We present an adaptive technique for the formation of multiple co-propagating and stationary filaments in a gaseous medium. Wavefront shaping of the initial beam is performed using a deformable mirror to achieve a complete two-dimensional control of the multi-spot intensity pattern in the laser focus. The spatial organization of these intensity spots yields reliable formation of up to five stable and stationary filaments providing a test bed for fundamental studies on multiple filamentatio

Gautier, J.

Hauri, C.P.

Papalazarou, E.

Trisorio, A.

Zeitoun, P.

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DOI: 10.1007/s00340-007-2906-1Appl. Phys. B 90, 391–394 (2008)Lasers and OpticsApplied Physics Bc.p. hauri1,j. gautier2a. trisorio2e. papalazarou2p. zeitoun2Two-dimensional organization of a largenumber of stationary optical filamentsby adaptive wave front control1 Paul Scherrer Institute (PSI), Villigen, Switzerland2 Laboratoire d’Optique Applique´e, ENSTA – Ecole Polytechnique, CNRS UMR 7639,91761 Palaiseau, FranceReceived: 5 October 2007/Revised version: 6 December 2007Published online: 19 January 2008 • © Springer-Verlag 2008ABSTRACT We present an adaptive technique for the forma-tion of multiple co-propagating and stationary filaments ina gaseous medium. Wavefront shaping of the initial beam isperformed using a deformable mirror to achieve a completetwo-dimensional control of the multi-spot intensity pattern inthe laser focus. The spatial organization of these intensity spotsyields reliable formation of up to five stable and stationary fila-ments providing a test bed for fundamental studies on multiplefilamentation.PACS 42.65.Jx; 52.38.Hb; 42.65.SfBeam break-up of a powerful laser into several filaments inspace happens when the peak power of the laser pulse exceedsmany times the critical power for self-focusing. The mechan-ism of multiple filament (MF) formation during self-focusingof a powerful laser was explained by transverse modulationinstability (MI) in the spatial intensity profile giving rise toa splitting of the initial beam into small-scale cells, whichtrigger the formation of MF [1–3]. This mechanism is accom-panied by stochastic shot-to-shot fluctuations of the initiallaser beam [4], which may result in an arbitrary and non-stationary MF pattern being different for consecutive lasershots. Experimentally, different schemes have been success-fully introduced to control MF formation. Deterministic MFpatterns have been produced by imposing astigmatism on thelaser beam with the help of a tilted lens [5], by use of anamor-phic prisms to transform a Gaussian-like into an ellipticalintensity beam profile [6] or by applying circularly polarizedlaser light [7]. Control of MF by those schemes, however, wasrestricted to one-dimensional transverse to the beam propa-gation. Experimental approaches towards a two-dimensionalcontrol of MF formation have recently been explored by useof a periodic mesh placed in the beam path for spatial reg-ularization of a high-power femtosecond laser pulse [8] orby shaping the laser beam profile with spatial masks [9].These techniques, however, suffer from substantial energy Fax: +41 56 310 4197, E-mail: christoph.hauri@psi.chlosses and do not allow adaptive control of MF formation inspace.In this letter we use a reflective deformable mirror as anadaptive spatial phase shaper in order to gain a completetwo-dimensional spatial control of the formation of a largenumber of stationary, independently co-propagating multiplefilaments. We believe that our novel approach for organizingMF offers some noteworthy advantages over the techniquesformerly described. First, no laser energy is sacrificed for ourtechnique to work, since our scheme contains all-reflectiveoptics and abstains lossy spatial masks. Second, contrary toa liquid-crystal-based wave front shaping technique recentlyused for stabilizing [10] and enhancing the beam quality ofone single filament [11], the scheme presented here is scalableto the multi-TW level since deformable mirrors withstand-ing high flux are commercially available and routinely used inhigh power laser chains [12]. We believe that our approach istherefore of particular interest for laser-based atmospheric an-alysis techniques, such as femtosecond lidar, where the con-trol of MF is crucial [13, 14] and where the optical elementfor