Giorgia Sparapassi Winter College on Extreme Nonlinear Optics Attosecond Science and Highfield Physics 06022018 ICTP Trieste Goals of pulseshaping Shape the temporal and spectral ID: 1012591
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1. Ultrashort Pulse ShapingGiorgia SparapassiWinter College on Extreme Non-linear Optics, Attosecond Science and High-field Physics06/02/2018 - ICTP (Trieste)
2. Goals of pulse-shapingShape the temporal and spectral profile of the pulse forPulse compression/stretchingEnvelope phase/delay controlReplica generationSpectral filteringInformation encoding/decoding…LaserPulse shaper
3. x(t)tPulse shaping by linear filteringy(t) = (x∗ h) (t) = ∫ x(t’) h(t-t’) dt’Y(w) = X(w) H(w)Impulse h(t)?Frequency H(w)X(w)x(t)tResponse functionsY(w)Very hard to act on the pulse on the femtosecond time scale & very convenient to use frequency dispersion
4. Zero dispersion line or 4f-line“4f line”ffffX(w)Y(w)xA pair of identical dispersive elements and lensesFourier plane
5. Mask at the Fourier plane of a 4f-lineConvenient to exploit spatial dispersion by using a spatial “mask” M(x) at the Fourier planeFocal spot size of a spectral component: X0 = Linear dispersion: = Eout(w,x) = Ein(w,x) M(x) Ein(w,x) = X(w) e The mask is designed with the purpose of obtaining the desired Y(w)Y(w)Fourier planeX(w)d xX0 Ein(w,x) Eout(w,x)M(x)
6. Fourier planeAmplitude and phase masksTwo masks can be used, one modulating the amplitude of the spectral components,one modulating the phase of the spectral componentsX(w)Y(w)xM(x) = |M(x)| ei fM(x)
7. Y(w) = H(w)X(w)Mask: Gaussian approximationSelecting the fundamental Hermite-Gaussian modeH(w) = M(x’) e dx’ xX(w)M(x)Ein(w,x) Eout(w,x)Spatially filtering the beam after the FPConvenient to exploit spatial dispersion by using a spatial “mask” M(x) at the Fourier planeFourier plane
8. M(x) Square waveformNoise burstsPulse trainM(x) M(x) Time delay [ps]Time delay [ps]Intensity [a.u.]Intensity [a.u.]Cubic, flat,quadraticphase gradientTime delay [ps]Time delay [ps]-4 -3 -2 -1 0 1 2 3 4-4 -3 -2 -1 0 1 2 3 4Intensity [a.u.]Intensity [a.u.]Mask examples*phase only*phase only*phase only*amplitude onlyMultiple masks allow independent amplitude and phase modulation but cannot be modified during experiment
9. Static mask (SM) are a special case of this approach!Micro-machined deformable mirror (mDM)Acousto-optic modulator (AOM)Spatial light modulator (SLM)4f-line pulse-shapersProgrammablePC
10. 4f-line pulse-shapersMicro-machined deformable mirror (mDM)Actuator electrodesPrinted circuit board for applying electrostatic potential DV with a software controlled patternDeformable membrane (Si3N4) with reflective coating (material depends on wavelength)Anchoring postsDVOptics Letters, 1999, 24.7: 493
11. 4f-line pulse-shapersMicro-machined deformable mirror (mDM)www.okotech.comActuator electrodesInterferometric testing of a mDM for:No voltage appliedVoltage applied on all electrodesVoltage applied on 20-37 electrodesVoltage applied on randomly chosen electrodesa)b)c)d)
12. 4f-line pulse-shapersMicro-machined deformable mirror (mDM)The membrane deforms according to the applied voltage (DV)2 Phase only modulationintroducing a continuous optical path difference:df (l,DV) Allows to build high order phase gradients Path difference allows phase modulation
