Giorgia Sparapassi Ultrashort Pulse Shaping Winter College on

Giorgia Sparapassi Ultrashort Pulse Shaping Winter College on Extreme Non-linear Optics, Attosecond Science and High-field Physics 06/02/2018 - ICTP (Trieste)

Goals of pulse-shaping Laser Pulse shaper ▪ Shape the temporal and spectral profile of the pulse for – – – Pulse compression/stretching Envelope phase/delay control Replica generation Spectral filtering Information encoding/decoding …

Pulse shaping by linear filtering x(t) y(t) = (x∗ h) (t) = ∫ x(t’) h(t-t’) dt’ t t Response functions Impulse h(t) X(w) Frequency H(w) Y(w) = X(w) H(w) ? Very hard to act on the pulse on the femtosecond time scale & very convenient to use frequency dispersion

Zero dispersion line or 4 f-line Fourier plane A pair of identical dispersive elements and lenses x Y(w) X(w) f f f “ 4 f line” f

Mask at the Fourier plane of a 4 f-line Convenient to exploit spatial dispersion by using a spatial “mask” M(x) at the Fourier plane Ein(w, x) The mask is designed with the purpose of obtaining the desired Y(w) Eout(w, x) x d M(x) Y(w) X(w) Eout(w, x) = Ein(w, x) M(x)

Amplitude and phase masks Fourier plane x M(x) = |M(x)| ei f (x) M X(w) Y(w) Two masks can be used, one modulating the amplitude of the spectral components, one modulating the phase of the spectral components

Mask: Gaussian approximation Convenient to exploit spatial dispersion by using a spatial “mask” M(x) at the Fourier plane Spatially filtering the beam after the FP Eout(w, x) Ein(w, x) x M(x) Y(w) = H(w)X(w) Selecting the fundamental Hermite-Gaussian mode

Mask examples M(x) *phase only Time delay [ps] Intensity [a. u. ] Noise bursts Intensity [a. u. ] Square waveform -4 -3 -2 -1 0 1 2 3 4 Time delay [ps] *amplitude only M(x) *phase only Time delay [ps] Intensity [a. u. ] *phase only Pulse train Intensity [a. u. ] Cubic, flat, quadratic phase gradient -4 -3 -2 -1 0 1 2 3 4 Time delay [ps] Multiple masks allow independent amplitude and phase modulation but cannot be modified during experimen

4 f-line pulse-shapers – Static mask (SM) are a special case of this approach! – Micro-machined deformable mirror (m. DM) Programmable – Acousto-optic modulator (AOM) – Spatial light modulator (SLM) PC

4 f-line pulse-shapers Micro-machined deformable mirror (m. DM) Deformable membrane (Si 3 N 4) with reflective coating (material depends on wavelength) Optics Letters, 1999, 24. 7: 493 Anchoring posts DV Actuator electrodes Printed circuit board for applying electrostatic potential DV with a software controlled pattern

4 f-line pulse-shapers Micro-machined deformable mirror (m. DM) Actuator electrodes a) b) c) d) Interferometric testing of a m. DM for: www. okotech. com a) No voltage applied b) Voltage applied on all electrodes c) Voltage applied on 20 -37 electrodes d) Voltage applied on randomly chosen electrodes

4 f-line pulse-shapers Micro-machined deformable mirror (m. DM) Path difference allows phase modulation

4 f-line pulse-shapers Acousto-optic modulator (AOM) Refractive index variation induced by the traveling acoustic wave Acousto-Optic crystal (Te. O 2, Ge, fused Si) • Finite travel time of AW (can be reprogrammed every ~ms) • AW has limited lifetime Acoustic wave f(x=t/v. AC) Piezoelectric transducer ∿ Software- controlled modulating RF voltage delivering an arbitrary waveform (beware of acoustic attenuation and nonlinearities)!

4 f-line pulse-shapers Acousto-optic modulator (AOM) From 260 nm to 5 μm UNDIFFRACTED LIGHT Tilting of FP ∿ Induced diffraction grating allows amplitude and phase modulation

4 f-line pulse-shapers Liquid crystal based spatial light modulator (LC SLM) IR to UV Glass Transparent pixelated indium tin oxide (ITO) film z Liquid crystals (nematic phase) x DV Transparent ITO film Glass z y x anchorage direction z x anchorage direction

4 f-line pulse-shapers Liquid crystal based spatial light modulator (LC SLM) Single-layer 1 D arrangement The incoming light is polarized along the anchorage axis +90° The optical path-length difference is adjustable for each wavelength and enables spectral phase modulation

4 f-line pulse-shapers Liquid crystal based spatial light modulator (LC SLM) Double-layer 1 D arrangement Pol. axis: 90° Anchorage directions: +45° & -45°

4 f-line pulse-shapers Liquid crystal on silicon based spatial light modulator (LCo. S SLM) Single-layer 2 D arrangement Folded geometry LCos SLM DV Incoming & outgoing beams Reflective layer z y x anchorage direction Silicon layer with pixelated electrodes Very high electrode density

