCRIPTION 37 the file contains on the first line the refractive index n assumed to be constant in the sampling plane followed on the second line by Nz Ny Lr Ly and complex valued field distributions F z y E x y E x y followed by and H x y H x y H v y The fields are sampled on a uni form grid with steps L N and L N in xz and y directions The variable is equal to the FDTD grid cell size in a direction normal to the plane and at the position of the plane on which F and H fields are sampled Negative values of 6 specify that H
80. ontaining on the first line a single word for example Dielectric x y z followed by Nng x n x n entries Nijk Cijk for each point t J k of the grid defined in section 4 3 The data is read from the file in the following order for i 1 to nx for j l to ny for k 1 to nz read nli j k sigmali Lj k 6 2 Debye model The parameters for a dispersive medium based on the single pole Debye model correspond to a complex valued frequency domain susceptibility func 6 MATERIAL FILE DESCRIPTION 51 tion y w and permittivity function e w Ae Oo x w W E x w i 6 T IF iwr WE with T the pole relaxation time the relative permittivity at infinite frequency Ae E where is the static or zero frequency relative permittivity An example set of parameters for gold n 0 16 3 957 at A 700nm Material Label string Gold model Debye tau femtosec 4 84371 eps_inf relative 1 0 delta_eps relative 2832 73 conductivity Li Cohm m 5 17818e6 The Debye model can be used to simulate materials which have a dispersion relation that can be approximated by the expression 6 over some frequency band The Debye model can also be used to represent materials with complex valued refractive index n kz at a specified frequency In such cases given two parameters n and k the choice of four Debye model parameters is not unique Figure 14 At any given frequency w the real and imagina
81. pace on an M by N by P lattice The unit center specifies the position of one of the unit ele ments of the pattern and unit size sets the size of the unit element along the x y and z axis The parameters of the geometric objects that constitute a unit element are the same as those used when specifying a single object by itself but the name of the object is used without the Add prefix The pattern objects can be nested as in the following example AddPattern unit center micron 0 0 0 0 0 0 unit size micron 1 0 1 0 0 8 M N P number 3 3 1 Cone material string GaAs x y center micron 0 0 0 0 rir micron 0 4 0 3 z_min max micron 0 6 0 6 Pattern unit center micron 0 15 0 15 0 0 unit size micron 03 03 0 3 M N P number 2 2 2 Disk material string Si02 x y center micron 0 0 0 0 radius micron 0 1 z_min max micron 0 1 0 1 7 3 Geometric objects for optical data storage media modeling 7 31 Bumps pits A bump or a pit can be added to a layer Three types of bump objects are defined sphero cylindrical cap corresponds to the type Round defined in DIFFRACT software sphero cylindrical stadium and elliptical stadium corresponds to the type Flat defined in DIFFRACT software For all bump types material specifies the material of the layer on which bump is put while substrate specifies the material under the bump The 7 GEOMETRY FILE DESCRIPTION 67 w 2 1 4 pa x layer mater
82. phere Left the dielectric sphere of radius 0 24um and refractive index ng 1 54 is illuminated by the planewave with wavelength A 0 6um in a medium with n 1 0 Vertical lines mark the boundaries of the dielectric sphere Right the metal spheres are embedded in a dielectric with n 1 5 and have radii r4 0 24um and rag 0 5pm was used for the dielectric sphere A 5nm for the Al sphere and both A 10nm uniform grid and Amin 5nm Amaz 20M non uniform grid for the Ag sphere The following material model parameters were used for aluminum at A 0 65um and silver at A 0 85um Material Label string Aluminum 9 APPLICATION EXAMPLES 19 model Debye tau Lfemtosec 1 95595 eps_inf relative 1 0 delta_eps relative 1522 91 conductivity 1 ohm m 7 40866e6 Material Label string Silver model Lorentz omega0 Hz 1 63991e15 delta Hz 4 18345e13 eps_inf relative 3 0 delta_eps relative 32 0 conductivity 1 ohm m 0 0 9 4 Laser beam scattering from a mark In this subsection we discuss input required for computation of scattering of a focused beam from a single pit formed in a d0nm thick layer of aluminum coated on a dielectric substrate To simulate the focused beam distribu tion the Diffract source option is used in the input parameter file The diffract_source dat file created with DIFFRACT software contains E and H field distributions in the X Y plane obtained by bringing to a focus a b
