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Johaness Hallier

1. mately a phase change of zero and full transmission Then the other mask is calibrated 5 1 Labview program 38 Figure 5 6 Automated calibration setup A notebook computer a sends a drive value to the SLM b and the output power of the assembled beam is measured with a power meter c The analog output of the power meter d is measured through an oscilloscope e which is integrated into the LabVIEW program on the computer by increasing the drive value from zero to maximum in equally spaced steps The trans mission value is recorded by measuring the output beam with a power meter Using equations 3 5 and 3 6 the phase for the individual arrays can be calculated as Ep arccos VT 5 1 y arccos VT 5 2 A Ad ml Awl gt where 5 needs to be added to avoid a negative phase retardance Lup04 Since the 5 2 Feedback with a genetic algorithm 39 transmission is oscillating that means it has several minima and maxima the func tion needs to be regarded as a steady function in order to have the phase retardance continously falling since all multiples of 27 added to the phase retardance result in the same transmission value This was solved by using an algorithm to change the sign of the arccos T term when maximum transmission was reached for recalculation of the phase retardance ion amp amp i L Fa J Phase retardance rad gt o 5 Es E ao pt 2 N S
2. 2 1 Assuming a harmonically oscillating wave in time which spatial amplitude can in general be described using a complex phasor U r t U r e 2 2 which includes the amplitude and the phase of the wave at time t 0 Inserting this into the wave equation leads to Ww V a U r e 0 2 3 where e 0 V t Substituting k yields h x Vt Sub k yield V k U F 0 2 4 This is the Helmholtz equation which contains solutions such as the planar or the spherical wave A laser beam however is not a completely planar wave Every beam 2 1 Optics 4 Figure 2 1 Wave at different distances within a small cylinder around the axis a Spherical wave b ellipsoidal wave c paraxial wave Compare at SaT91 experiences a certain angle of divergence although the angle may be very small such that the divergence is only visible at great distances from the laser source The wave fronts differ from the planar wave U r A e777 2 5 and become slightly curved which can be approximated using a spherical wave from a distant source within a small diameter around the propagation axis see figure 2 1 Taking the planar wave equation a paraxial wave can be described using the slowly varying amplitude approximation SVA UN A e 2 6 which means that AA lt A within a wavelength A Applying 2 6 together with the SVA on the wave equation result in the paraxial Helmholtz equation f
3. Palmer E Loewen Diffraction Grating Handbook Sixth edition New port Corporation 2005 A Praekelt et al Compact robust and flexible setup for femtosecond pulse shaping Review of Scientific Instruments 74 11 2003 D H Reitze A M Weiner D E Leaird Shaping of wide bandwidth 20 fem tosecond optical pulses Applied Physics Letters 61 11 1992 A M Weiner Femtosecond pulse shaping using spatial light modulators Review Article Review of Scientific Instruments Volume 71 Number 5 2000 M M Wefers K A Nelson Analysis of programmable ultrashort waveform generation using liquid crystal spatial light modulators Journal Optical So ciety America B Vol 12 No 7 1995 A M Weiner et al Programmable Shaping of Femtosecond Optical Pulses by use of 128 Element Liquid Crystal Phase Modulator IEEE Journal of Quantum Electronics Volume 28 Number 4 1992
4. at Polarized Light A B Figure 2 5 Twisted nematic crystals a without voltage applied light changes polar ization according to the crystals direction b a voltage causes the molecules to align along the electric field and no light transmits ChC07 2 2 Spatial Light Modulator Also called a Liquid Crystal Modulator LCM a Spatial Light Modulator SLM is equipped with an array of liquid crystals which is a liquid in a state that has crystal properties like uniformity and alignment of molecules as well Unlike crystals the alignment of molecules can easily be changed by applying low voltages Here the crys tal array is aligned along the x axis the vertical axis of each pixel is the y axis and the z axis is the direction of light travelling through the device The crystals are molecules shaped ellipsoidal with one axis larger than the other Cam04 There are two ways of using a LCM as a Phase or as an Amplitude modulator The crystal structure is slightly different for both Phase modulation is achieved by apply ing a voltage across the length of the SLM The crystals tilt from their idle state and cause a change of the refractive index for y polarized light see figure 2 6 Thus the phase of the beam will be changed as the beam is delayed when passing through the crystal This effect is wavelength dependent but as each pixel only has a very small part of the whole spectrum the wavelength can be assumed constant over t
5. Generation SHG FROG A typical setup of a FROG device is shown in figure 3 7 whereas the photomultiplier has to be replaced with a spectrometer The three measured parameters time delay frequency and amplitude Cry SHG Crystal L Lens M TS BS Beam Splitter M Mirror z Filter Ph Photodetector W2 Wave Plate TS Translation Stage e pe Figure 3 7 Setup of SHG FROG Tre97 are combined in a spectrogram From this trace a computer algorithm deducts am plitude and phase in time and frequency domain by iteratively comparing a theoretical with the measured plot and minimizing the error Tre97 The FROG has proven to be a reliable device for measuring ultrashort pulses however some problems are the necessity of a relatively high power for the SHG FROG and the comparatively long time to completely characterise a pulse Other techniques are also available and should be taken into consideration for each individual application 3 4 Feedback design If the required pulse characteristics are unknown or if the calibration does not yield a sufficient accuracy a feedback design based on evolutionary strategies can be used BBS97 A feedback parameter such as a second harmonic generation signal by a nonlinear crystal serves as the evalutation function see section 2 3 If the parameters 3 4 Feedback design 20 for the pattern to shape a desired pulse are unknown or do not lead to optimum results because of error
6. Spectrum Measured Output H Desired Output o T Normalized Amplitude o o o o o o o kh a o N o e iv 0 1 980 785 790 795 805 810 815 820 800 wavelength nm Figure 6 1 Shaping of a rect function in the spectral domain The input spectrum is a Gaussian black measured without the SLM inserted The output red varies from the desired spectrum blue due to errors introduced by the SLM Input Spectrum Measured Output Desired Output bal o a m O D N Normalized Amplitude o o gt a 980 785 790 795 800 805 810 815 820 wavelength nm Figure 6 2 A modified input spectrum measured with the SLM inserted does not significantly improve the results 6 2 Feedback shaping The feedback shaping program was designed to allow to start either with a start so lution or with completely random solutions When a start solution was chosen the spectral shaping procedure needs to be used beforehand to calculate a SLM pattern 6 3 Shaping in time domain 44 4000F Mask Mask 3500L Mask2 3500 Mask2 v 3000 3000 2 S 2500 J S 2500 Qo oO 2 2 5 2000 3 2000 oO oO 8 1500 4 8 1500 o o gt 1000 gt 4000 500 4 500 0 2 i m r 0 r j i 7 7 7 0 100 200 300 400 500 600 0 100 200 300 400 500 600 Pixel number Pixel number a Spectrum without SLM b Sp
7. Therefore cylindrical lenses or mirrors should be used when the intensity of the laser is critical Usually there is a tradeoff as cylindrical lenses are more widely available but increase optical errors for shorter pulses whereas cylindrical mirrors are often not available in the required sizes It may also become necessary to increase the size of the beam to match the height of the pixels and then redesign the other components so that the focused width also fits the size of one pixel If the gratings are not used in a Littrow configuration the in fluence of the different angles on the beam diameter also needs to be included figure 4 4 Here a larger angle away from the grating normal results 4 2 Characteristics of the SLM device 24 in a smaller beam diameter light of constant blue wavelength light of constant red wavelength Figure 4 4 Width of spectral components of equal wavelength on the focusing element 4 2 Characteristics of the SLM device The SLM used in this project is a CRi SLM 640 D VN model It has 640 pixels in two masks for separate phase and amplitude modulation Its dimensions are 64x5mm whereas each pixel has a width of 100m and an interpixel gap of 2um It s polarizers are optimized for a wavelength range of 488 to 900nm The losses are given by Pr lt 6 plus coating losses of Ph coa lt 3 and polarizer losses of Pr po 25 leading to an overall transmission of a 68 Its pulse da
8. amplitude Position vector Time Imaginary unit Angular frequency w 271 f Wave number Transverse nabla operator Vr 2 gt Amplitude of electromagnetic wave Radius in cartesian coordinates p x y Rayleigh range Beam diameter Beam radius Phase retardance of wavefronts Wavelength Grating groove spacing Grating groove frequency Input angle at grating Output angle at grating Diffraction order Total number of illuminated grooves Grating resolving power Resolvable wavelength difference Blaze angle of ruled gratings Index of refraction Angle of light to refractive material Focal length Spherical mirror radius Electric field in frequency domain Electric field in time domain Transfer function Phase of electromagnetic wave III m x Big Cn rect Xl Width of spectral components on SLM Power Transmission Spatial mask pattern Filter coefficients for SLM Dirac function Rectangular function Difference of frequency components to center frequency Distance of mask to focal plane Spot size of beam IV Chapter 1 Introduction Ultrafast laser pulses in the femtosecond time domain have changed many existing and opened new fields since their invention in the 1980 s Improvements in the techniques of the used lasers and compression systems have resulted in the creation of pulses consisting of only a few femtoseconds or a few cycles of visible light Along with shorther pulses have come tec
9. and phase Using the Fourier transform the waveform after the SLM can be written as Eoul w 9 2 Ein Q m aQ 3 7 3 2 Design types 15 with the spatial profile g x of the input pulse the mask pattern m x Q w wzo and a the first order coefficient which relates a frequency component to its spatial position on the SLM The spatial mask filter m x can be written as a series of rectangular filters for pixels and gaps N 2 1 m x 6 a tp B 9 1 nw rect n N 2 By x n 5 rect E u 88 with the filters B y mask filter can be used to calculate the electric field after the SLM With two masks separated at an equal distance from the focal plane the electric field becomes for pixel n and gap g respectively The fourier transform of the 00 out t nN 00 cf A 2 2 2 25 A in t nT e 2 xe 3 9 with the coefficients c for pixel n here for both masks and an exponential term which incorportates spatial effects of the spot size a the distance of the masks from the focal cos Af plane Z and a factor x con Ba with parameters from the optical system WeN95 3 2 Design types The first design introduced used lenses and gratings along one optical line see figure 3 1 It allows an easy alignment procedure as there is only one height for the beam throughout the setup and distances can easily be measured Howev
