Compact direct space-to-time pulse shapingwith a phase-only spatial light modulator

T. Mansuryan,* M. Kalashyan, J. Lhermite, E. Suran, V. Kermene, A. Barthelemy, and F. LouradourXLIM Institut de Recherche, Université de Limoges, Centre National de la Recherche Scientifique,

123 Avenue Albert Thomas, 87060 Limoges Cedex, France*Corresponding author: tigrancho@gmail.com

Received January 18, 2011; revised March 16, 2011; accepted March 24, 2011;posted March 30, 2011 (Doc. ID 141279); published April 27, 2011

A very compact and innovative pulse shaper is proposed and demonstrated. The standard architecture forpulse shaping that is composed of diffraction gratings associated with an amplitude-phase spatial light modulator(SLM) is replaced by a single phase-only SLM. It acts as a pulse stretcher and as an amplitude and phase modulatorat the same time. Preliminary experiments demonstrate the accurate control of amplitude and phase of shapedpulses. © 2011 Optical Society of AmericaOCIS codes: 320.7080, 320.5540.

Along with the great success of femtosecond pulse gen-eration, computer-controlled high resolution pulse shap-ing becomes a powerful tool for numerous applications.Fourier transform pulse shaping (FT-PS) is the mostwidespread apparatus for high repetition rate pulse shap-ing [1]. However, besides FT-PS there exists an alterna-tive technique that relies on the direct mapping inside aspectroscope arrangement, without Fourier transform,between the transmission profile of a spatial mask andthe temporal profile in the output optical signal. Directspace-to-time pulse shaping (DST-PS) has indeed beensuccessfully applied to picosecond [2,3], and then to fem-tosecond pulse shaping [4,5]. DST-PS exhibits several ad-vantageous features with respect to FT-PS. It avoidsunwanted temporal replicas and space–time couplings.It does not require Fourier transform computation to de-termine the masking function, which should become akey restriction for ultrahigh update rate ultrafast opticaldata packet generation [5].Interestingly, because it is based on a simple spectro-

scope arrangement, DST-PS could lead to an easy-to-align and very simple setup. This feature has beenpartially demonstrated by means of integrated devices[5] or by means of diffractive optics [6,7]. However, untilnow DST-PS devices involving readily available compo-nents were still as complex as the FT-PS devices [seeFig. 1(a)]. Recently, an innovative reconfigurable opticalfilter was proposed [8], involving a phase-only liquid-crystal spatial light modulator (LC-SLM). It has a config-uration similar to the one proposed in the present paper,but it deals only with spectral shaping.In this Letter, we report a simplified and very compact

DST-PS setup by using for the first time to our knowledgea phase-only high resolution LC-SLM, without additionalmask, relay optics, and diffraction grating as in conven-tional DST-PS [3,4]. Furthermore, we show that it is pos-sible to perform high-fidelity pulse shaping both inamplitude and in phase with a single phase-only LC-SLM.A conventional DST-PS is depicted in Fig. 1(a). First,

the input beam is expended with a telescope [see lensesℓ1 and L1 in Fig. 1(a)]. Then the beam is coherentlyshaped by an SLM, which more generally modifies ampli-tude and phase. Next, the SLM is imaged with a secondtelescope [see lenses L1 and L2 in Fig. 1(a)] onto a

diffraction grating inside a spectroscope arrangement.This scheme images the SLM on the grating withoutany added phase-front curvature, which would lead to

Fig. 1. Conventional (a) and simplified (b) DST pulse shaper.The setup depicted in (a) is a combination of previously re-ported schemes [3,4]. In both cases the diffraction grating ispreferentially in Littrow configuration.

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a chirp in the output temporal waveform [9]. At the cen-ter of the exit plane of the spectroscope, a small slit isintroduced before collimation of the beam by a last lens.The output pulse profile is simply the convolution be-tween the input signal and the impulse response of thegeneralized spectroscope, which gives a directly scaledmapping from space to time of the coherent spatial filter-ing imposed by the SLM onto the grating [4].What we propose [see Fig. 1(b)] consists first in remov-

ing the amplitude and phase SLM, the grating, and thelenses L1 and L2. Then we introduce a single phase-onlyhigh resolution SLM simulating an inhomogeneousblazed phase grating. This computer-controlled elementplays the role of both the spatial mask and of the disper-sive element of the spectroscope. Amplitude and phasemodulation of the wave diffracted in the first order bythe synthesized grating are performed independentlycontrolling respectively the blaze angles and the absolutephases of the local phase gratings that are displayedalong the SLM.The blazed phase grating, which is depicted in Fig. 2,

can be represented by the following reflectivity:

rðx; yÞ ¼ rect

�xp

�exp

�jð2παðxÞ x

pþ φðxÞÞ

�

�Xn

δðx − npÞ; ð1Þ

where x and y are the spatial coordinates in the SLM plan[see Fig. 1(b)]; the grating grooves are parallel to the ydirection; p denotes the grating period; α is the blaze fac-tor. In case of α ¼ 0, all the energy is lost in the 0 diffrac-tion order; when α ¼ 1, the wave is 100% diffracted in thefirst order. αðxÞ and φðxÞ denote the blaze factor and thebias phase variations according to the x axis.αðxÞ and φðxÞ are slowly varying functions, so that they

can be considered as constants on a domain extendingon few periods, p (i.e., the notion of “local grating”sounds valid). The wave amplitude locally diffracted inthe first order can be calculated [10,11] performing theplane wave decomposition [12] of the field reflectedby the SLM.Then, it can be demonstrated that the SLM applies a

spatial filtering, mðxÞ, to the field diffracted in the firstorder that is described by

mðxÞ ¼ sinc½1 − αðxÞ� exp½jφðxÞ�: ð2ÞThe temporal profile at the signal exiting the slit is the

convolution between the input pulse and a scaledrepresentation of this filtering function [4]:

EoutðtÞ ¼ EinðtÞ � ½mðt=γÞAðt=γÞ�: ð3Þγ ¼ T=p0 is a space-to-time scaling factor, p0 ¼

p cosðθLittrowÞ is the grating period under Littrow angleincidence, and T is the optical time period (i.e., the in-verse of the carrier optical frequency). AðxÞ denotesthe input beam transverse profile incident onto theSLM. The time amplitude modulation is mainly relatedto sinc½1 − αðt=γÞ�. Independently, the phase modulation

is related to φðt=γÞ. Aðt=γÞ plays the role of an apodizationterm, which sets the available time window of the shaper.

As a proof of concept, we carried out the following ex-periment. A Ti:sapphire oscillator centered on 803 nmproducing pulses with 200 fs autocorrelation duration(FWHM) fed the setup depicted in Fig. 1(b). A 2D HOLO-WEYE phase-only programmable LC-SLM was used (re-flective LCOS microdisplay; 1920 × 1080 pixels; 8:0 μmpixel pitch; ≈3π phase-shift at 800 nm; 60Hz frame rate).The grating periodic modulations were set parallel tothe small dimension of the device [i.e., y direction inFig. 1(b)]. Each three pixels of the LC-SLM were asso-ciated as one grating groove (i.e., p ¼ 24 μm). The result-ing blazed grating (15:36mm width, 41:66 grooves=mm)gave a calculated space-to-time scale factor γ amountingto 111 fs=mm and a time window close to 1:62 ps. This isin very good agreement with measured data, whichamounted respectively to 110 fs=mm and 1:61 ps [seeFig. 3(a)]. For those measurements, we used an intensitycross-correlator, using a fraction of the oscillator asreference. In order to test the shaper flexibility for am-plitude modulation, various pulse doublets were synthe-sized with pulses having different amplitudes and/ordifferent durations [Fis. 3(b) and 3(c), respectively).More generally, Fig. 3(d) illustrates a pulse sequence in-volving five equidistant pulses. Note that measured cross-correlation signal was in very good agreement with thecalculated one from Eq. (3).

The ability of the phase-only SLM to induce about 3πphase-shift has been used for phase modulation demon-stration. A pulse doublet was synthesized with first iden-tical and then opposite phase relationship. The registeredspectra (see Fig. 4) of the two sequences clearly show thephase control. Spectral fringes are shifted by half-periodwhen the π phase-shift is added. Phase modulation can beachieved working with two different absolute phases forthe two related local gratings. A contribution to thisphase-shift can also come from the translation along thex direction of one of the two local gratings by one or twopixels that results respectively in 2π=3 or 4π=3 additionalphase-shift. We have checked that both phase and ampli-tude modulations can be independently achieved withoutcouplings.

The diffraction efficiency in the first order of a uniformblazed phase grating synthesized by the LC-SLM wasmeasured to be 36%. It is rather close to what would re-sult from the association of a dual mask amplitude-phaseLC-SLM and a diffraction grating inside a standard DST-PS setup (i.e., ≈60% for the amplitude-phase LC-SLM and≈80% for a conventional diffraction grating). In spite ofthis, the global efficiency was small, amounting to fewpercents depending on the desired pulse profile. Indeed,it is known that DST-PS basic principle results in rather

Fig. 2. Phase distribution ΦðxÞ introduced along the x axis bythe phase-only LC-SLM, which mimics an inhomogeneousblazed phase grating. The grating groove density p is constant.

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low throughputs [13]. However, it still presents an inter-est for applications requiring small excitations, such asnonlinear microscopy. An amplified system is anothercase for which DST-PS efficiency is not a highly detri-mental issue. At the same time, DST-PS provides advan-tageous features, such as absence of time replicas andabsence of space–time couplings.It is well known that LC-SLM update rate is rather low

(i.e., 60Hz for the current device; 1 kHz at best). Few tensof kilohertz could be easily reached in a manner similarto the one proposed by E. Frumker and Y. Silberberg forFT-PS [14], with the addition of a y scanning mirror at theinput and with a y-varying blazed phase grating acrossthe 2D LC-SLM.As a conclusion, a new programmable DST femtose-

cond pulse shaper using a phase-only LC-SLM has beendemonstrated. The experimental setup is very simple andcompact. The flexibility of the shaper for amplitude andphase control has been demonstrated by the generationof various pulse sequences with tailored intensity and

phase (in the range of π). Extension to wideband ultra-short pulses and to polarization state pulse shaping arethe subjects of future studies.

This work was supported by the Limousin Region,under contract DIL AVRUL.

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Fig. 3. (Color online) Cross-correlation signals measured atthe output of the DST shaper in case of amplitude modulation.(a) Doublet with maximal time separation. The time window ofthe shaper amounted to 1:6 ps. (b) Double pulse with differentamplitude. (c) Double pulse with different durations. (d) Se-quence of five equidistant pulses: in red solid curve, measuredcross-correlation; in black solid curve, calculated cross-corre-lation from Eq. (3); the RMS difference between measuredand calculated curves is 2.6%.

Fig. 4. (Color online) Phase modulation. A double pulse se-quence was synthesized with two different phase relationships:0 and π. As a consequence, the two related spectra are shiftedby half a fringe.

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