July 1, 1998 / Vol. 23, No. 13 / OPTICS LETTERS 1043

Wave-front correction of femtosecond terawatt lasersby deformable mirrors

Frederic Druon, Gilles Cheriaux, Jerome Faure, John Nees, Marc Nantel, Anatoly Maksimchuk, andGerard Mourou

Center for Ultrafast Optical Sciences, University of Michigan, 1006 I.S.T. Building, 2200 Bonisteel Boulevard,Ann Arbor, Michigan 48109-2099

Jean Christophe Chanteloup

Laboratoire pour l’utilisation des Lasers Intenses (LULI), Centre National de la Recherche Scientifique (CNRS), Unite Mixtede Recherche 7605, Ecole Polytechnique 91128 Palaiseau Cedex, France

Gleb Vdovin

Department of Electronic Instrumentation, Technical University of Delf t, P.O. Box 5031, 2600 GA Delf t, The Netherlands

Received March 2, 1998

Wave-front correction and focal spot improvement of femtosecond laser beams have been achieved, for thefirst time to our knowledge, with a deformable mirror with an on-line single-shot three-wave lateral shearinginterferometer diagnostic. Wave-front distortions of a 100-fs laser that are due to third-order nonlinear effectshave been compensated for. This technique, which permits correction in a straightforward process thatrequires no feedback loop, is also used on a 10-TW Ti:sapphire–Nd:phosphate glass laser in the subpicosecondregime. We also demonstrate that having a focal spot close to the diffraction limit does not constitute a goodcriterion for the quality of the laser in terms of peak intensity. 1998 Optical Society of America

OCIS codes: 160.0160, 320.0320, 320.7080.

The chirped pulse amplif ication (CPA) technique1

has facilitated the development of ultrashort, high-intensity pulsed lasers. For many applications ofCPA lasers, such as development of ultrafast x-raysources, electron acceleration, and relativistic plasmaphysics, experimentalists are interested in reachingthe highest intensity focused on a target.2,3 Mostefforts toward achieving these higher intensities havebeen concentrated on increasing the energy, reducingthe pulse duration, and temporally cleaning the pulsesfrom the CPA systems. Although they are oftenneglected, the wave-front distortions of the beam arealso crucial elements that need to be considered indesigning for optimum intensity. In fact, the wavefronts of multiterawatt lasers, because of nonlineareffects and diffraction on the elements used in the CPAsystem, suffer from distortions of as much as severalwavelengths.4 These distortions can significantlyaffect the spatial quality and thus the focusability ofthe beam, thereby severely reducing the attainablefocused intensity. Furthermore in many experimentsa spatially clean beam will prevent undesired effectsfrom arising from the energy deposited outside thecentral focal spot. Correction of the wave front andbetter confinement of the energy are thus more cost-effective solutions than adding one more amplifierstage to the laser chain. In this Letter we presentand demonstrate a simple and reliable method for thecorrection of wave-front distortions of lasers beamsthat uses three-wave interferometry and deformablemirrors.

To quantify the peak focused intensity we use thenormalized Strehl ratio, which is the ratio of the peak

0146-9592/98/131043-03$15.00/0

intensity at focus of a beam with a distorted wave frontand a near-field intensity profile to that of the sameintensity distribution with a f lat wave front. To mea-sure wave-front distortion with good accuracy we usean achromatic three-wave lateral shearing interferom-eter,5,6 which has been shown to be particularly wellsuited to single-shot measurement of phase and inten-sity profiles of femtosecond pulses.4 Using the resultsobtained with this wave-front sensor, we can calcu-late the Strehl ratio and quantify accurately the lossin the peak intensity at focus. To correct the wavefront we use one of two deformable mirrors with 19and 37 actuators. These mirrors are originally f lat towithin 0.05 mm (rms), but when a voltage is applied toone actuator the mirror is locally deformed; the overalldeformation given by the whole set of actuators de-fines the new mirror shape. With these tools, a simpleand straightforward process of correction is elaborated.All the measurements are made in the near f ield ofthe laser beam, where the deformable mirror is located(Fig. 1), and the effect of each actuator on the wavefront can be quantified and located precisely. First,we establish a map of the mirror by measuring thewave-front distortion created by each actuator indi-vidually. This mapping has to be done only once andcan be processed with any collimated laser beam. Thesecond step consists in the measurement of the dis-torted wave front that needs to be corrected (Fig. 1).We then use this image of the distorted wave front tofind the set of voltages to be applied to the actuatorsfor the most efficient correction. The optimal mirrorshape is found with a linear algebraic method, whichconsists in minimizing the amplitude of the wave front