10. e gf a Normalized transmissi es oe 2 a Sg ae o f i y i 7 y 500 1000 1800 2000 2600 3000 3600 4000 0 500 1000 1500 2000 2500 3000 3500 A000 Drive voltage 2 44mV Drive voltage 2 44 mV a b Figure 5 7 Transmission values and the calculated phase retardance of one mask with a calibration procedure with 1024 steps 5 2 Feedback with a genetic algorithm A feedback implementation for the pulse shaper was developed to demonstrate the capabilities of a feedback design and to see how it can be integrated into the program code First a suitable feedback parameter was required and a FROG measurement could not satisfy the needs of such a design as a measurement takes far too long about 15 minutes per single measurement and often needs to be recalibrated One option for the future could be a faster device such as the Grenouille FROG system which provides real time measurements We decided on a Spectrometer which is used for the optimization of the spectral amplitude This is related to the output pulse but as the phase is missing the pulse is not completely characterized However it can be used for certain purposes where only the amplitude of the pulse is required The Spectrometer is an OceanOptics HR2000 which provides a high resolution of 0 035nm FWHM It is connected to the PC via a USB connector and drivers for LabVIEW are provided which makes it easy to integrat
11. gt 2 304 Q lt 20 N 10 04 rt 300 400 500 600 700 800 900 1000 1100 1200 WAVELENGTH nm Figure 4 7 Efficiency curve for gratings Thorlabs GH13 18V Tho07 easier alignment of the input angle The design according to figure 3 4 was chosen over the setup depicted in figure 3 6 because of the larger size of the spherical mirrors which was required by the wide active width of the SLM compared to the proposed setup in PWA03 Due to the large diameter of the spherical mirrors large tilting angles for the grating and mirror would have been required with a subsequent increase in optical errors A possible solution is as the spectrum on the spherical mirror only spreads horizontally across the center axis to cut a hole in the spherical mirror This would allow us to send the input beam closely above the diffracted spectrum into the setup and decrease the required tilting angles of grating and mirror figure 4 8 Cutting a mirror is permanently and makes them not usable for other purposes This procedure is therefore only recommended for space critical applications however it provides the possibility to use very long focal lengths as well An overview of the components is given in table 4 2 The D shaped mirrors spherical mirrors cut in half replaced conventional round mir rors as folding mirrors because of their ability to keep the input beam and the diffracted beam close together especially when spherical mirrors wit
12. shows a measured mapping file As obvious the curve is only slightly nonlinear and a quadratic polynom was sufficient to interpolate between the different values 5 1 Labview program 37 2500 one pixel blocked ane pixel transmitting 2000 H 1500 Amplitude arb units E f 805 121 f do 785 790 795 800 wavelength nm Figure 5 3 Comparison of two different mapping procedures where one pixel in this case pixel 320 was switched either to transmitting or blocking state The reflective setup was used with a 3x beam expander 820 815 o O pare a o T T a 7 wavelength nm oO oO O SQ is 7 N a 7 aj O 0 100 200 30 400 50 60 Pixel number Figure 5 4 Measured pixel to wavelength mapping in the reflective pulse shaper setup 5 1 3 SLM response calibration tool The phase change for an applied voltage drive value is nonlinear and given by the supplier of the SLM For our device a graph is given in figure 5 5 which could be used for simple purposes However if more precise values are required a SLM specific calibration table is recommended Therefore a tool was developed which automated the calibration process by integrating a power meter into the LabVIEW enviroment Figure 5 6 shows the setup in the lab The program first sets one mask to its maximum drive value which equals approxi
13. t eat 3 1 which can be found at the Fourier plane before the SLM The SLM modulates amplitude and phase of the signal and can be represented by the linear transfer function H w A w A 3 2 with the amplitude modulation A w and the phase factor w Pour w Qinlw The shape of the output waveform in frequency is given by Evulw H w Ein w 3 3 which can be rewritten in time domain using the inverse Fourier transform but a different approach is to define the output waveform in time domain calculate the cor responding Eyu w and then calculate the transfer function using the measured input waveform The transfer function in frequency domain can be mapped to a function in space by a calibration procedure where the wavelength components impinging on the SLM are mapped to their respective pixels Also the connection of space to frequency has been studied theoretically by Wefers and Nelson WeN95 For an SLM with two masks having a perpendicular crystal axis alignment to each other a filter for one pixel n can be written as 1 B ei AP1 A9 cos 5 A A 3 4 This represents a filter for amplitude and phase and if we consider that when speaking of transmission usually the intensity and not the amplitude is meant a transmission function pa cos A0 _ Ady 3 5 and a phase function p 80 AB 3 6 can be calculated which allow a definition of an arbitrarily shaped pulse in amplitude
14. term of survival of the fittest Therefore the sum of all fitness factors is calculated and a probability for each chromosome calculated which relates its fitness to the overall fitness Then a cumulative probability for each chromosome is calculated whereas the last chromosome sums all probabilites and equals 1 A random value between 0 and 1 selects a chromosome for the new generation whereas higher probabilites increase the share of the space between 0 and 1 and therefore have a higher probability to be selected When this process is iterated pop_ size times a new generation has been se lected Apparently some fitter solutions can be selected more than once After that the solutions are being mixed in the crossover process Here individual equal parts of the chromosomes are exchanged An example of a crossover process is shown in figure 2 8 A randomly selected part of the parent solutions is exchanged and results in new offspring solutions Then the third step the mutation process selects random bits of the binary solution and swaps them A 0 turns to a 1 and a 1 to a 0 This process is important for the solutions to escape local minima An evaluation function with many local minima requires a high probability for a mutation process Genetic algorithms require the chromosomes to be binary coded Often a problem has to be modified so that the solutions are mapped to binary values to be suitable for a genetic algorith
15. the SLM is large enough all spectral components still pass through the crystal array However the quality of the reassembled beam is not as good as the one with a smaller beam diameter Therefore the input angle was changed to a slightly smaller angle than the dispersed spectrum so that it could pass next to the folding mirror on the same height The grating did not need to be tilted then which improved beam quality again The damage threshold of the SLM also had to be considered An average energy at the input of the SLM of about 500mW at a repetition rate of 80M Hz leads to an energy of 6 25nJ per pulse Focused to a height of 100um and spread to a width of 64mm this equals a fluence of 9724 which is far below the damage threshold With the MaiTai laser the SLM can be used without fear of destroying it For more powerful lasers however this value has to be recalculated 4 5 Upgrading for other laser systems As the laser source is exchanged the setup usually has to be reconfigured Most im portantly is the width of the pulse where a shorter pulse relates to a broader spectrum due to the uncertainity principle A broader spectrum can be diffracted wider which results in either a shorter distance or a grating with a lower groove frequency which makes the choice of the components in general easier A second laser system was available which contains a SpectraPhysics Tsunami a Ti Sapphire laser pumped by a solid state laser genera
16. 6 6 o ee 4 2 Characteristics of the SLM device 2 2 2 2 nn nn nennen 4 3 Lens Setup r sr A Bor 4 A 4 4 Spherical mirror SUP 4 5 Upgrading for other laser systems 2 2 2282 28 ee ee ee o o Nn 00 wo aw 11 13 13 15 19 19 CONTENTS II 5 Program control 33 5 1 Labview program goaa bana on 33 5 1 1 Control panel 2 2 0 0 0 020020000000 eee 34 5 1 2 Mapping tool 0 0 02 0 002 eee 36 5 1 3 SLM response calibration tool 2 22 2222 nn nn 37 5 2 Feedback with a genetic algorithm 2 2 2 220 22 0 0208 39 6 Experimental results 42 6 1 Spectral shaping of a rect function o 42 6 2 Feedback sh ping o pea ad AER ar 43 6 3 Shaping in time domain terra a Se eg 44 7 Summary 48 7 1 Improvements for the present pulse shaper 48 T2 F ture work gita Fata 2 22 a e Eee er 49 A Appendix 50 A 1 Alignment procedure for a lens setup 2 2 22 22 nn nn nn 50 A 2 Alignment procedure for a reflective setup 51 A 3 Performance curves of used materials 2 2 2 2 nn nn 53 A 4 Manual for the control program eo pra as og ae ern a 53 A 5 Manual for the mapping program 2 2 2 nn nn nn 54 A 6 Manual for the SLM response calibration program 55 Anh ange Bibliography 57 List of Symbols gt a E E A lt Pag Bk Qe See Ses gt Vblaze Rsm Nabla operator V 2 gt 2 Speed of light Wave
17. LINCE HELMUT SCHMIDT UNIVERSITAT Universit t der Bundeswehr Hamburg Johannes Hallier Design of an ultrafast laser pulse shaper using a spatial light modulator and evolutionary strategies 2 Fachbereich Elektrotechnik Laser Engineering and Materials Science Univ Prof Dr rer nat Hermann Harde Helmut Schmidt University University of the Federal Armed Forces Hamburg Postfach 70 08 22 22008 Hamburg Telefon 040 6541 2147 Telefax 040 6541 3764 Email harde hsu hh de Internet http www hsu hh de laser Erkl rung Hiermit erkl re ich Johannes Hallier Matr Nr 793090 dass ich die vorliegende Diplomarbeit selbst ndig ohne fremde Hilfe ange fertigt habe und keine anderen Quellen als die angegebenen verwendet habe Hanover den 28 02 2007 CONTENTS Contents 1 Introduction 2 Fundamental principles Ded OPTICS an a e nin Mons Gh E 3E Zo Lal BeamcOptics a it an pa de me 2 1 2 Diffraction Crating A EE 23 EOS 3 4 aar A e A A re 2 14 Spherical MIO La ri iii ad ee a dk A 2 2 Spatial Light Modulator Silao rata al A ti OG 23 GeneticalgorithmMS ses ea ar di in e Pulse Shaping 3 1 Principle of Fourier transform pulse shaping 3 23 DESTE DOS a ee ee ne eda bs ONG aud all aca arcane ng 3 3 Measurement of ultrashort pulses 22 2 m nn nn 3 4 Feedback design 4 4 259 era bod Pre Daran Design and setup 4 1 Design parameters and criteria 2 40