83. r waveguide source for Ex_Hy_Hz or Hx_Ey_Ez mode is specified by its effective index neff 3 k where is a mode propagation constant and k 27 X is a free space wavenumber The refractive index is n2 for the waveguide and nl n3 for the cladding layers The position of the center and width of the waveguide and refractive index values n1 n2 n3 must cor respond to the structure and material properties specified in the geometry and material definition files The sourced mode has a wavevector along the positive direction of the y or z axis 4 PARAMETER FILE DESCRIPTION 36 Waveguidesource Wavelength micron 0 65 Mode Hx_Ey_Ez ModeNumber O n_eff ni n2 n3 1 49797 1 0 1 75 1 0 center width micron 3 0 0 3 ymin ymax micron 0 0 6 0 zmin zmax micron ORo Or The ymin ymax zmin zmax specify the extent of the source The source is applied along the y or z aligned coordinate lines so either zmin zmax or ymin ymax must be equal Figure 12 For example for a waveguide run ning along the z axis the waveguide mode is sourced across the waveguide along the y axis so zmin must be equal to zmax and equal to the desired z location of the source line The range of ymin ymax should be large enough to cover the regions where the source field amplitudes are not negligible If the ymin ymax zmin zmax extend outside of the computational domain they are reset to the edge of the computational domain or PML region 4 20 File format versi
84. rallel performance and load balancing 98 C Staggered field location for user defined sources 101 D Monitor file formats 0 0 0008 103 E Article reprints 2 2 2 00000002 eee 105 Sim3D_Max FDTD code User Manual November 29 2009 This document describes the user interface to a software module for so lution of the time dependent vector Maxwell equations in three dimensions using the Finite Difference Time Domain FDTD method 1 The main features of the program are full vector field description in 3 D Cartesian geometry computation speed up with Acceleware hardware compatibility with DIFFRACT software non uniform grid support non dispersive and dispersive material models UPML absorbing boundary conditions arbitrary geometry input e parallel implementation for multi processor platforms based on the Message Passing Interface MPI 2 standard Maxwell s equations along with the constitutive relations are discretized in space and time using FDTD method based on the second order accurate staggered central difference operators In MKS units the relevant equations can be written as follows Vx H oE V D EE V B 0 Ot OP D GE P B H J where E Volts m is the electric field D Coulombs m7 electric flux den 5 1 SYSTEM REQUIREMENTS 6 sity H Amperes m magnetic field B Webers m magnetic flux density J Amperes m elect
85. rdy coordz Exr Exi Eyr Eyi Ezr Ezi gt gt Hxr Hxi Hyr Hyi Hzr Hzi gt gt Sx Sy Z plane monitor of energy flux integral in 3D 3D integral Sn fourier transform Nfreq frequency integral_over_area_sn Appendix E The Publications subdirectory of the distribution CD provides article reprints illustrating application of Sim3D_Max to modeling optical disk storage media elements M Mansuripur A R Zakharian J V Moloney Interaction of light with sub wavelength structures Optics and Photonic News March 2003 pp 56 61 M Mansuripur A R Zakharian J V Moloney Transmission of Light Through Small Elliptical Apertures Part I Optics and Photonic News March 15 2004 pp 38 43 M Mansuripur A R Zakharian J V Moloney Transmission of Light Through Small Elliptical Apertures Part IT Optics and Photonic News April 15 2004 pp 44 48 A R Zakharian J V Moloney M Mansuripur Computer simulations of the near field effects in high density optical disk data storage IEEE Computing in Science and Engineering Nov Dec 2003 pp 15 21
86. ric polarization current density and P Coulombs m is the electric polarization vector Material properties are defined by elec tric conductivity o 1 Ohm m permittivity ee and polarization P where 9 8 854 x 107 Farads m and uo 4r x 107 Henrys m are free space electric permittivity and magnetic permeability and e is the relative permittivity The version of the program described in this document allows compu tation of the scattered field for a given structure and a given incident field distribution created in DIFFRACT 3 The input and output file formats are compatible with the file formats used by the FDTD interface option of the DIFFRACT software Sections 1 and 2 provide information on the system requirements and in stallation Section 3 describes command line arguments of the program In section 4 the structure of the input parameter file is given Boundary condi tions material model and geometry input are described in sections 5 7 The last section provides some example problems along with the corresponding input files 1 System requirements Binary executables of the program are available for A32 and EM64T AMD64 platforms running Windows NT 2000 XP or XP x64 operating systems Hardware acceleration is supported for Windows 2000 XP Pro XP Pro x64 operating systems and requires a PCI Express x16 slot s for the Acceleware Accelerator card s Table 1 Supported architectures and Windows