4 f-line pulse-shapers Liquid crystal on silicon based spatial light modulator (LCo. S SLM) Single-layer 2 D arrangement: effects of pixelization Portion of incident pulse reflected by gaps (not shaped) Pixel size: tens of mm Linearly chirped pulse (shaped) Gaps are usually ~ mm wide

In-line pulse-shapers Acousto-optic programmable dispersive filter (AOPDF) Ordinary axis Acoustic wave Incoming collimated beam ∿ RF waveform generator and acoustic transducer Extraordinary axis x Acousto-Optic crystal www. fastlite. com

In-line pulse-shapers Acousto-optic programmable dispersive filter (AOPDF) • Ordinary axis Incoming light is polarized along the ordinary axis • Acoustic wave – light wave coupling: diffraction on the orthogonal polarization occurs when x-dependent phase matching conditions are fulfilled: w. E = w. AC(x) + w. O E AC(w. AC(x)) + O(w. O) (w. E) = Amplitude of diffracted spectral components depends on acoustic wave strength EOUT(w) E IN(w) SAC (bw) b = Dn (v. AC/c) x Extraordinary axis Diffraction allows amplitude and phase modulation • • Nonlinear effects (high peak intensity) Refresh rate limited by AW propagation (~ps)

Comparison between different pulse shapers Type Advantages Trade-offs SM • Independent amplitude and phase modulation • Cannot be modified during experiment m. DM • • Computer controlled High order spectral phase control Smooth phase variations High actuator density • AOM • • • Computer controlled Can be reprogrammed every ~ms No sharp boundaries • Efficiency limited by imperfect phase matching • Distortions introduced by RF waveform amplitude • Acoustic wave (AW) has limited lifetime SLM • • • Computer controlled High waveform complexity Polarization control • Pixelation & gaps effects • Refresh rate limited by LC rotation time (~ms) AOPDF • • • Computer controlled Can be reprogrammed every ~ps No sharp boundaries • • Phase only modulation Nonlinear effects (high peak intensity) Imperfect synchronization of AW to pulses

Comparison: resolution Type Temporal window Frequency resolution M(x) 4 f AOPDF T = Dng L cos 2(qin) / c dl = l 2 / (c. Dn. Lcos 2(qin) ) r 0 d T x rin 2010 J. Phys. B: At. Mol. Opt. Phys. 43 103001 f f

Comparison: resolution Type Temporal window 4 f AOPDF T = Dng L cos 2(qin) / c Frequency resolution M(x) dl = l 2 / (c. Dn. Lcos 2(qin) ) r 0 Spatio-temporal coupling 2010 J. Phys. B: At. Mol. Opt. Phys. 43 103001 d x rin The 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 mask f f

Comparison: resolution Type Temporal window Frequency resolution T = Dng L cos 2(qin) / c dl = l 2 / (c. Dn. Lcos 2(qin) ) 4 f AOPDF θin is the angle between the incident wave vector and a reference crystallographic axis L is the length of the AO crystal The window and the spectral resolution in an AOPDF are determined mainly by the crystal thickness and its anisotropy Input light wave Ordinary axis Optical wave x Extraordinary axis Acousto-Optic crystal

Case study: our experiment Pump Probe Laser BS Pulse shaper Sample Spectrometer We 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 amplitude

LCo. S SLM-based pulse shaper @ T-Re. X Folded 4 f line: reflection geometry Diffraction grating Cylindrical lens LCo. S SLM Incoming & outgoing pulses (beams are sligthly angled)

LCo. S SLM-based pulse shaper @ T-Re. X ▪ Main characteristics of this SLM: – – – 512 x 512 pixels matrix (total size: 12. 8 x 12. 8 mm) 25 mm x 25 mm pixel pitch Low inter-pixel cross talk Diffraction efficiency 88% The beam is dispersed, can be used with high power Arbitrary waveform can be chosen

LCo. S SLM-based pulse shaper @ T-Re. X Folded 4 f line: reflection geometry Diffraction grating Cylindrical lens ▪ Other elements in the setup: – Diffraction grating with 1800 g/mm – qi = 50°, qd = 40° – Focal length of lens f = 100 mm LCo. S SLM ▪ Laser beam parameters: – l 0 = 375 THz – Incoming beam radius rin = 2 mm Incoming & outgoing pulses (beams are sligthly angled)

LCo. S SLM 2 D patterns Build 2 D mask starting from amplitude and phase: 0 1 2005 Opt. Lett. 30 (3) 343 f(n) A(n) n n 0 Sawtooth with amplitude A(n) and period d Spectral phase f(n) 1 Optimization 0 1

Shot-to-shot and point-by-point Phase and amplitude modulation 0 1 Amplitude modulation 0 1

Conclusions ▪ Several kinds of pulse shapers are available – Advantages & trade-offs have to be considered ▪ Pulse shapers are very versatile tools, and allow to: – – – – Optimize the output of a laser Produce any waveform from the pulses Delay, replicate pulses Filter the spectrum Change spectral phase Add noise on top of the spectrum …

T-Re. X group @ Elettra Daniele Fausti Group Leader Filippo Glerean Ph. D student Alexandre Marciniak Post. Doc Jonathan Tollerud Post. Doc Francesca Giusti Ph. D student

Thank you for your attention!