13. Acousto-Optic crystal (TeO2, Ge, fused Si)Piezoelectric transducerSoftware- controlled modulating RF voltage delivering an arbitrary waveform (beware of acoustic attenuation and nonlinearities)!Period = vAC/fRF ∿Acousto-optic modulator (AOM)4f-line pulse-shapersAcoustic wave f(x=t/vAC)Refractive index variation induced by the traveling acoustic waveFinite travel time of AW(can be reprogrammed every ~ms)AW has limited lifetime
14. Phase difference between 1st and 0th orderf(l,fRF) = ∿Acousto-optic modulator (AOM)4f-line pulse-shapersInduced diffraction grating allows amplitude and phase modulation1st order max for sin() = (phase matching condition) From 260 nm to 5 μmUNDIFFRACTED LIGHTTilting of FP
15. Liquid crystal based spatial light modulator (LC SLM)Liquid crystals (nematic phase)Transparent ITO filmDV4f-line pulse-shapers = 0 ≠ 0(birefringence reduced) xxzxzzyEach pixel is a waveplate introducing an angle f(w,DV) = t IR to UVGlassTransparent pixelated indium tin oxide (ITO) filmGlassanchorage directionanchorage direction
16. Liquid crystal based spatial light modulator (LC SLM)Single-layer 1D arrangement4f-line pulse-shapersThe optical path-length difference is adjustable for each wavelength and enables spectral phase modulationThe incoming light is polarized along the anchorage axis+90°
17. Liquid crystal based spatial light modulator (LC SLM)Double-layer 1D arrangementPhase and amplitude shaping with complex transfer function H(w) = 4f-line pulse-shapersPol. axis:90°Pol. axis:90°Anchorage directions:+45° & -45°
18. Liquid crystal on silicon based spatial light modulator (LCoS SLM)Single-layer 2D arrangement4f-line pulse-shapersDVxzySilicon layer with pixelated electrodesanchorage directionReflective layerLCos SLMFolded geometryIncoming & outgoing beamsVery high electrode density
19. Liquid crystal on silicon based spatial light modulator (LCoS SLM)Single-layer 2D arrangement: effects of pixelization4f-line pulse-shapersGaps are usually ~ mm widePortion of incident pulse reflected by gaps (not shaped)Linearly chirped pulse (shaped)Pixel size: tens of mm
20. ∿In-line pulse-shapersAcousto-optic programmable dispersive filter (AOPDF)Ordinary axisExtraordinary axisAcousto-Optic crystalAcoustic wavexRF waveform generator and acoustic transducerIncoming collimated beamwww.fastlite.com
21. In-line pulse-shapersAcousto-optic programmable dispersive filter (AOPDF)Ordinary axisExtraordinary axisxDiffraction allows amplitude and phase modulationIncoming light is polarized along the ordinary axisEOUT(w) EIN(w) SAC (bw) b = Dn (vAC/c) Acoustic wave – light wave coupling: diffraction on the orthogonal polarization occurs when x-dependent phase matching conditions are fulfilled:Amplitude of diffracted spectral components depends on acoustic wave strengthwE = wAC(x) + wO E(wE) = AC(wAC(x)) + O(wO) Nonlinear effects (high peak intensity)Refresh rate limited by AW propagation (~ps)
22. Comparison between different pulse shapersTypeAdvantagesTrade-offsSMIndependent amplitude and phase modulationCannot be modified during experimentmDMComputer controlledHigh order spectral phase controlSmooth phase variationsHigh actuator densityPhase only modulationAOMComputer controlledCan be reprogrammed every ~msNo sharp boundariesEfficiency limited by imperfect phase matchingDistortions introduced by RF waveform amplitudeAcoustic wave (AW) has limited lifetimeSLMComputer controlledHigh waveform complexityPolarization controlPixelation & gaps effectsRefresh rate limited by LC rotation time (~ms)AOPDFComputer controlledCan be reprogrammed every ~psNo sharp boundariesNonlinear effects (high peak intensity)Imperfect synchronization of AW to pulses