controlling MF needs to sustain a high laser peak power(> 5 TW). Third, our scheme is independent of the initiallaser beam parameters, due to the adaptive nature of the de-formable mirror, and offers a full two-dimensional control ofthe MF arrangement in space. Furthermore, the reliable andstable formation of MF provided by our scheme offers a testbed to study fundamental aspects of MF and to explore re-cent theoretical predictions of attraction, fusion, repulsion andspiral propagation of MF [15, 16]. Finally, many applicationsprofit from controllable and stationary MF, such as filament-based ultrafast optical switches [17], multi-beam few-cyclefemtosecond sources, and studies on propagation of MF inturbulent air [18].Unlike the natural formation of MF, which has its ori-gin in the MI triggered by the nonlinear response of thegas, our technique is based on active control of the laserenergy distribution in the focal plane. This is achieved bywavefront shaping of the laser beam prior to the last focus-ing optics and linear propagation of the beam towards thegeometrical focus where nonlinear pulse propagation (fila-mentation) sets in for individual focal spots due to an in-crease in peak intensities (> 1013 W/cm2). The formation of392 Applied Physics B – Lasers and OpticsFIGURE 1 Experimental setup for organizing multiple filaments by wave-front control. 1-kHz Ti:sapphire CPA system with deformable mirror (activearea 1600 mm2, 31 actuators) steered by a computer; xenon-filled tubehosting multiple filaments; diagnostic tools like a CCD camera and a Shack–Hartmann wave front analyzer. The inset shows the intensity profile of thelaser beam at the position of the deformable mirrormultiple intensity spots in the focus and consequently theformation of MF becomes controllable. Depending on thewavefront imposed by the laser beam the resulting inten-sity profile in the laser focus exhibits a specific number oftransversely separated multiple foci. These foci are of dif-ferent origin than the “hot-spots” stemming from MI sincethe multiple-focus pattern is existent even if the nonlinearityprovided by the gas is not present (i.e., gas cell evacuated).Ideally, each of the multiple foci generated by wave frontshaping only conveys a power high enough for driving fila-mentation, which results in the formation of a set of individualand stationary co-propagating filaments. Since a deformablemirror wavefront shaper provides control on the amount ofpower deposited in each individual intensity spot secondaryfilament splitting is avoided. Therefore, a stationary MF pat-tern is formed until the individual filament processes are ter-minated by both energy loss due to ionization and naturalbeam divergence.For our proof-of-principle experiment, we used the 1-kHzhigh-power laser facility at LOA delivering linearly polarized6-mJ, 40-fs pulses (≈ 0.15 TW) with a Gaussian-like spa-tial beam profile. A deformable mirror of 45 mm in diameterequipped with 31 piezo-electric actuators (BIM31, Silas) isapplied to manipulate the laser beam wave front, which ischaracterized by means of a commercially available Shack–Hartmann (SH) sensor (HASO, Imagine Optic). The SH sen-sor consists of a set of lenslets arranged in a matrix of 32 ×40and is placed in the plane conjugated to the deformable mir-ror to provide optimal conditions for wave front optimization.Due to the radial symmetric beam profile the wave front is ac-curately reconstructed by a set of Zernike polynoms (ZP) upto order 33.Reflected by the silver-coated deformable mirror the am-plified laser beam is focused into a gas tube, after passinga telescope to match best conditions for filamentation (Fig. 1).The 3-m-long gas tube is filled with 1.5 bar xenon and sealedwith fused silica windows (3 mm thick, 40 mm in diameter).Xenon has been chosen since it offers the lowest critical power(≈ 0.8 GW at 1.5 bar) of all (non-radiating) rare gases. It is,therefore, mostly suited to provoke the largest number of MF.In principle, air or other gases could also be used, wheneverthe laser system provides enough peak power to launch MF.FIGURE 2 (a) Beam intensity profiles in the proximity of the geometricalfocus for different wave front configurations (see Fig. 2). Intensity spots withsufficient peak power for launching filamentation are marked by dashed cir-cles for better visibility. (b) Pattern