Includes bibliographical references (pages 183901-4).We report direct measurement of the electromagnetic-field spatial distribution in a neonlike Ar capillary discharge-driven soft x-ray laser beam. The wave front was fully characterized in a single shot using a Shack-Hartmann diffractive optics sensor. The wave front was observed to be dependent on the discharge pressure and capillary length, as a result of beam refraction variations in the capillary plasma. The results predict ~70% of the laser beam energy can be focused into an area 4 times the size of the diffraction-limited spot, reaching intensities of ~4 × 1013 W/cm2

Aeitoun, Ph.

Dhez, P.

François, M.

Idir, M.

Le Pape, S.

Rocca, Jorge J.

English

We report direct measurement of the electromagnetic-field spatial distribution in a neonlike Ar capillary discharge-driven soft x-ray laser beam. The wave front was fully characterized in a single shot using a Shack-Hartmann diffractive optics sensor. The wave front was observed to be dependent on the discharge pressure and capillary length, as a result of beam refraction variations in the capillary plasma. The results predict ~70% of the laser beam energy can be focused into an area 4 times the size of the diffraction-limited spot, reaching intensities of ~4 × 1013 W/cm2

François, M., author

Rocca, Jorge J., author

Dhez, P., author

Idir, M., author

Aeitoun, Ph., author

Le Pape, S., author

American Physical Society, publisher

Mountain Scholar (Digital Collections of Colorado and Wyoming)