23. Comparison: resolutionTypeTemporal windowFrequency resolution4fT 1 / = / AOPDFT = Dng L cos2(qin) / cdl = l2 / (cDnLcos2(qin) )TypeTemporal windowFrequency resolution4fAOPDFT = Dng L cos2(qin) / cdl = l2 / (cDnLcos2(qin) )Focal spot size of a spectral componentr0 Dispersion between spectral components M(x)d xr0 ffrinT2010 J. Phys. B: At. Mol. Opt. Phys. 43 103001
24. Comparison: resolutionThe mask acts on more than one spectral component (finite size focus, finite beam size, mask spatial features too fine).Can show up also as an amplitude modulation after a phase only maskTypeTemporal windowFrequency resolution4fT 1 / = / AOPDFT = Dng L cos2(qin) / cdl = l2 / (cDnLcos2(qin) )TypeTemporal windowFrequency resolution4fAOPDFT = Dng L cos2(qin) / cdl = l2 / (cDnLcos2(qin) )2010 J. Phys. B: At. Mol. Opt. Phys. 43 103001M(x)d xr0 ffrinSpatio-temporal coupling(T )
25. Ordinary axisExtraordinary axisAcousto-Optic crystalOptical wavexInput light waveComparison: resolutionTypeTemporal windowFrequency resolution4fT 1 / = / AOPDFT = Dng L cos2(qin) / cdl = l2 / (cDnLcos2(qin) )TypeTemporal windowFrequency resolution4fAOPDFT = Dng L cos2(qin) / cdl = l2 / (cDnLcos2(qin) )The window and the spectral resolution in an AOPDF are determined mainly by the crystal thickness and its anisotropyθin is the angle between the incident wave vector and a reference crystallographic axisL is the length of the AO crystal
26. Case study: our experimentWe want to uncover the statistical correlations introduced in the sample by the material,thus we need to shape differently each mask and independently in phase and amplitudeBSPumpProbeProbeSampleLaserSpectrometerD Pulse shaper
27. LCoS SLM-based pulse shaper @ T-ReXLCoS SLMDiffraction gratingCylindrical lensIncoming & outgoing pulses(beams are sligthly angled)Folded 4f line: reflection geometry
28. LCoS SLM-based pulse shaper @ T-ReXMain characteristics of this SLM:512 x 512 pixels matrix (total size: 12.8 x 12.8 mm)25 mm x 25 mm pixel pitchLow inter-pixel cross talkDiffraction efficiency 88%The beam is dispersed, can be used with high powerArbitrary waveform can be chosen
29. LCoS SLM-based pulse shaper @ T-ReXOther elements in the setup:Diffraction grating with 1800 g/mmqi = 50°, qd = 40°Focal length of lens f = 100 mmLCoS SLMDiffraction gratingCylindrical lensIncoming & outgoing pulses(beams are sligthly angled)Folded 4f line: reflection geometryLaser beam parameters:l0 = 375 THzIncoming beam radius rin = 2 mmSpectral features at the FP:Focus of a frequency X0 = 29 mmAngular dispersion a = 78.5 mm/THzFrequency resolution dw = 0.06 THz
30. LCoS SLM 2D patternsSawtooth with amplitude A(n) and period dSpectral phase f(n)2005 Opt. Lett. 30 (3) 343Build 2D mask starting from amplitude and phase:A(n)f(n)nn0 10 1Optimization0 1
31. Shot-to-shot and point-by-pointPhase and amplitude modulation0 1Amplitude modulation0 1
32. ConclusionsSeveral kinds of pulse shapers are availableAdvantages & trade-offs have to be consideredPulse shapers are very versatile tools, and allow to:Optimize the output of a laserProduce any waveform from the pulsesDelay, replicate pulsesFilter the spectrumChange spectral phaseAdd noise on top of the spectrum…
33. T-ReX group @ ElettraDaniele FaustiGroup LeaderAlexandre MarciniakPostDocFilippo GlereanPhD studentFrancesca GiustiPhD studentJonathan TollerudPostDoc
34. Thank you for your attention!