87. rical cap material string Aluminum substrate string Vacuum x0 micron a y_0 micron 0 9 ZO micron 260e 3 width micron 700e 3 height micron 50e 3 length micron 800e 3 thickness micron 160e 3 angle degrees 75 Absorbing boundary conditions are applied along the x y and z axis The Diffract source is applied near the top of the computational domain at z 0 33um The reflected field is sampled just above the source at z 0 338um and the top surface of the layer in which marks are made is at z 0 l unm Hence the reflected beam propagates 0 438um inside FDTD grid before being saved to a file for later import into DIFFRACT After reflected fields are computed in FDTD for all incident beams they can be imported into DIFFRACT and propagated to the image plane Remarks Vacuum wavelength um 1 000000 NVIRON 1 000000 FDTD Interface FDTD Length_Units um Export Import Import Filename sr01 dat Amplitude phase mask MASK Length_Units um Shape Rectangle MCX MCY 0 000000 0 0000 9 APPLICATION EXAMPLES 91 Length Width Alpha 5 000000 5 0000 0 000000 Orientation angle Theta O 000000 1 000000 0 0000 0 000000 0 0000 Inside amplitude phase Outside amplitude phase Spatial Filter FLTR Length_Units um Computation Method DFT CSX CSY 5S0 0 000000 0 0000 1 000000 Inside A0 Phi0O 1 000000 0 0000 Outside A1 Phi1 0 000000 0 0000 New Mesh NMAX NMAY 512 512 New Mesh LMAX LMA
88. ross its computational sub domain 2 The output files that contain user defined source data interpolated into the FDTD grid section 4 18 are also written separately by each processor with rank of the processor appended to the filename Figure 39 shows an example of a 2D computational domain with a monitor and user defined source The domain is partitioned among six processors The resulting 3 output monitor files and 2 output interpolated source data files will have different number of spatial points Appendix B Parallel performance and load balancing The parallelization of the code is based on the Single Program Multi ple Data parallel programming model with partitioning of the spatial grid between a number of processors that simultaneously advance the solution in time The explicit time update and short finite difference stencil of the FDTD method lead to a high degree of memory access locality and enable good speedup as shown in Figure 36 using two types of tests The tests on i Opteron SMP Linux cluster Altix Itanium SGI Origin 3000 Figure 36 Measured relative runtime vs number of processors for a Linux cluster of AMD Athlon tm MP 2400 workstations connected by a 1Gb s network 4 processor Microway Opteron846 system SGI Altix Itanium and SGI Origin 3400 systems Benchmark tests were identical only for Altix and Opteron systems and these can be cross compared Altix and Opteron systems
89. ry parts Refer gL Relea In e A Ine n a ee e ee ooo m i a a 200 300 400 500 600 700 800 900 1000 200 300 400 500 600 700 800 900 2 nm nm Figure 14 Dependence of complex valued permittivity and refractive index on the wavelength 27c w computed using single pole Debye model 6 with two sets of model parameters for gold n 0 16 3 95z at A 700nm 1000 6 MATERIAL FILE DESCRIPTION 52 of the equation n ki provide two conditions for the choice of Debye parameters Ae 1 wr AEwWT o oT ede a 1H wT wep which can be rewritten in the following form Ae liur r k t 7 o Ink an ae 8 nk am WT n Eo 8 By setting 1 parameters o and 7 are determined by equation 8 linear in both unknowns with Ae following from equation 7 The Debye model corresponding to a given permittivity at source frequency can be realized by specifying n ki or in the material definition file for example Material Label string Aluminum model Debye n ki dimensionless 2 7i Material Label string Gold model Debye eps relative 15 0 1 2i A multi pole Debye model corresponding to the relative permittivity N pe 0 doct dL j p l 1 JWT WEY can be set by specifying the number of poles Np followed by the list of pa rameters for each pole in the format shown below 6 MATERIAL FILE DESCRIPTI