of stable multiple filamentation recordedby a CCD. The MF patterns (i)–(iv) are generated by corresponding inten-sity spot patterns depicted in (a). Each picture shows the integrated signalof 50 consecutive laser shots (integration time: 50 ms) indicating excellentstationary stabilityPlotted in Fig. 2a are four different intensity distributionsat a position a few millimeters in front of the geometrical fo-cus where filamentation is supposed to set in. The intensitypatterns are generated by imposing specific wave fronts (de-picted in Fig. 3) on the amplified input pulse by means ofthe deformable mirror. The initial Gaussian-like beam profileas well as the input energy remained unchanged throughoutthe experiment. Initially, the laser wave front was optimizedfor best flatness (rms < 0.08λ), yielding a very unstable MFpattern since P  Pcrit. Our procedure for achieving the re-quested intensity pattern in the focal plane is based on onlinediagnostics of the laser focus and manual modification of thewave front by tailoring Zernike polynomial coefficients (seebelow). This procedure was successful for the formation ofone (i), two (ii) three (iii) and more (iv) transversally separatedspots in the focal plane as shown in Fig. 2a. The individual in-tensity spots exhibit all a diameter of 100–150 µm and mostof them (indicated by dashed white circles) carry sufficientenergy for triggering self-focusing and filamentation.Filamentation driven by the laser foci shown in Fig. 2ayields the MF pattern exposed in b. Depending on the numberof intensity “hot-spots” one stationary filament (i) or multi-HAURI et al. Two-dimensional organization of a large number of stationary optical filaments by adaptive wave front control 393FIGURE 3 Wave front shaping by a deformable mirror. The wave fronts(i)–(iv) are used to generate corresponding “hot-spot” intensity profiles(Fig. 1a,(i)–(iv)) in the geometrical focus. For each wave front the corres-ponding rms and peak-to-valley (PV) values are displayedple filaments with 2, 3 and 5 individual channels are observed(ii–iv). The laser intensity patterns in the focus (a) and the cor-responding MF patterns recorded in the far field (b) are in verygood agreement. Case (i), illustrating the formation of a sin-gle filament, is generated with the beam wave front shown inFig. 2(i) deviating most of the energy outside the focal regioninto an annular profile. Three Zernike polynom (ZP) coeffi-cients have been modified, namely ZP 8 (third-order sphericalaberration, 0.14λ), ZP 6 (coma 0◦, 0.11 λ) and ZP 4 (astig-matism 0◦, 0.09λ). The remaining single intensity spot in thecenter of the beam with roughly 550 µJ is powerful enough todrive non-linear propagation while the annular part keeps itslinear propagation and does not undergo filamentation due tothe low intensity.A well-resolved twin configuration of intensity spots(a,(ii)) is generated by introducing astigmatism at 0◦ (ZP 5,0.24λ) and 45◦ (ZP 6, 0.1λ) to the initially plane wave frontresulting in a stationary formation of twin filaments (b,(ii)).The energies measured for filament 1 and 2 are 490 µJ and500 µJ, respectively. Stable MF patterns with three indepen-dent self-guided channels are depicted in (b,(iii)) with thecorresponding lateral focal spots arranged annularly aroundthe beam propagation axis (a,(iii)). In this case three-foil at90◦ (ZP 10) in combination with 5th-order astigmatism at 0◦(ZP 11) are the major aberrations leading to the measuredwave front shown in Fig. 3(iii). The energy carried by fila-ment 1 (2, 3) is 380 µJ (470 µJ, 490 µJ) and its measurementis performed in the far-field (i.e., 5 m from the filament’s end)where the well-defined self-guided core (whitelight) can eas-ily be separated from the reservoir (pure infrared radiation) bymeans of a diaphragm.The MF patterns shown in (b) are recorded by a CCD cam-era three meters after the filaments’ end. To improve the qual-ity of the pictures a color filter (BG39) was used to block thefundamental (i.e., non-filamenting) light of the amplifier andthe reservoir contribution. This filtering turned out to increasethe image contrast especially for case (i)–(iii) (Fig. 2a) wheremost of the amplifier energy does not undergo filamentationand white-light generation but simply linear propagation. Thestrong IR background signal would therefore lead to a satu-ration of the CCD. The acquisition time for each picture was50 ms, which corresponds to an integrated signal of 50 con-secutive laser shots. The well-resolved and sharp patterns inFig. 