18. Mapping tool In order to precisely assign wavelengths to pixel values after the setup of the SLM a mapping calibration needs to be carried out Using an idea found in Hof06 a single pixel is switched to active state and a dip is visible in the output spectrum as the corresponding frequency component is blocked Measuring the wavelength of the amplitude dip for several pixel values and interpolating between those values with a linear or polynomial function a precise calibration can be made which can be used for all measurements as long as the optical components are not moved away from their original position The resulting mapping can therefore be stored in a file which can be loaded directly in the control program A slightly different approach would be to switch only one pixel to the transmission state such that the assembled beam consists only of one sharp frequency peak This has the advantage that the calibration process could be automated if the spectrum is taken and loaded into LabVIEW automatically Finding the peak in the data returns the wavelength of the pixel that was set to transmission However we found that the energy especially of the sidebands was too weak to allow a calibration with this procedure Figure 5 3 shows two measured spectra with both techniques It is obvious that the dip is much clearer than the single peak Moving closer to a sideband makes this even more dramatic and a calibration becomes impossible Figure 5 4
19. The FROG measurement was a little more complicated First the reduced power caused problems when the peak of the second harmonic beam was searched for Also more data points became necessary due to the longer pulse width When loaded into the FROG phase and amplitude retrieval program a lot of datapoints were necessary to have a comparatively low error As the results figure 6 9 show the desired time domain pulse could not be obtained One of the possible reasons is the lack of higher frequency components as only two sidelobes were considered For a comparison a superposition of a sin x function and the two higher order harmonics sin 3x and sin 5x is shown in figure 6 10 It is obvious that more frequency components are necessary to shape a rect in time A shorter broader input pulse is much better suitable for this purpose than the input used Also the error from the FROG program was not very low It is doubtable that this shape has the least error but since calculation 6 3 Shaping in time domain 47 Voltage drive value 0 100 200 4300 400 50 600 Pixel number Figure 6 8 Voltage drive value pattern for the master mask blue and the slave mask green for a sinc function requires a lot of time for a complex pulse the calculation had to be stopped some time e e o gt o T T T Normalized Amplitude o N T L00 400 200 0 200 400 600 time fs Figure 6 9 Measured amplitude of
20. The program requires to measure a spectrum beforehand and to define a desired out put waveform based on the same wavelength vector as the measured spectrum It then uses the calibration and mapping values to calculate the pattern for the two masks of the SLM First a spectrum was used that was measured without the SLM inserted Figure 6 1 shows the result It is obvious that the output waveform has approximately the same sharp sidebands as the desired rect function but the amplitude is not uni form which is due to effects of the SLM such as pixelation or interpixel gaps Also the total number of measurement points for the amplitude is less than the number of SLM pixels since the spectrum is very narrow Therefore a precise mapping is not possible instead an interpolation procedure should be used Additionally we tried to improve the results by using the spectrum measured after the SLM as an input function for the program As one can see the results are not much better but the average of the values seems to be more uniform than in the first measurement The patterns with the pixel voltage drive values look similar figure 6 3 The second pattern is a little noisier as it tries to compensate for the input spectrum Also obvious is that since the spectral modulation is a pure Amplitude modulation some drive values are zero which means a large phase shift that is neglected here 6 2 Feedback shaping 43 Input
21. Therefore the surface of a grating is made of small grooves each of them having the same angle to the grating plane Figure 2 2 shows the principle of a grating with an incident beam and a reflected beam at angle a and 3 respectively The reflected beam of angle 8 shows constructive interference if two components from different grooves of the grating have a difference in wavelength of Using the relations A sin a a 2 15 Ad sin 8 a 2 16 2 1 Optics 6 a Definitions on a grating b Wavefront interference Figure 2 2 Principle of a diffraction grating and the groove frequency G 4 yields the grating equation sin 8 sin a mG 2 17 Typical gratings are produced by either cutting the surface pattern ruled gratings or using holographic procedures where the pattern becomes sinusoidal resulting interfer ence pattern from two laser beams A coating for specific wavelengths can be applied in order to increase the efficiency due to higher reflectivity as gold is more suitable than Aluminum for infrared applications for example Usually one wants to use the grating in one specific diffraction order m only e g m 1 and the efficiency should be as high as possible for this specific order By differentiating the grating equation the angular dispersion _ mG cos B can be obtained which is proportional to the groove frequency Another important 2 18 parameter is the resol
22. a desired rectangular function in time domain sin x 1 3 sin 3 x 1 5 sin 5 x Figure 6 10 A superposition of only 3 frequency components does not result in a rect function Therefore more higher order components are necessary Chapter 7 Summary In this work an ultrafast pulse shaper based on a spatial light modulator was devel oped A software for a flexible use based on the LabVIEW program has been created Together with the hardware the pulse shaper has proven to be capable of creating arbitrily shaped pulses although a lot of considerations need to be taken if more com plicated waveforms need to be shaped An easy function in time domain is often much more complicated in frequency domain where pulse shaping takes place The funda mentals for a feedback design have been proposed and integrated into the setup The algorithm has proven to work but it certainly needs improvements for better results 7 1 Improvements for the present pulse shaper For the device built several potential upgrades have been proposed in this work On the side of the optical components cylindrical mirrors or lenses would allow to use higher power lasers A different setup could be used for more space critical applica tions If a higher phase modulation is required a reflective design as proposed would help The software can be improved in the feedback design with the genetic algorithm Here more sophisticated techniques for evoluti
23. aining horizontally polarized components 2 3 Genetic algorithms 11 leave the crystal and eliminates the vertically polarized part of the beam If the light is completely shifted to vertical polarization the transmission will drop to zero In between any value can be adjusted Tys00 Figure 2 7 shows a SLM with a phase and an amplitude mask dual mode The device can also be used in reflection mode if a mirror is attached after the second mask However going through the mask two times any effect on the beam will be doubled which allows higher phase modulation rates 2 3 Genetic algorithms Optimization problems in complex systems are sometimes hard to handle if almost no information is present about how a change of a parameter influences the solution Comparable to the natural selection process in nature where the genetic parameters change over generations to adopt best to the natural conditions Therefore the param eters that influence the solution are sometimes called chromosomes An initial set of chromosomes is created and serves as start solutions which are used to calculate the optimizing function which is also called fitness function or evaluation functon as it describes how well the chromosomes adopt to their enviroment The fitness factor which is higher for better solutions is used for the next step the selection Here the fittest of the solutions are being selected which can be compared to the misleading
24. an also be important if a particular pattern is known and has to be uploaded The definition of the output pulse is the most useful function if the pulse shape required by an application is known Therefore the time domain data which is a measurement taken before the pulse shaper for the input pulse and a defined output pulse given in a text file format are read into the program Using a Matlab script the FFT is calculated As the spectrum is centered around zero it is shifted by the center wavelength of the input pulse which has to be entered by the user A zero padding procedure is used to increase the number of datapoints of the spectrum and the interesting spectral parts in a user defined range are extracted for further calculations Theoretically a division of the output spectrum by the input spectrum yields the transfer function for amplitude and space as described in section 3 1 Practically if both functions are normalized to 1 a larger spectral amplitude value of some components of the output pulse would require a gain which the pulse shaper cannot provide Picture 5 2 shows the influence of not adapting the whole desired waveform Parts of the spectrum might be modulated as desired but others are not and the whole pulse becomes distorted A better solution is to modify the waveform in the calculations beforehand which requires wasting energy of attenuated components Nevertheless it maintains the shape of the outgoing waveform T
25. anged at this point Initially power measurements showed that the output beam was very weak The rea son for that was a change in the polarization of the laser due to a Faraday rotator which was used to prevent damage from light reflected back into the laser The grat ings however are polarization dependent The efficiency curve for the used grating is shown in figure 4 7 It is obvious that for the center wavelength of 800nm the efficiency is highest in the S plane which is the horizontal polarization Therefore a polarization 4 4 Spherical mirror setup 26 SLM A higher beam level mirror polarization a rotator NS lower beam level N Figure 4 5 Drawing of the setup with lenses along an optical axis beam steerer rotator had to be inserted to maximize the output power after the second grating Initially the beam was diverging too much after the setup which made it almost impossible to perform a FROG measurement to characterize the temporal properties of the pulse Two plano convex lenses separated by two focal lengths which if one lens is moved a little bit off focus can collimate the beam were used to improve the results It is necessary to have a collimated beam at the input as the two lenses in the pulse shaper cannot be used to compensate for this effect The pulses could be measured despite the low power and poor collimation Nevertheless the setup was far from being optimized and the calibr