90. ry where the program will look for all input geometry material boundary conditions source files and where it will write the output files e g Working directory home username Maxwell FDTD or Working directory C username Maxwel1l FDTD For all input files the program looks for the file e g file material input described in the next subsection in the directory specified under Working directory However if the filename includes explicitly the path C User myfiles material input or material input then the filename is used as specified Directory and file names containing the space character must be enclosed by double quote characters C User Name My Data Files 4 6 Material Definition File The Material Definition File sets a filename of a file containing material model specifications see section 6 e g Material Definition Filename material input 4 7 Geometry Definition File The Geometry Definition File sets the filename of a file containing geom etry specifications see section 7 e g Geometry Definition Filename geometry input Same rules regarding filename apply as specified above 4 8 Boundary Conditions File Boundary conditions can be set using the file specified under the Boundary Conditions Filename entry see section 5 For example 4 PARAMETER FILE DESCRIPTION 17 Boundary Conditions Filename boundaries input 4 9 Material index output The material index o
91. t contains the refractive index n distribution in the computational domain For the ma 4 PARAMETER FILE DESCRIPTION 21 e O sak 2 oe s w m PRAS Figure 5 S S components of a 3D Gaussian beam from Fig 4 terials based on Lorentz and Debye material models instead of nef a value m is written into Ml bin out file where m is the order number in which the material is defined in the material definition file For the materials of type Debye x y the conductivity in MKS units is used in the MI1 bin out file for each point of the domain occupied by the Debye x y materials The binary data format of the material layout file is the same as that of the field files The file coords contains on the first line the number of points nz Ny nz followed on the second line by the number N of outputs done and the computation output times in seconds e g t tinar N 2 x tmar N tmaz on the third and following lines The files coordx coordy coordz contain a single column corresponding to the coordinates of each cell in the x y z direction 4 11 Checkpoint files The CheckpointFile block sets the file output and input options for sav ing and restarting the computation RestartFromCheckpointFile option allows the computation to be continued from a previously saved checkpoint file WriteCheckpointFile requests that a checkpoint file be created at the 4 PARAMETER FILE DESCRIPTION
92. t fortran_binary Grid Type collocated zZ location micron 10000e 3 In this example the output of the material index field and checkpoint files is switched off The desired output from the simulation is obtained with the ExportRe flected option and represents the distribution of the reflected light sampled in the X Y plane The Export ransmitted sampling plane is also specified but its location along the z axis is set out of bounds of the computational domain so it will be ignored Figure 31 Computational domain with a non uniform grid refined in the center at the location of the pit The sphero cylindrical pit made in 50nm aluminum layer is 400nm wide 600nm long and 60nm deep The 2D plot shows a zy cross section of the 3 D domain PML absorbing boundary conditions are set for all axes in the boundary 9 APPLICATION EXAMPLES 82 x um Figure 32 Transverse amplitude 4 E2 E distribution of the light reflected from a pit in aluminum layer for a geometry shown in Figure 31 Scattering of the light from the walls of the pit focuses it toward the center of the pit conditions input file BoundaryConditions x axis PML nx_pml 15 Sligma kappa 0 OQ y axis PML ny_pml 15 Sligma kappa 0 OQ z axis PML nz_pml 15 Sligma kappa O OQ The input material definition file defines a transparent dielectric substrate material called in this example i02 and material Aluminum modeled using Lorentz model P
93. terial string AlAs x z center micron 0 0 0 0 Z ri r2 micron 0 2 0 4 y_min max micron 0 5 0 5 XoY X y Figure 18 Definition of parameters for cone center o yo radii 71 72 thickness Zmin Zmaz 7 GEOMETRY FILE DESCRIPTION 60 7 2 5 Disk AddDisk material string Vacuum Z x y center micron 0 0 0 0 radius micron 1 0 z_min max micron 450e 3 70e 3 X y Figure 19 Definition of parameters for disk cylinder center o yo radius r thickness Zmin maz Alias AddCylinder can be used instead of AddDisk 7 2 6 Polygon AddConvexPolygon py Ey material string Al0x X Y X Y vertices number 5 x1 y1 micron 0 25 0 5 E x2 y2 micron 0 25 0 5 x3 y3 micron 0 5 0 0 x4 y4 micron 0 25 0 5 J 7 xy x55 micron 0 25 0 5 Zz min max micron 0 25 0 25 Figure 20 Definition of parameters for convex polygon number of vertices list of vertex coordinates i Yi thickness Zmin Zmaz 7 2 7 Ellips AddEllips material string Silver x z center micron 0 0 0 0 Z a b micron 1 0 1 5 angle degrees 45 0 X Y ci y_min max micron 450e 3 70e 3 X y Figure 21 Definition of parameters for ellipse center o Yo semi major axis a b angle of rotation a a gt 0 thickness Zmin Zmaz 7 GEOMETRY FILE DESCRIPTION 61 Definitions for other geometric objects AddCappedRectangle material string Si02 y z center micron 0 0 0 0 radius micron 1 0 length micron