1998 Optical Society of America

1044 OPTICS LETTERS / Vol. 23, No. 13 / July 1, 1998

Fig. 1. Experimental setup for measurement and correc-tion of the wave front. The deformable mirror is imagedon the CCD, so the wave front is measured in this plane,which is considered to be the near f ield of the laser beam.A telescope made with two lenses s f1, 1 m; f2, 25 cmd isused to create a Fourier plane. This plane is the far fieldof the laser beam, where a pinhole can be inserted to spa-tially clean the phase of the beam. ATWLSI; achromaticthree-wave lateral shearing interferometer.

by projecting the image of the distorted wave front onthe basis of the actuators. The displacements of theactuators are not independent from one another, andas we move one actuator a small displacement is cre-ated on its neighbors. This effect is taken into accountwhen the system is solved. The main advantage ofthis method is that all the measurements are madeon the wave front in the near f ield directly and not onthe image of the focal spot, which is in the far field.That is why the wave front can be corrected in a singleshot with a linear algebraic algorithm, which doesnot require any feedback loop. We present results ob-tained with this new method applied for two importantcases: the correction of wave-front distortions that aredue to the third-order nonlinear effect and the correc-tion of terawatt-type system wave fronts.

At high intensity levels the third-order nonlineareffect can cause wave-front distortions in even a smallamount of material and, thus, significantly decreasethe peak intensity of the focal spot. To perform ademonstration experiment, we focus a 100-fs, 5-mJpulse from a 780-nm, 10-Hz Ti:sapphire laser7 througha 50-cm focal-length lens into a 1.33-cm-thick piece ofglass inserted in the path of the beam to create someB-integral distortion. For correction we use a micro-machined adaptive mirror8 of 1-cm diameter controlledby 19 electrostrictive actuators. The measured dis-torted wave front is shown in Fig. 2(b). These wavefronts are averaged over f ive shots at 10-Hz to decrease

Fig. 2. Experimental results for correction of a wave front that is distorted by third-order nonlinear effects: (a) intensityprofile of the distorted beam, (b) measured phase profile of the distorted beam (amplitude, 0.67l), (c) calculated phaseprofile applied to the deformable mirror for wave-front correction, (d) measured phase profile of the corrected beam(amplitude, 0.28l).

the inf luence of shot-to-shot f luctuation of the laser.As expected, this wave front is proportional to theintensity profile [Fig. 2(a)] with a peak value of 0.67l,which is equivalent to a B integral of 4.1. The Strehlratio for this distortion is 57%. Figure 2(c) showsthe phase compensation given by the adaptive mirror.This f igure is similar to that for the distorted wavefront but is smoother because of the slow spatialvariation of the actuators. Thus the final, measuredcorrected phase [Fig. 2(d)] prominently shows thefast-varying background. The amplitude is now0.28l, and the Strehl ratio has increased to 88%. Thefocal intensity is 1.54 greater than without correction.Second, because third-order nonlinear effects arelinearly dependent of the intensity, the B-integralwave-front correction for CPA lasers is limited by thestability of the laser output intensity. This correctionthat is based on an integrated measurement over thepulse duration cannot fit the B integral distortions,which are instantaneous, during the entire pulse.