26. ation never returned the proper results Therefore we decided to change to a setup with reflective optics 4 4 Spherical mirror setup As mentioned earlier reflective optics are preferred for ultrafast pulses as they reduce dispersive effects Additionally a reflective setup is in general more compact than a lens setup since folding mirrors can be used which allows for a reduction in the total length of a pulse shaper by at least a factor of 2 compared to a 4f lens setup as shown in figure 3 1 As space issues are especially a problem for our wider 640 pixel SLM which requires longer focal lengths a reflective setup became necessary Spherical mirrors with a more than double focal length compared to the lens setup were chosen which allowed a higher flexibility and over all better performance The setup can be used in a Littrow configuration increasing total power throughput and allowing for an 4 4 Spherical mirror setup 27 beam steerer _ a I rotator Cm in f 7 I a gt 7 sy ES Figure 4 6 Picture of the setup with one optical axis The beam path is highlighted in red for a better illustration 4 4 Spherical mirror setup 28 1800 GROOVES MM OPTIMIZED FOR THE VISIBLE 100 5 90 s 4 a AVG 80 g Hh gt 104 2 res G 60 A 9 17 i 504 wi i a u H 5 SA E Ba
27. ations They include the following functions e Initialize Returns important data from the SLM device such as number of pixels or number of masks e Mask Select Chooses which mask in a dual mask system should be used to write the frame pattern to e Define Pixel Sets a pixel in the selected frame to a defined drive value e Read Pixel Returns pixel drive value http www mathworks com products matlab http www labview com labview 5 1 Labview program 34 e Save Frame Writes a whole array of values for all pixels into the selected frame e Read Frame Returns the array values e Select Frame Changes the currently used frame e Cycle Changes the active frame to the next available frame which are all necessary for enabling all of the SLM functions The functionality of the Pulse Shaper should include the capability of reading defined patterns but especially the definition of a desired output waveform was necessary Also the potential to include a feedback design was desired The program was therefore structured into a main control panel and two SubVIs for calibration purposes 5 1 1 Control panel The control panel should include all functions necessary to use the pulse shaper The flowchart on figure 5 1 shows its main functionality not availabl i Figure 5 1 Flowchart of the SLM control program 5 1 Labview program 35 Loading a pattern is essential for testing the main functionality and it c
28. considered as their dispersion efficiency varies with different types and they should be most efficient at the design wavelength and match the input polarizers of the SLM device Therefore the grating is the first component to be selected as it is the most critical of all for a high quality setup Following the grating a lens or spherical mirror with a specific focal length has to be chosen Achromatic lenses which reduce chromatic aberration and antireflection coatings for higher transmission rates are preferred Spherical mirrors should have gold or silver coatings for a higher reflectivity To find suitable focal lengths for the lenses or mirrors a program was written to calculate the incident angle fitting the parameters focal length spectral width and LCM width as these parameters define the deviation in the angles for the two wavelenghts Figure 4 2 shows how the different design parameters are connected to each other geometrically The angle which the lowest wavelength of the spectrum is diffracted to can be calculated as Bt Bm arctan 4 1 with w w wp as the width of the spectrum Calculating the deviation of the two angles 3 Gy a common incident angle for both can be found Ideally a near Littrow configuration is used which can be found by trying different focal lengths available from the optic manufacturers The tuning parameter to find a Littrow angle is usually the spectral width for which small varia
29. d a calculated pattern that is already close to the right solution This solution in general has a high fitness factor and if it is implemented correctly can serve to find an optimum solution much faster If only these values were taken as a first generation however the algo rithm might stop in a minimum which it could not escape from The diversity of start solutions is important to find the optimum solution faster 5 2 Feedback with a genetic algorithm 41 Algorithm 2 Genetic algorithm with feedback parameter 1 Calculate random first generation 2 while Fitness factor lt Required accuracy do 3 10 4 5 6 T 8 9 for i 1 to size of population do Upload new chromosome to the SLM and measure feedback end for Evaluate solutions with a fitness function Select a new generation by weighted fitness Select solutions for crossover according to Pross Crossover Mutation according to Put 11 end while Chapter 6 Experimental results In order to show the capability of the pulse shaper to generate arbitrarily shaped pulses some examples representing different applications have been performed 6 1 Spectral shaping of a rect function For testing of the spectral shaping program a rectangular function was chosen to be shaped since it is a comparatively easy waveform Spectral shaping can be interesting when information is transmitted in the spectrum of the pulse such as in optical com munication
30. d a desired waveform which should be based on the same wavelength vector than the spectrometer which is used as a feedback parameter uses Select a population size in one generation number of chro mosomes and the probabilites for crossover and mutation In the upper right corner enter an integration time for the spectrometer If the measurement shows saturation reduce this value Also enter a left and right cut off wavelength for the measurement to have a better range for visualization of the results Click on Optimize and the algorithm starts The actual measured solution is visible on the graph on the right Left to the graph is the status of the algorithm that is the number of the present generation the solution that is being examined and a graph of the last fitness factors Also a start solution can be used Push the slide button to Use and enter the filename of the pattern which serves as a start solution This can be stored in the Spectral shaping program A 5 Manual for the mapping program 1 Measure the output spectrum of the assembled beam with a spectrometer 2 Choose a calibration vector and a smoothing function For a polynomial function choose its order too 3 Click calibrate The program will turn individual pixels to its dark state and prompt for the corresponding transmission value Enter the value from the spec trometer program with the large amplitude dip 4 After finishing the calibration the val
31. e distance from the beam to the folding mirror can be examined Also a card in the Fourier plane can be used to check for uniform attenuation like in the lens setup For the femtosecond alignment vary the distance of the gratings to the folding mirrors and measure the beam in time domain until it is as short as it was entering the setup A 3 Performance curves of used materials 53 Pulse Shaper Control Panel E Mapping function SLM response Maski SLM response Mask2 SLM Initialization and Calibration VISA Resource Name dualfsingle oF pixels O suis El jo Load mapping Mapping Tool single OPEN e IN e a i 7 3 E T le SLMresponse tool Load Frame Pattern Tie domain shaping Spectral domain shaping Feedback optimization Pal O amplitude Input Amplitude Input a al Load o Phase Input Phase Input Pulse time time o 3 Lsignals Amplitude Output Amplitude Output Time properties py Phase Output z Spectral properties Phase Output pasren nm 1 de o Lower wavelength nm Right wavelength nm o Le 6 4 2 UE 800 600 400 200 0 200 400 600 800 Figure A 1 Screenshot of the control program with the register for shaping of a time domain pulse opened A 3 Performance curves of used materials A 4 Manual for the control program 1 Choose the device in the VISA Resource field name is related to the COM port it is con
32. e pz according to Snell s Law n sin Y1 na sin pa 2 20 Concave lenses spread light whereas convex lenses collect and focus light The latter can be made of two convex surfaces but combinations of planar and convex surfaces are also available which reduce the angle of the surface to light entering the lens and therefore minimizing optical errors Parallel light entering a convex lens will be focused at the focal point and ideally having a zero diameter figure 2 3 However using a laser beam under the paraxial approximations of section 2 1 1 the beam diameter at the focal point will not be zero but finite Assuming a well collimated beam with zo gt f the beam focuses at the focal length f with a radius A Wi 2 21 nn 2 21 Simple singlet lenses are usually designed for monochromatic light However the refractive index of a medium is usually wavelength dependent Different wavelength 2 1 Optics 8 components will be refracted to different angles in the medium leading to beam di vergence and spatial errors This phenomenon is called chromatic aberration and can be reduced by using a lens of different materials A so called achromatic doublet has two materials whereas the second one compensates for errors of the first and keeps the wavelength components closely together around the focal point of the lens Therefore optical errors will be reduced 2 1 4 Spherical mirror Comparable to convex lenses sph
33. e it into the control program First a data structure for the chromosomes had to be chosen As a genetic algorithm 3http www swampoptics com products_ grenoverview htm http www oceanoptics com products hr2000 asp 5 2 Feedback with a genetic algorithm 40 works with binary variables a long vector of bit values was used which contains 12 bits as a drive voltage for each pixel altogether 640 pixels and this for both masks in the SLM This adds up to a total of 15360 bits for each chromosome Together with the whole population of one generation this was stored in a matrix as shown in figure 5 8 2 masks ee A A ee A a en 640 pixels 12 bit each pixel OOO population 1 10110110001 NI 2 1010010111 0 0 MOMENT n 11000111100 o Figure 5 8 Data structure for the chromosomes of the genetic algorithm Each pattern is stored in one array and each chromosome forms one line of a matrix which stores one population The start solutions were uploaded to the SLM and a spectrometer measures the spec trum The spectrum needs to be processed as it has constant background noise added which needs to be substracted Then the fitness function was applied and a fitness value calculated Through the steps of selection crossover and mutation a new gen eration was created The fitness factors were recorded and shown on a graph so that the progress was visible After starting with random values we implemented a function to loa