94. th CFL 0 4 The time step delta_t can be set in two ways The first format delta t automatic with CFL CFL_NUMBER specifies that the time step should be computed from the spatial grid cell sizes Ax Ay Az according to dt CFL_NUMBER x min Aqa Ay Az c where c is the speed of the light in a vacuum and CFL number should be a number less than the stability limit CFL NUMBER lt 1 V3 The second format delta_t nanoseconds 1 0e 8 sets the value of the time step explicitly in nanoseconds For problems in which time harmonic continuous wave solution is sought the convergence of the solutions can be verified by increasing the value of tmax With all other problem parameters unchanged and repeating the sim ulation Similarly convergence of the solution with respect to the value of 4 PARAMETER FILE DESCRIPTION 11 the time step can be verified by decreasing the time step At or equiva lently decreasing the CFL NUMBER See section 4 3 for accuracy and convergence dependence on the spatial grid cell size 4 3 Spatial grid specification A uniform grid can be specified by setting the number of cells and compu tational domain size as follows e g Uniform Grid nx cells 120 ny cells 150 nz cells 200 xmin micron 8 0 xmax micron 5 0 ymin micron 6 0 ymax micron 4 0 zmin micron 0 0 zmax micron 15 0 The cell size along x axis will then be a constant Av Emar min Nz and simi
95. to the transmitted beam in order for it to propagate along the z in agreement with the convention used in DIFFRACT The coordinate system rotations described above are applied by default to the field distributions of the source and Export lTransmitted X Y planes but not XZ or Y Z planes when Diffract input file is used as a source The default can be changed with an optional entry CoordinateSystem code where code can take a value of Sim3d_Max no rotation or DIFFRACT coor dinate system rotation is applied 4 PARAMETER FILE DESCRIPTION 39 4 22 Export file specification The spatial distribution of the amplitude and phase of the E and H fields on a specified plane and at the frequency of the source can be obtained using ExportReflected and Export Transmitted entries These objects can be used with any source and produce files in a format compatible with the FDTD import export interface of the DIFFRACT software The difference between ExportReflected and Export Transmitted entries is that the reflected field is sampled on the X Y plane at a predefined position while the Export Transmitted can specify any coordinate plane with arbitrary location The Export Reflected plane will be positioned just above the source plane when used with a PlanewaveSource or DiftractSource at its default location so that only the reflected field is sampled Because of the possibility to arbitrarily place the source a
96. uccessful completion the installation creates a directory named lt NLCST Sim3D_Max Version Number gt under lt Program Files gt folder and places a shortcut to the Sim3D_MaxGUI executable on the Desktop Within the installed directory you will find the following folders lt GUI gt lt Bin gt lt Docs gt lt Examples gt lt GUI gt supporting files for the Graphical User Interface of the program lt Bin gt Sim3D_Max executables and supporting files lt Docs gt manuals publication reprints and other documentation lt Examples gt folders with sample input files and test cases Follow instructions in Readme pdf to complete the installation For the computations that use the DIFFRACT source the input beam i e the complex light amplitude distribution that enters the FDTD mesh must be generated by DIFFRACT using the menu option FDTD in Export mode then imported to the Sim3D_Max exe All output distributions computed by Sim3D_Max exe will be stored on hard disk in files within the working direc tory specified in the parameter input file of Sim3D_Max exe Subsequently these output files may be imported by DIFFRACT using the menu option FDTD in Import mode and displayed using the option PLOT or processed as any other beam cross section is processed in DIFFRACT 3 Command line arguments For serial computations the executable program called Sim3D_Max can be invoked with a single argument the
97. ulation f t of the time dependent source f t sin wt eo TimeProfile f t L LsuperGaussian tO nanoseconds 400 0e 6 FWHM nanoseconds 80 0e 6 n 2 0 Valid options for the f t entry are sech L superGaussian tanh or file The functional dependence and parameter values for these op 4 PARAMETER FILE DESCRIPTION 23 tions are given in the Table 2 The default time profile is a tanh function with tO set to 3 fs and tau to 1 fs In the case of a user defined time profile TimeProfile f t file Filename string user_time_profile input the specified ASCII file is expected to contain on the first line the num ber of points N present in the file followed by a single column of the values of the function f t sampled at each computation time step t i dt 1 1 2 During the simulation for t gt N dt the f t is set to the value on the last line of the input file Table 2 Source time profile parameters ft Fanction Parameter 1 Parameter 2 Parameter 3 Saye cama ayre eye a ed superGaussian exp t to t to FWHM 27 m2 n es e a O tna ser defined O fome S o o For any choice of the profile the amplitude of the time profile function can be set by specifying an optional entry in the following form amplitude V m 2 0 or amplitude A m 2 0 If this line is omitted a default value of 1 0 is assumed for the amplitude The default value of the ph