1b confirm that the role of noise in the organization of MFis tenuous in our experiment and that the spatial MF stabilityis excellent since no blurring is observed, even for a larger ac-cumulation of shots (≈ 1000). Note that for a perfectly (i.e.,diffraction-limited) focused beam with a flat wave front, onlystochastic filament patterns are observed resulting in a com-plete blurring of the pictures shown in Fig. 1b even for anaccumulation of 50 consecutive laser shots.In general, the largest possible number of stable filamentsis restrained by the pulse energy of the amplifier and thecapability of the beam wave front shaper to generate well-resolved hot spots in the focus. Our experimental conditionsas well as our simple manual procedure for shaping the wavefront allows the formation of maximal five independent fil-aments, as shown in Fig. 2b,(iv). This MF pattern demon-strates the beautiful arrangement of five individually prop-agating plasma waveguides launched by the correspondingintensity spots depicted in Fig. 2a,(iv). To achieve the com-plex energy distribution in the focus the plane laser wavefront is distorted by astigmatism at 0◦ (ZP 5), 5th-order astig-matism at 45◦ (ZP 12) and tetrafoil at 0◦ (ZP 16). The en-ergies transported in the individual filaments are measuredto be 450 µJ for filament 2 and 480–500 µJ for filament 1,3, 4 and 5, respectively. The intensity pattern in (iv) revealsthat the formation of well-resolved multi-spots is challengingby manually adapting the wavefront since the optimal wavefront is composed by a larger (> 3) number of Zernike poly-noms than required for MF pattern shown in case (i)–(iii).Not all of the visible intensity spots carry sufficient energyfor self-focusing which prevents those beams from filament-ing. Formation of more sophisticated intensity distributionsin the focal plane requires therefore an iterative or adap-tive learning algorithm to optimize a set of specific Zernikepolynoms. We believe that such an optimization procedureis of particular interest when a more powerful laser is usedfor two-dimensional arrangement of a large number of fil-aments as requested by femtosecond lidar applications, forexample.In conclusion we have demonstrated an adaptive and com-plete two-dimensional control of multiple filamentation bywave front shaping of the amplified laser beam. The de-formable mirror in combination with a Shack–Hartmann sen-sor is shown to be a powerful scheme to achieve station-ary multi-filament patterns by introducing higher-order phaseaberrations to the initial beam wave front. Such stable MFformation with up to five individual filaments can serve asa test bed to explore fundamental aspects of MF and is of in-terest for many applications including multi-beam few-cyclesources and ultrafast optical switches. The scalability of ourscheme to the TW level offers the potential for well-resolvedMF-based atmospheric remote sensing applications and forthe study fundamental aspects of MF in (turbulent) air.394 Applied Physics B – Lasers and OpticsREFERENCES1 A. Campillo, S. Shapiro, B. Suydam, Appl. Phys. Lett. 23, 628 (1973)2 A. Campillo, S. Shapiro, B. Suydam, Appl. Phys. Lett. 24, 178 (1974)3 S. Skupin, L. Berge´, U. Peschel, F. Lederer, G. Mejean, J. Yu, J. Kas-parian, E. Salmon, J.P. Wolf, M. Rodriguez, L. Woeste, R. Bourayou,R. Sauerbrey, Phys. Rev. E 70, 46 602 (2004)4 V.I. Bespalov, V.I. Tantalov, J. Exp. Theor. Phys. Lett. 3, 307 (1966)5 G. Fibich, S. Eisenmann, B. Ilan, A. Zigler, Opt. Lett. 29, 1772 (2004)6 T.D. Grow, A.L. Gaeta, Opt. Express 13, 4594 (2005)7 A. Trisorio, C.P. Hauri, Opt. Lett. 32, 1650 (2007)8 V.P. Kandidov, N. Akozbek, M. Scalora, O.G. Kosareva, A.V. Nyakk,Q. Luo, S.A. Hosseini, S.L. Chin, Appl. Phys. B 80, 267 (2005)9 G. Mechain, A. Couairon, M. Franco, B. Prade, A. 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Two-dimensional organization of a large number of stationary optical filaments by adaptive wave front control

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Two-dimensional organization of a large number of stationary optical filaments by adaptive wave front control

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