34. each different laser source The width of the spectral components at the SLM was calculated to be 397um for a beam radius wo 1 2mm and a wavelength A 820nm This is 4 times higher than the width of a pixel When the SLM is used and only one pixel is switched to its dark state the decrease in intensity for the corresponding wavelength is only very weak which shows that each frequency component is spread over several pixels and then transmitted as well although some of its central peak power is reduced For this a beam diameter of 1 2mm and the highest available wavelength component of 820nm has been used Therefore a larger beam diameter is necessary A magnification of at 4 4 Spherical mirror setup 30 27 Polarization gt 8 rotator a T _ gt Spherical mirror Figure 4 9 Picture of the setup with spherical mirrors 4 5 Upgrading for other laser systems 31 least a factor of 3 if the wavelengths are considered is necessary A larger magnifi cation would be even better for suppressing the influence of wavelength components on neighboring pixels on the SLM In the lab a beam expander with a magnification of 3 was available and used to check if the results were any better The alignment of the setup becomes more difficult as the bigger beam diameter requires a larger separation between the incoming beam and the folding mirror resulting in a spectral tilt in the Fourier Plane As the active area of
35. ectrum with SLM Figure 6 3 Voltage drive values for both input spectra from theory This is stored in a file and can be read in the feedback program Then it serves as the first solution to use for the first generation the rest of the population is created as a random bit string For the feedback an algorithm calculates the difference between the measured and the desired spectrum in every pixel squares these values and sums them up This serves as a fitness factor in this case the lower the value the better the function Therefore not the highest fitness value but the lowest was to be looked for The probabilites are calculated for each chromosome with the fitness factor but then inverted so that lower fitness factors receive a higher chance of being selected After a renormalization of the probabilites the algorithm was started By the time of several generations the one start solution dominated the selection process The fitness factors finally varied between two values see figure 6 4 which is supposed to be a storing error in the program A better pulse shape than the calculated one was not obtained This was maybe also due to another problem that both arrays measurement and desired spectrum have been normalized Since the maximum value is one only a few single peaks cause the average spectrum to be much lower than the desired spectrum and the function can not approach the optimum from both sides This is believed to be the maj
36. er the setup is comparatively large and the lenses may cause problems for ultrashort pulses the shorter the pulse duration the less suitable lenses are as they introduce chromatic errors and cubic phase dispersion and therefore broaden the pulse As a better solution setups with reflective optics especially concave cylindrical mirrors were introduced First there is the possibility to reflect light directly from the grating onto the mirror but the distance between both components needs to equal one focal length which requires the grating to be positioned next to the SLM as there is no more space for the mount see figure 3 3 Therefore a large tilting angle of the mirror is necessary but this comes with off axis aberrations This design type has been tested with a high resolution SLM SHF01 To reduce these errors and therefore to keep the angles small a folding mirror is required which is possible because the spectrum only expands in one dimension Spectrum and beam can be separated at close distance and the tilt of the mirror does not have to exceed more than 1 to 2 degrees to the optical axis 3 2 Design types 16 Figure 3 1 4f setup with lenses as focusing elements SLM folding mirror Uy N Figure 3 2 Lens setup with folding mirrors with the two mirrors and the SLM This setup only requires two focal lengths in one direction which halves the dimensions of the lens setup figure 3 4 However a ti
37. erical mirrors collect light from one source and focus it on a specific point depending on the radius of the mirror gt 2 22 which is valid under the paraxial approximation KIF86 In contrast to lenses the incoming light does not travel through the medium in case of metallic front surface mirrors and therefore chromatic errors due to a different diffraction of spectral com ponents do not occur These errors have a large influence on pulses of less than 100 fs FWHM full width half maximum Achromatic lenses do not significantly reduce the errors as they introduce CPD cubic phase dispersion which also broadens the pulse RWL92 Therefore the use of mirrors instead of lenses is preferred for a flexible setup suitable for short pulses Spherical mirrors however are not free from errors f gt gt Figure 2 4 Spherical mirror The perfect shape of a concave mirror is paraboloidal whereas parallel light will be perfectly focused to a single point A spherical mirror is easier to produce but does not focus parallel light perfectly However using the paraxial approximation 2 6 a spherical mirror is a paraboloid reflector to first order The angles between incoming and outgoing light should be small to avoid off axis aberrations 2 2 Spatial Light Modulator 9 Unpolarized Light Unpolarized Light Ad xen YA Electrodes Yoltage on NT gt gt aai a a mc No Light
38. es a smaller part of the most important parts of the spectrum concerning the energy A cut off criterion is the simplest solution to choose as only those parts of the spectrum with intensities of more than 2 or 3 of the maximum value contribute enough to be considered important for the shaping of the pulse Figure 4 1 shows a spectrum of a pulse from the MaiTai laser recorded directly after the laser output In this example a reasonable wavelength range choice could be from 780 820 nm in order not to lose any important components and to guarantee a high resolution as well After choosing a wavelength range the grating equation is solved to calculate the diffracted angles for the cut off wavelengths To do so the groove frequency of the grating has to be chosen In general a higher groove frequency has a higher diffraction efficiency which leads to a shorter distance for spreading the spectrum to the required http www newport com Mai Tai One Box TiSapphire Lasers 368124 1033 catalog aspx 4 1 Design parameters and criteria 22 Amplitude 0 1 1 770 780 790 800 810 820 830 wavelength nm Figure 4 1 Measured spectrum of an unshaped pulse of the MaiTai laser width In general the choice of the grating is not an easy task as there are only a few gratings with high groove frequencies suitable for wavelengths around the center frequency of our laser Also the efficieny curves of the gratings have to be
39. f the Fourier transform pulse shapers and their different implementations 3 1 Principle of Fourier transform pulse shaping The most common implementation of a Fourier transform pulse shaper also called the 4f setup consists of 4 optical components each of them separated by the focal length of a focussing component such as lenses or spherical mirrors The input pulse is spatially dispersed by a reflection grating which is placed one focal length from a lens or a spherical mirror The single frequency components will then propagate parallel to each other as long as the input beam is perfectly collimated does not diverge significantly and the distances precisely equal the focal length f Another distance f away the frequency components will show their minimum beam waist ac cording to the lens equation 2 21 Here the wave components can be attenuated and retarded in order to change their amplitude and phase Therefore an SLM device an Acousto Optic Modulator AOM Wei00 or a fixed mask pattern is used which is 3 1 Principle of Fourier transform pulse shaping 14 also suitable for micro fabricated devices Thu86 One focal length further the second lens or spherical mirror focuses the beam onto the second grating which if all angles are symmetric assembles the outgoing beam Wei00 Mathematically such a pulse shaper can be described using the Fourier transform of the input pulse in time domain e t co Ein w ein
40. h f 20cm were used The required tilting angles caused COMA but the biggest problem was the vertical tilt of the spectrum in the Fourier plane Although this is an inevitable systematic error it can be minimized with the D shaped or rectangular mirrors An alignment procedure can be found in the appendix The first measurements were taken with a 1800428 grat ing but later replaced with a 2000 es grating The first gratings allowed a Littrow configuration at 45 for both the input and the output angle with a spectral width from 773 to 827 nm and therefore a shorter width of the necessary parts of the spectrum 4 4 Spherical mirror setup 29 Figure 4 8 A hole in the mirror allows the beam to enter the setup at close proximity to the dispersed spectrum Component Part number Technical data Diffraction grating Newport 10HG2000 475 1 holographic reflective 25mm G 2000 Spherical mirror Edmund Optics NT32 831 d 76 2mm f 457 2mm Au coating Folding mirrors Thorlabs PDF10 03 M01 D shaped mirror surface flatness Au coating Polarization rotator Newport PR 950 700 1200 nm 10mm clear aperture Table 4 2 Components used for the spherical mirror setup This could be solved by using the higher resolution gratings where the spectrum is spread from 779 to 821nm at an angle of 53 resulting in a higher resolution for the pulse shaper This shows the necessity of carefully choosing the components for
41. he width of a pixel The phase change as a function of voltage is nonlinear and is usually given 2 2 Spatial Light Modulator 10 Figure 2 6 Liquid crystals for phase modulation In idle state the crystals are aligned along axis y After applying a voltage across the length z the crystals tilt and cause a change in the refractive index for y polarized light WLP92 in the documentation of a SLM or can be measured liquid crystal cell B liquid crystal cell A 4 Polarizer selects horizontal polarization component 3 Average retardance A B 2 modulates phase entrance polarizer 2 Differential retardance A B alters polarization state 1 Input beam becomes horizontally polarized Figure 2 7 Phase and Amplitude Modulation in a SLM in transmission mode Cam04 An amplitude modulator uses nematic crystals which have the property to be naturally aligned in one direction with little variation over different molecules This direction is called the director The incoming light is horizontally polarized with an entrance polarizer When passing through the crystals the beam changes its polarization as the crystals change the orientation of their director figure 2 5 a If the structure was created such that the directors rotate by 90 over the length of the modulator the light would experience a shift from horizontal to vertical polarization After the crystals an exit polarizer ensures that only the rem