98. ure 25 Definitions of parameters for the bump types sphero cylindrical stadium and elliptical stadium Angle a determines the steepness of the walls which have a constant thickness t when measured along the local unit vector normal to the surface a XZ cross section is shown for the case of l 0 zero elongation b XY cross section of the sphero cylindrical bump and c XY cross section of the elliptical bump Lelliptical stadium the parameter wall_angle specifies angle a defined in Figure 25 For the bump type Lelliptical stadium instead of a width parameter the major axis a b of the elliptical cross section of the bump are specified see Fig 25 Examples of the stadium type bump pit setup AddBump bump_type l sphero cylindrical stadium material string Aluminum substrate string Si02 x_0 micron Les y_0O micron lie z_0 micron 70e 3 width micron 400e 3 height micron 60e 3 length micron 500e 3 thickness micron 50e 3 wall_angle degrees 60 0 Any of the bump types can have an optional last line specifying the an 7 GEOMETRY FILE DESCRIPTION 69 gle measured counter clockwise from the x axis of the bump rotation in the XY plane angle degrees 60 The default value for this rotation angle is zero AddBump bump_type Lelliptical stadium material string Aluminum substrate string 5102 x_0 micron 1 5 y_0 micron 1 5 z_0 micron 70e 3 a b micron 500e 3 750e 3 height micron 6
99. utput provides an option to write to a file a 3D spatial distribution of the material logical index set up from the material and ge ometry files Example Material index Write to file no Filename mindex out Write to file must be followed by yes or no The resulting file is in ASCII format It contains the total number of cells Nng ny nz followed by the logical enumeration value of the material for each cell 2 7 k of the com putational grid This logical value is simply a number corresponding to the order in which materials are defined in the material definition file The order of the cell output is one in which k changes first then 7 then 2 as illustrated in the following pseudo code segment for i 1 to nx for j l to ny for k 1 to nz write read material enumeration value in cell i j k The same file structure is used in the geometry object defined in 7 1 The co ordinates of the cells are written into ASCII files coordx coordy coordz in microns i e the cell 7 j k has cell center coordinates x i y j z k found on lines 2 7 in files coordx coordy and coordz respectively These files can be used to plot and verify the material and geometry setup specified in the input files Sample plots are shown in Figures 2 and 3 2 4 10 Field output Spatial distribution of the E and H fields can be optionally written into files at specified equal time intervals 4 PARAMETER FI
100. velength Nopw Ao NsubAz 9 1 Order of convergence Figure 28 shows a time snapshot of the distribution of the y component of the E field and the computed error as a function of the grid step size for 9 APPLICATION EXAMPLES 76 a reflection transmission problem A TE E E H polarized planewave with Ay 650nm is incident at an angle of 50 on an air glass interface The Poynting vector is computed along the z axis at y 0 with a monitor at source frequency The difference between computed and exact S normal ized by the incident energy flux indicates second order O Az convergence of the numerical solution to the exact solution R 0 0268 T 0 9732 In the problems that have material interfaces not aligned along the grid lines the staircased approximation of the curved material interfaces on the finite difference grid in general will reduce the order of convergence to the exact solution to O Az 9 2 Reflection from a bi layer In this example we compute reflection of a planewave and of a laser beam from a two layer stack embedded in a medium with refractive index n 1 55 The stack consists of materials and has layer thicknesses similar to those commonly used in optical data storage media a layer of ZnS SiOs ex tending from Zmaz 502M tO Zmin Onm followed by a 50nm layer of GST from Zmaz ONM tO Zmin 50nm In the case of a planewave source the light has a unit elictic field amplitude free space wavelength

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