The second experiment with this new technique isperformed on the hybrid Ti:sapphire–Nd:phosphateglass laser, which delivers 450-fs pulses of energy upto 2.5 J. In this CPA system, in which the size ofthe output beam is 5 cm, distortions of the wave fronteasily reach an amplitude of l, even at low energy. Infact, good quality for optics of this size is expensiveand difficult to obtain, a fact that further motivatesus to correct the wave front with adaptive optics. Toimprove the focusability of the complete system wecorrect the wave front at the end of the laser chainat low energy. In this case we wanted to compensatefor the distortions that are independent of the energy,such as those that occur in the optical compressorelements. For the correction we use a Xinetics mirrorwith 37 electrostrictive actuators and a diameter of5 cm. To correct the wave front we compare themeasured distorted wave front with a reference f latwave front that we obtain by putting a pinhole inthe Fourier plane. The goal of the correction is toset the voltages on the deformable mirror to yield awave-front distribution as close as possible to thatof the reference. The measured distorted wave frontis shown in Fig. 3(a) (Phase A), and the correctedmeasured wave front is shown next to it on thesame scale (Phase B). We improved the wave front bydecreasing the distortions from 0.7l to 0.3l (peak-to-peak value). The Strehl ratio was thus increased from35% to 88%, or by a factor of 2.5. The computation of

July 1, 1998 / Vol. 23, No. 13 / OPTICS LETTERS 1045

Fig. 3. (a) Experimental results for a distorted wavefront (Phase A) and a corrected wave front (Phase B) forthe 10-TW Ti:sapphire–Nd:phosphate laser, with peak-to-peak values of, respectively, 0.7l and 0.3l. The figurebelow the phases represents line-outs of the focal spotscalculated with the intensity and phase measurements: Awith Phase A, B with Phase B, and C with a f lat phase.For each of these curves the FWHM normalized to thediffraction-limited spot is indicated. (b) Experimentalspot sizes A, without correction and B, with correction.The figure below spots A and B represents line-outs of thesefocal spots.

the far-field intensity distribution with the measuredintensity and phase is represented in Fig. 3(a): PhaseA without correction, Phase B with correction, andPhase C with a f lat wave front (diffraction limited).The FWHM normalized to the diffraction-limited spotfor each beam has also been calculated to show that asignificant loss in the peak intensity at focus does notnecessarily lead to a large broadening of the spot. Infact, the noncorrected wave front has a broadening ofonly 1.29 for a loss of the maximum focused intensityby a factor of 3.

The experimental results of measurements of thetwo focal spots are shown in Fig. 3(b). These spotswere measured at the focus of a 1-m focal-length lensin plane F of Fig. 1. In Fig. 3(b), spot A is the onewithout correction and spot B is the one with theapplied voltages on the mirror that were found fromthe measurement of the wave front. The plots belowspots A and B show line-outs of these spots. Theresults fit well with the previous calculations basedon the wave-front measurements, and they clearlyshow an improvement of the focal spot intensity bya factor of 1.7. In fact, the small difference fromthe previous estimated result can be explained bythe experimental setup: To measure the spot sizeswe added an additional mirror, some density filtersto attenuate the beam, and a microscope objective for

the imaging. All these new elements introduce somedistortions to the wave front, which were not taken intoaccount during the correction process.

In summary, single-shot wave-front characterizationof femtosecond laser beams by use of an achromaticthree-wave lateral shearing interferometer ATWLSIand subsequent correction with an adaptive mirror hasyielded significant improvement in the focusability ofa 100-fs 780-nm beam distorted by nonlinear effectsand also in a 450-fs 1053-nm terawatt-type system.The correction of the B integral with this on-line wave-front sensor promises to be interesting for manyapplications that are now limited by the B-integralwave-front distortion and self-focusing. Another ap-plication of this new system of wave-front correction,because of its straightforward process, is for multi-joule terawatt laser systems to compensate for thedistortions from the large optics and, eventually, forthe thermal effect in glass amplif iers, which couldallow the focused peak intensity of a system to be in-creased without increasing the energy. Furthermore,in many experiments a spatially clean beam will alsoprevent undesired effects that arise from energy de-posited outside the central focal spot. The correctionof the wave front by a deformable mirror permits bothspatial cleaning of the beam and a sizable gain in thepeak intensity on target. Finally, we show that usingthe close-to-diffraction-limited focal spot criterion toevaluate the quality of laser chain and focusing is mis-leading and does not represent well the actual Strehlratio deterioration of severe wave-front distortion.

This research was supported by the National Sci-ence Foundation (NSF) through the Center for Ul-trafast Optical Science (CUOS) under contract STCPHY 8920108. LULI and CUOS acknowledge a NSF–CNRS collaboration (grant 94N92/0043).

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