42. his is implemented by attenuating the whole waveform so that the output spectrum contains no higher amplitude value than its equivalent in the input spectrum Then the calibration values where a specific wavelength is mapped to each pixel are a b c Figure 5 2 Effects of normalization to the available spectral amplitudes a Available spectrum black with desired spectral waveform dashed red b Without normal ization maximum power but desired waveform is falsified c Attenuated amplitude allows to shape desired waveform used to find the wavelengths in the input and output spectrum array that are closest to each pixel value An interpolation could also be used for a higher accuracy but does not seem to be necessary The input and output values yield a transmission and phase value for each pixel on the SLM see 1 Using the SLM calibration values see 5 1 Labview program 36 subsection 5 1 3 a drive value is stored for the amplitude and for the phase mask respectively Algorithm 1 Pattern calculation algorithm for waveform shaping 1 for i 1 to number of pixels do 2 calculate index j for which input _ wavelength j is closest to pixel_ wavelength i 3 calculate index k for which output _wavelength j is closest to pixel_ wavelength i 4 Transmission i Output_amplitude j Input_amplitude k 5 Phase i Output_ phase j Input _ phase k 6 end for 5 1 2
43. hniques to modulate its amplitude and phase Possible applications have appeared in the field of optical communication or in the control of chemical reactions also called femtocontrol For communication purposes an arbi trarily shaped femtosecond pulse can be used to carry data modulated with WDM or CDMA techniques which have in common that the desired shape of the pulse is known before sending it through the pulse shaper ShG02 For femtocontrol experiments this is usually not the case Here a feedback param eter from the experiment can serve as an indicator for the suitability of the used pulse By using genetic algorithms the shaping parameters can be optimized to find the best solution This is necessary because the systems are too complex to be described by a model that could help to find the best solutions Then studying the optimum solu tion leads to a deeper understanding of innerlying effects in molecular reactions Lup04 In this work a pulse shaper was developed that needed to be as flexible as possible as potential requirements for different experiments may vary from time to time There fore a control program was written which allows to shape a pulse in time domain in frequency domain and also to integrate a feedback parameter for a genetic algorithm which is a very flexible solution since only the measurement of the feedback parameter needs to be changed and integrated into the control program For the calibration
44. ing mirror before the first grating to match the required input angle 6 Place the second grating one focal length after the second lens and turn it to a symmetric position to the first grating 7 Redirect the laser beam onto the steering mirror which needs to be rotated to project the beam at the center of the first grating Check the beam height before and after the steering mirror and make sure it is parallel to the optical table at its defined height 8 Observe the dispersed and the reflected beam order 0 and 1 of the grating tilt the grating iteratively for both beams traveling parallel to the table 50 A 2 Alignment procedure for a reflective setup 51 9 Observe the spectrum on the first lens and make sure it is centered by tuning the grating angle over a small range 10 The spectrum should focus at the Fourier Plane and also be centered at the second lens 11 Tilt the second grating for a parallel beam similarly to the first one 12 The outgoing beam should be reassembled at the same angle as the beam impinges on the first grating To make sure the angle is correct the beam can be examined in the far field and a card can be sweeped through the dispersed components in the Fourier plane If no spatial errors are present the beam should be uniformly attentuated when some frequency components are blocked Otherwise an image of the card travels through the assembled beam Optimize the result by precisely r
45. irror The folding mirrors reflect the whole width of the spectrum and need to be larger The advantage is that the large width of the whole SLM is completely used for the distance between gratings and focusing mirrors This setup therefore is extremely compact figure 3 6 Another possibility to reduce the need of two focal lengths with a reflective folding design is the use of a mirror immediately after the SLM The spectrum is reflected and passes twice through the SLM which also doubles the amplitude and phase modulation A slight tilt of the reflecting mirror needs to be introduced to be able to spatially separate the incoming and outgoing beam after the grating which is now used for dispersion and assembly of the beam also see figure 3 5 3 3 Measurement of ultrashort pulses 19 3 3 Measurement of ultrashort pulses Laser pulses have originally been measured with photo diodes but their integration time limits their applicability to lengths in the picosecond domain ps Shorter pulses require autocorrelation techniques such as the Frequency Resolved Optical Gating FROG The pulse is divided into a reference pulse and a delayed version of itself which are both focused on a nonlinear crystal Here nonlinear effects cause a multi plication of both pulses resulting in a pulse with doubled frequency This frequency measured with a spectrometer is a result of a second harmonic effect giving the de vice its name Second Harmonic
46. lt of the gratings and of the folding mirrors are necessary as the beams are situated in two planes the one for the incoming beam which enters above the first mirror which is also the height of the beam between the two focusing mirrors and a lower level at the folding mirror Therefore the spectrum is deflected downward from the grating to the folding mirror and then reflected upwards to the focusing mirror Folding mirrors can also be used with lens setups in order to build a more compact design However they need to be larger as the full width of the diffracted pulse will be folded see figure 3 2 Such a design has been used in an earlier work for a pulse shaper in an amplifying system Fet99 Another variation was presented in PWA03 Here one focal length determines the 3 2 Design types 17 gt f SLM f lt gt lt gt Figure 3 3 Reflective setup with spherical mirrors as focusing elements Figure 3 4 Reflective setup with folding mirrors to increase grating efficiency and reduce optical errors 3 2 Design types 18 separating mirror Figure 3 5 A tilt of a mirror immediately after the SLM can separate the incoming beam blue from the outgoing beam red Figure 3 6 Compact reflective setup with high mechanical precision PWA03 length of the setup which is the distance from the grating to the folding m
47. m The choice of a suitable coding method is very important In 2 3 Genetic algorithms 12 parents OI offsprings HAMM 0 o 01011001101110 Figure 2 8 The crossover process in Genetic Algorithms Here two parts of the parents solutions red and yellow are broken out and exchanged to generate offspring solutions The remaining solution is unchanged difference to that evolutionary programs do not change the coding but instead apply suitable operators to the parameters Mic96 Chapter 3 Pulse Shaping Femtosecond pulse shaping usually describes the complete arbitrary manipulation of amplitude and phase of an ultrashort laser pulse limited by the available bandwidth power and resolution of the used components Today there exist direct and indirect techniques The first ones modulate a pulse in space and shape the pulse in the time do main whereas the latter use the Fourier transform to modulate pulses in the frequency domain Direct space to time techniques for example use a mask and slit apparatus to generate pulse trains that can be used in optical communications or other applications LeW01 Indirect techniques work in the Fourier domain where the single frequency components of an ultrafast pulse are spatially separated from each other A modulation of the amplitude and phase in the frequency domain results in a pulse in time domain determined by its inverse Fourier transform This chapter describes the fundamentals o
48. m close to the folding mirror and onto the grating Make sure the spectrum diffracts parallel to the optical table Turn the grating so that it is centered on the folding mirror which can be seen with an IR viewer The height of the folding mirror can be adjusted such that no spectral components are lost a dip in upper region of the reflected spectrum However the height should not be unnecessary high to avoid large tilting angles Rotate the folding mirror so that the diffracted spectrum is centered on the spherical mirror The height has to equal the height of the beam in the focal plane which is also the height of the center of the spherical mirror Tilt the spherical mirror vertically to make sure that the spectrum is parallel to the optical table and on the correct height in the Fourier plane Rotate it so that the spectrum is centered on the second mirror IR viewer Tilt the second mirror such that the spectrum fits onto the second folding mirror Observe the diffracted spectrum from the second folding mirror and make sure it is parallel to the optical table and at the correct height If not adjust height by tilting the second spherical mirror and the folding mirror iteratively Place the second grating at its defined position and tilt it so the O order and l order beams are on their correct height and parallel to the table The outgoing angle should now be the same as the input angle which means th
49. mage threshold is given with 20044 at 890nm for a 50 fs pulse at a repetition rate of 1kHz The pixels can be adressed with a voltage from 0 to 10V in a 12 bit resolution 4 3 Lens setup The first setup that was built used two lenses All optical components were aligned along an optical axis compare to 3 1 Table 4 1 shows the components used For the axis optical rails were used on which the components could easily be trans lated in one dimension The two gratings were each positioned on a rotational mount a vertical post and a gimbal prism mount which allows to position the grating at the rotation center of the mount A precise alignment concerning the distances between grating and lenses can be achieved by using this rotation center where the beam im pinges on the grating The whole setup mainly due to the rail is higher than the input http www cri inc com products components asp 4 3 Lens setup 25 Component Part number Technical data Diffraction grating Thorlabs GH13 18V holographic reflective visible light 12 7mm G 1800 Lens Thorlabs LA1353 d 75mm f 200mm singlet no AR coating Beam steerer Newport 670 RCT Vertical beam translator Mirrors Newport 10B20UF 25 Ultrafast 45 Dielectric broadband mirror Polarization rotator Newport PR 950 700 1200 nm 10mm clear aperture Table 4 1 Components used for the lens setup beam so a vertical beam steerer was used to translate i
50. many 2006 M V Klein T E Furtak Optics Wiley 1986 Daniel E Leiard Andrew M Weiner Femtosecond Direct Space to Time Pulse Shaping IEEE Journal of Quantum Electronics Vol 37 No 4 2001 Cosmin Lupulesco Femtosecond Analysis and Feedback Control of Molec ular Processes in Organometallic and Alkaline Systems Dissertation Freie Universitat Berlin 2004 Zbigniew Michalewicz Genetic Algorithms Data Structures Evolution programs Springer 1996 B E A Saleh M C Teich Fundamentals of Photonics Wiley Interscience New York 1991 G Stobrawa et al A new high resolution femtosecond pulse shaper Applied Physics B 72 627 630 2001 p BIBLIOGRAPHY 58 ShGog Tho07 Thus6 Tre97 Tys00 PaLO5 PWA03 RWL92 Wei00 WeN95 WLP92 A Sharan D Goswami Prospects of ultrafast pulse shaping Current Sci ence Vol 82 No 1 2002 Thorlabs Diffraction grating specification http www thorlabs com Thorcat 11700 11779 SO1 pdf R N Thurston et al Analvsis of Picosecond Pulse Shape Synthesis by Spectral Masking in a Grating Pulse Compressor IEEE Journal of Quantum Electronics Vol QE 22 5 1986 R Trebino Measuring ultrashort laser pulses in the time frequency domain using frequency resolved optical gating Review of Scientific Instruments 68 9 1997 Robert K Tyson Adaptive Optics Engineering Handbook New York Marcel Dekker Inc 2000 C
51. nected to Click Initialize and make sure the fields dual single and t of pixels return the parameters of your used SLM model 2 If a mapping file for the setup exists load a mapping file by selecting the filename and click Load The graph should be visible in the right graph tab 3 If a SLM response file exists load it by selecting the file and click Load This file should also be visible in the graph to the right 4 If one of the calibration files has not yet been created refer to the next section for these tools 5 Choose an option in the lower tab Loading a pattern and defining an output pattern is available 6 To load a pattern select the file and click Load The pattern is visible on the graph Clicking Load pattern to SLM uploads it to the device A 5 Manual for the mapping program 54 7 To shape a desired waveform select an input file which should have been recorded before the input of the pulse shaper Then select a file with the desired waveform which ideally uses the same timebase as the input signal The desired time signal should not be shorter than the input signal because no additional bandwidth can be generated by the pulse shaper Clicking on Load time signals displays both signals to the left of the two graphs and the calculated spectra on the right graph Then Shape uploads both patterns to the SLM masks and the output can be measured 8 To use the feedback program loa
52. ngular pulse in time domain gt T non Normalized Amplitude Phase rad N N T en a 200 200 100 100 200 300 time fs Figure 6 5 Input time domain data in amplitude blue and phase red as measured with a FROG device The amplitude is normalized to 1 a Fourier transform calculated a corresponding sinc function in frequency space In order to use as much power as possible only three sidelobes could be considered The calculated spectrum is shown in figure 6 6 Using this function the mapping procedure was applied to calculate the transmission values for each pixel As the phase shift should remain zero the phase function equals zero over all pixels Finally the SLM calibration values were mapped to the transmission values and the patterns for the master and the slave mask of the SLM were calculated They are shown in figure 6 3 Shaping in time domain 46 e e o gt o T T T Normalized Amplitude o N L A i 1 1 L 1 0 785 790 795 800 805 810 815 820 wavelength nm Figure 6 6 The sinc function is the frequency domain equivalent of a rect pulse in time domain This function was used to calculate a pattern to shape a rect pulse in time domain o o o gt o T T T Normalized transmission o N 0 100 200 300 400 500 600 700 Pixel number Figure 6 7 Normalized transmission values for the SLM to shape a sinc function 6 8
53. onary algorithms can help to obtain better results Starting from easier implementations such as double crossover which allows crossover within a chromosome and a better evaluation function and the exper imentation with the parameters population size and the probabilites for mutation and crossover more difficult topics can be tackled One could be to find a normalization for the output spectrum that allows an average approach of the measured function to wards the evaluation function which is supposed to increase results significantly Also the coding of the parameters can be improved Since the accuracy does not need to be perfect in the first place one can start with a coding of 8 bits instead of 12 bits for the voltage drive values for the SLM Also an adaptive increase and decrease of 7 2 Future work 49 chromosome size is possible which makes sure that the solutions approach the desired function quickly and additional parameters then allow to increase the accuracy 7 2 Future work With a more reliable feedback implementation a lot of different topics such as optical communication or absorption experiments can be investigated using a pulse shaper Today the approach towards understanding complex systems is often to understand simple concepts first and then build a model that describes the phenomena that have been observed Pulse shaping especially in the feedback implementation can help to obtain new experimental data tha
54. or problem for the algorithm Absolute values are not suitable to be taken however it might be possible to normalize the measured spectrum to an average value in the interesting area 6 3 Shaping in time domain For shaping in time domain a FROG measurement of the input pulse was taken The idea was to define a pattern that was able to shape the amplitude in time and the phase 6 3 Shaping in time domain 45 Load Frame Pattern Time domain shaping Spectral domain shaping Feedback optimization Desired spectrum Integration time Left wl nm Right wl nm Measured Spectrum y C Documents and Settings YUFFelabl 10 780 820 TA DesktoplPulse ShaperiSLM WI 200702271 l gt Desired IS o Current algorithm Start solution oe don t use lt gt use Number of generation Start solution voltage drive values ia k C Documents and SettingsUffelab DesktoplPulse ShaperiSUM WI 200702271 Number of chromosome 2 Population size Fitness factors of chromosomes Je Mutation o 5 Crossover d gt wavelength nm chromosome Figure 6 4 Feedback shaping with a start solution The initially calculated solution has not been improved retardation through the pulse shaper should remain zero For the output pulse the time base of the input was used to create a rectangular shaped pulse and stored as a file The input pulse can be seen in figure 6 5 Based on the recta
55. or the complex amplitude A 7 OA 2 9 a A og which has several analytical solutions One of them is the Gaussian beam with the VA j2k 2 7 complex amplitude AP Ao Zu 7 um 2 8 Z 37 2 1 Optics 5 where z is the Rayleigh range for which the diameter of the pulse does not exceed y2 times the minimum beam radius W Overall 2 6 can be written as Ao Wo 5 hoj fc 5 2 U r W2 z e J INSTR TI 3 2 9 3 jzo W z with A Wal a4 2 10 T W W it 2 11 0 R z 21 gt 2 12 0 Elz arctan 2 13 0 where W z is the beam radius within which the intensity decreases to 4 of its peak value R z describes the curvature of the beam s wavefronts under the paraxial ap proximation and z is the phase retardation compared to a planar wave as different points of the wavefront reach the position of a comparable planar wavefront at different times SaT91 2 1 2 Diffraction grating Gratings are based on the principle that a beam of a finite width which is reflected from a mirror like surface will only experience constructive interference if the different spatial components of the beam diameter have discrete differences that match multiples of the wavelength of the incident beam If the input beam is a pulse containing a spectrum of different wavelengths each wavelength will be dispersed at a different angle leading to a spatial dispersion of the spectral components
56. otating the grating 13 If the input beam does not have the polarization required by the gratings and the SLM place a polarization rotator before the first grating and measure the power of the outgoing beam Rotate the polarization plane to maximize output power This should match the polarizer specifications of the SLM as the setup was designed for a specific plane of polarization 14 Measure the outgoing beam s characteristics with an ultrafast measurement method such as FROG If the pulse is too broad adjust the positions of the two gratings to make sure the 4f condition is met This is a critical parameter which requires high accuracy A good way is to use precision translation mounts below the grat ings change their positions and compare the translation lengths with the width of the pulse A 2 Alignment procedure for a reflective setup 1 Place the mount for the SLM in the center of the setup 2 Place both mirrors one focal length in front of and behind the now defined focal plane A microtranslational mount is recommended for precise tuning of the 2f condition 3 Position the folding mirrors about t to z from the focal plane The first grating needs to be placed this distance from the folding mirror In this way the spectrum should not be broader than the folding mirror and no wavelengths are lost A 4 Manual for the control program 52 10 11 12 13 Use a steering mirror to direct the input bea
57. pur pose it was required to have an easy to use procedure that even if the setup is moved and needs to be recalibrated will allow to obtain the same results as measured at a Night at A 750nm has a cycle of t 2 5 fs 2Wavelength Division Multiplexing 3Code Division Multiple Access different place Since for most flexibility the pulse shaper needs to be moved to the experiment and not the other way around this can become very important The outline of the thesis is as follows First the theoretical background required for pulse shaping is given In greater detail the general design parameters required for the setup are illustrated and then applied to the setups used for this work Then control program and its subprograms are explained Finally some example measurements demonstrate the capability of the pulse shaper to generate defined pulse shapes and some suggestions are given to improve and extend the work Chapter 2 Fundamental principles A pulse shaper uses basic optical components to disperse and focus the different wave length components to the Fourier plane where the amplitude and phase of different spectral components can be individually modified In this paragraph the components of the setup and the principles for modifying the pulse shape in time and frequency domain will be introduced 2 1 Optics 2 1 1 Beam optics A laser beam is an electromagnetic wave which obeys the wave equation VU gt 0
58. s or miscalculations a genetic algorithm can help to find a better solution Figure 3 8 shows the cycle that includes the algorithm the upload of a new pixel pattern to the SLM and a measurement in this case a SHG signal as a feedback parameter selection evolutionary algorithm mutation individuals crossover new generation computer voltage encodings feedback SHG LC SLM detection Figure 3 8 Pulse shaping principle with an evolutionary algorithm and a feedback parameter for optimization of the pulse shape BBS97 Chapter 4 Design and setup First a pulse shaper in a 4f setup with lenses was experimentally investigated Later it was exchanged to a reflective setup with spherical mirrors 4 1 Design parameters and criteria A pulse shaper needs to be adapted to the laser source i e center wavelength spectral width output polarization and maybe output power The design was made for a SpectraPhysics Mai Tai ultrafast laser which has an output power of about 700mW and a pulse width of about 100fs around a tunable center wavelength which was set to 800nm The main criterion for a pulse shaper is the width of the liquid crystal array in the SLM device On the one hand a large bandwidth of the pulse should be used as no frequency components should be lost for an efficient modulation On the other hand the resolution increases with a smaller bandwidth so that each pixel modulat
59. t has not been recorded before Essential for the success of such an experiment is the knowledge about suitable feedback parameters Some experiments certainly still have the prospects for further research and systems like air or water do not necessarily need to be less complex than chemical experiments Such systems may have some potential for experiments that could result in a better understanding of them 50 A Appendix A 1 Alignment procedure for a lens setup The lens setup is easier to align than a reflective setup as all components can be placed on one straight line and the beam height does not need to be changed The following steps should be taken in order to have a functioning setup 1 Place one mirror on the table Redirect a laser beam from a calibration source collimated beam e g a HeNe laser through the mirror on a chosen height for the whole setup and adjust the height of the lens such that the beam travels parallel to the table before and after the lens 2 Place a second mirror approximately two focal lengths from the first mirror and adjust its height for a parallel beam 3 Observe the beam after the second mirror in the far field and change the mirror position until the beam diameter is minimized Then the 2fcondition should be fulfilled and the outgoing beam is collimated 4 Place the first grating one focal length before the first mirror and turn it to its calculated angle 5 Position a steer
60. ting pulses at a width of shorter than 100 fs at a repetition rate of 80 MHz This beam is then sent through a Spitfire Pro amplifying system which reduces the repetition rate to 1 kHz resulting in a much higher pulse energy and a pulse width of about 35 fs at a beam diameter of 12mm at the points Not only the broader spectrum has to be considered but es pecially the larger power can cause problems due to the damage threshold of the SLM Also the bigger beam diameter implies a smaller focused beam if dimensions are not changed 4 5 Upgrading for other laser systems 32 To solve the power problem the standard focusing components can no longer be used Instead as mentioned earlier focusing in only one dimension is a solution Lenses are no longer suitable for the short width of the pulse Therefore cylindrical mirrors need to be used They are now the first components to choose as choices are very limited for cylindrical mirrors As cylindrical mirrors from the standard suppliers have not been available in the required sizes for this pulse shaper only a few general considerations are given The general rules for choosing the components remain unchanged Considering a beam diameter of 5mm which is the maximum for the height of the SLM a wavelength of 850nm and a focused width of 100um the lens equation re turns a necessary focal length of f 462mm The illuminated area of the crystals is A 0 64cm Therefore in order not to e
61. tions from the desired width can be made to find a configuration with off the shelf components Also the width of individual pixels has to be considered as all the same frequencies in the beam form 4 1 Design parameters and criteria 23 lower wavelength blue higher wavelength red Figure 4 2 Connection of important design parameters a new beam of the same size at the focusing element see figure 4 4 At the focal point in the Fourier plane this beam experiences its minimum diameter whereas its width should not exceed the width of a single pixel of the SLM Using the lens equation 2 21 and the specifications of the SLM a minimum beam diameter can be calculated If the beam diameter in the setup was smaller a bigger spot on the SLM pixel would result in leakage of frequency components to more than one pixel Figure 4 3 Focusing in only one dimen sion allows a lower intensity on the crys tals For higher power applications the damage threshold of the SLM needs to be considered as well The wider models with a greater number of pixels do not only offer higher resolution but also a greater area allowing to divide the total pulse energy on a larger area and therefore a lower intensity Using the whole area is not trivial as most pixels are taller than wide in case of the used SLM the ratio is about 50 1 the spectral components should only focus in the horizontal direction see figure 4 3
62. ts height After the calcula tion of the angles for the grating the center wavelength at angle Bm see figure 4 2 is directed onto the optical axis The incident beam before the grating is reflected by a mirror which is placed at a position determined by the input angle Therefore this mirror should be as far away from the grating as possible to reduce geometrical errors since small errors from the positioning of the mirror cause relatively large errors for the incident angle which should be accurate to within 0 5 if possible to make sure the calculated spectrum size on the SLM does not differ too much from the real spectrum A mark on the grating mount and the holes on the optical table served to measure the distances necessary to place the mirror in its appropriate position If the incident light does not diffract perfectly onto the optical axis small adjustments of the rotational mount angle can be made At an input angle of 29 5 the shorter cut off wavelength of 775nm is diffracted to 64 6 and the longer wavelength of 825nm is diffracted to 82 8 respectively The second grating was mounted on a similar device as the first one but has a preci sion translation stage to make sure the 4f condition is met The calibration procedure is done without the SLM present and the geometric calibration makes sure that the pulse is not broadened after leaving the setup The SLM calibration itself follows but none of the other components are ch
63. ues are shown on the graph Save the file for a later use in the control program A 6 Manual for the SLM response calibration program 55 SLM Pixel to Wavelength calibration MISA Resource Name E E Pixels O linear Calibrate Predefined map Polynomial order lt Y select an item v Mapping function _ Mapping function zz Curve Fitting type i 300 400 500 pixel Write Calibration to File h gt Figure A 2 Screenshot of the pixel to wavelength mapping calibration program A 6 Manual for the SLM response calibration pro gram 1 Choose the number of datapoints that you would like to use for calibration 128 are suitable for a quick overview and 1024 datapoints take about 1 5 hours to complete but the accuracy should be high enough for most purposes 2 Select the VISA port which the oscilloscope is connected to and click Calibrate The program sends constant values to the whole frame and measures the trans mission values After calibration the phase retardance of the liquid crystals is calculated 3 Save the phase retardance to a file which is required by the control program The transmission values can be saved as well but this is usually not necessary A 6 Manual for the SLM response calibration program 56 Figure 100 90 80 70 60 50 Efficiency 40 30 20 0 0 1 Figure A 4 SLM response calibration stor Number of calibration in dex 1 Inde
64. ving power A N u R 2 19 which defines the ability to separate adjacent spectral lines AA is the required resolv able wavelength difference and N defines the total number of grooves illuminated on the grating Therefore a higher groove frequency but also a larger beam diameter on the grating improve the resolution Ruled gratings and some holographic gratings are blazed which defines the angle of the grooves to the grating surface For holographic gratings an ion etching procedure is applied which changes their sinusoidal to a sawtooth groove profile Used at a Littrow 2 1 Optics 7 a Figure 2 3 Plano convex lens configuration a B Y laze often maximizes their efficiency Even more impor tant for the grating efficiency is the polarization of the incoming light Performance curves usually showing the relative power in the desired diffraction order are there fore often measured for a polarization perpendicular S Plane or parallel P Plane to the groove surface which significantly changes the efficiency especially the wavelength range which they are designed for PaL05 2 1 3 Lens A lens is made of a dispersive material with a different refractive index than air Depending on the shape lenses can either diverge or focus light Therefore their surface is either formed convex planar or concave Often glass is used with n 1 5 Light enters the medium at an angle y and is refracted to an angl
65. x 2 t points fo fo lt 0 gt i i Transmission Maski Phase Maskl Transmission Mask2 Phase Mask2 5 a a E 2 1000 1500 2000 2500 3000 3500 Voltage drive level ca vo alre Write Phase Calibration to File Write Transmission values to File A 3 Screenshot of the SLM response calibration tool S Plane P Plane flectance of Aluminum 02 03 04 05 08 07 08 09 10 12 14 16 18 20 22 24 26 Wavelength um Efficiency curve for the 2000 Newport holographic grating BIBLIOGRAPHY 97 Bibliography BBS97 BSG99 Cam04 IChco7 Fet99 Hof06 KIF86 LeWO1 Lup04 Mic96 SaT91 SHF01 T Baumert et al Femtosecond pulse shaping by an evolutionary algorithm with feedback Appl Phys B65 779 782 1997 T Brixner et al Feedback controlled optimization of amplified femtosecond laser pulses Appl Phys B68 281 284 1999 Cambridge Research amp Instrumentation Inc Spatial Light Modulator SLM System CRi User s Manual 2004 Chris Conery Introduction to Liquid Crystals Liquid Crystal Group University of Boulder Colorado USA http bly colorado edu Icphysics lcintro tnlc html M R Fetterman Ultrafast Pulse Shaping Amplification Characterization and Applications Dissertation Princeton University 1999 M Hoffmann Novel Techniques in THz Time Domain Spectroscopy Disser tation University of Freiburg Ger
66. xceed the damage threshold of 20045 the pulse energy should not exceed 1284 J which is below the output energy of the laser amplifier The grating threshold can be a problem as it is lower for S polarization which is used here Also the coating is essential Holographic gratings with an Alu minum coating have a threshold of around 0 1 5 whereas gold coatings increase this value by an order of magnitude to around 1 4 PaL05 Chapter 5 Program control As an electronic device the Liquid Crystal Modulator is fully controllable with either a control program able to load predefined patterns with values for each individual pixel or with high level drivers for Matlab or LabVIEW LabVIEW was preferred because it offers drivers for most equipment in the lab such as spectrometers or power meters and can therefore integrate parameters for an automated feedback design Also it is able to use Matlab scripts when simple and fast manipulation of data is required LabVIEW is a graphical programming language in which devices can be placed and connected with elements from a virtual instrument screen the Front Panel where buttons controls and graphs can be displayed Data can be aquired processed and sent back to the device 5 1 Labview program The driver for the SLM comes with different Labview programs These so called Sub VI s can be used in a larger program and provide basic low level functions to adapt the SLM to individual applic

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