VOLUME 88, NUMBER 18 P H Y S I C A L R E V I E W L E T T E R S 6 MAY 200218390Electromagnetic-Field Distribution Measurements in the Soft X-Ray Range:Full Characterization of a Soft X-Ray Laser BeamS. Le Pape, Ph. Zeitoun, M. Idir, and P. DhezLaboratoire de Spectroscopie Atomique et Ionique, Bâtiment 350, Université Paris-sud, 91405 Orsay, FranceJ. J. RoccaDepartment of Electrical and Computer Engineering, Colorado State University, Fort Collins, Colorado 80523-1373M. FrançoisInstitut d’Electronique et de Microélectronique du Nord, Université des Sciences et Technologie de Lille,avenue Poincaré BP 69, 59652 Villeneuve d’Ascq, France(Received 6 July 2001; published 18 April 2002)We report direct measurement of the electromagnetic-field spatial distribution in a neonlike Ar capillarydischarge-driven soft x-ray laser beam. The wave front was fully characterized in a single shot using aShack-Hartmann diffractive optics sensor. The wave front was observed to be dependent on the dischargepressure and capillary length, as a result of beam refraction variations in the capillary plasma. Theresults predict 70% of the laser beam energy can be focused into an area 4 times the size of thediffraction-limited spot, reaching intensities of 4 3 1013 Wcm2 .DOI: 10.1103/PhysRevLett.88.183901 PACS numbers: 42.55.Vc, 41.50.+h, 52.58.Lq, 52.59.YeFor several decades, synchrotrons have been used as softx-ray sources for applications in disciplines ranging frombiology [1] to solid state physics [2]. The past several yearshave witnessed the emergence of high brightness table-top soft x-ray sources: high harmonic generation sources[3–5], and saturated soft x-ray lasers (SXRL) pumped byeither fast capillary discharges [6] or optical lasers [7].High order harmonics sources have been reported to gen-erate radiation at wavelengths as short as 2.7 nm at 1 kHzrepetition rate. Typically about 108 coherent photons perharmonic per pulse are generated in the spectral range from50 to 13 nm in pulses as short as several femtoseconds. Inturn, SXRL may produce very energetic pulses (more than1014 photons per pulse) at lower repetition rates. SaturatedSXRL amplification has been achieved at wavelengths asshort as 5.8 nm [8]. SXRL lasers have been used in sev-eral experiments that include the diagnostics of high den-sity plasmas relevant to inertial confinement fusion [9],and spatial interferometry of a niobium surface deformedby an ultrahigh electric field [10]. Of particular interestfor applications are tabletop capillary-discharge soft x-raylasers that can be fired repetitively to generate an averagepower of several mW with a very high degree of spatialcoherence [11].The development of these tabletop coherent soft x-raysources opens a wide field of applications in several disci-plines using techniques such as interferometry, phase con-trast imaging, and microscopy. Although an increase of thespatial coherence is important, the beam wave front mustalso be improved for such experiments. Indeed, imaginga sample with a phase contrast microscope and a coher-ent source having an aberrated wave front will result in aloss of resolution. On the other hand, wave front charac-terization can also impact applications such as two-photon1-1 0031-90070288(18)183901(4)$20.00ionization in the soft x-ray range, which requires focusingof the beam into a spot of micrometer dimension to reachradiation intensities of the order of 1013 W cm22. Surpris-ingly, despite its key role in applications, the wave front oftabletop soft x-ray sources had not been measured prior tothis work. A technique frequently used to obtain aberra-tion-free wave fronts consists in spatially filtering the beamby placing a small pinhole (typically 1 mm diam [12])at the focal spot of a focusing optic. However, since inmost cases the incoming beam is aberrated, the filteredbeam power is reduced by several orders of magnitudecompared to the incoming beam [12]. In contrast, coherentbeam brightness might be greatly increased by directly op-timizing the source parameters to improve the beam wavefront. Such development requires detailed maps of thewave fronts.With this objective, we have developed an extreme ul-traviolet (EUV) Shack-Hartmann wave front sensor. Thesensor is an extrapolation to the soft x-ray range of a tech-nique used in the visible spectral range [13]. In relatedwork, a point source diffraction interferometer has beenpreviously realized to test EUV lithography optics usingsynchrotron radiation [14]. The Shack-Hartmann wavefront sensor is based on mapping the wave vectors at nu-merous locations across the wave front. The beam pupilis sampled by a matrix of lenslets, each focusing a smallfractional area of the laser beam onto a detector. The focalspot positions are directly related to the local wave frontslope, whereas the spot intensity is associated with the lo-cal electric field amplitude. Such a diagnostic allows thereconstruction of the electromagnetic field in a single shotmeasurement. The measurements reported herein allowedthe full characterization of the electromagnetic field distri-bution in a tabletop capillary discharge pumped soft x-ray© 2002 The American Physical Society 183901-1VOLUME 88, NUMBER 18 P H Y S I C A L R E V I E W L E T T E R S 6 MAY 2002laser operating at a wavelength of 46.9 nm lSXRL in the3s 1P1-3p 1S0 line of Ne-like Ar [6]. The gain medium isan elongated plasma column generated in a capillary chan-nel by a fast discharge current pulse. The magnetic forceof the current pulse rapidly compresses the plasma to forma dense and hot column with length-to-diameter ratios ofnearly 1000:1. Gain saturation is reached after amplifica-tion in a 14 15 cm long column. The capillary lengthused in most of the present experiment was 35 cm, whichcorresponds to a highly saturated amplifier. The output en-ergy increases by nearly a factor of 10 while the plasmacolumn is elongated from 16 to 35 cm.Figure 1 illustrates the experimental setup used in thewave front measurements. The wave front sensor wasplaced at 2.5 m from the capillary end in order to optimizethe spatial sampling of the beam. The soft x-ray Shack-Hartmann wave front sensor is composed of an array of200 diffractive lenses working in reflection at an incidenceangle of 22.5±. Diffractive lenses were chosen becausethey do not generate aberration while working off axis.The lenses that have a radius of 700 mm were etched ona 1 in. diam flat silicate substrate. Each lens has nine cir-cular grooves, the outer one with a width of 26 mm. Thegroove’s height was selected such that the waves reflectedfrom the bottom and from the top of the groove profileare in phase, leading to the highest focusing efficiency. A1000 Å layer of iridium was coated on the entire substratesurface to provide 10% reflectivity. The selected focallength of 50 cm leads to a resolution on the wave frontslope of 0.1 mrad, corresponding to lSXRL300 on thewave front. The focal spots were recorded with a cooledback-illuminated CCD array of 1300 3 1340 pixelsplaced at the focal plane of the lenses. The capillarydischarge SXRL is sufficiently powerful to record highcontrast images in a single shot, avoiding errors that oth-erwise might possibly arise from shot-to-shot variations.In fact, the laser beam had to be significantly attenuatedto avoid saturation of the detector. This was accomplishedwithout altering the wave front by leaking a controlledamount of Ar gas in the detector chamber. Figure 1includes an image acquired in the focal plane of the lensarray, displaying the array of focal spots correspondingto each of the microlenses. To obtain absolute wavefront measurements, it is crucial to measure wave frontdistortions that can be caused by the substrate using aspherical wave front. Indeed, the lenses are etched on a6-mm thick substrate, where deformations can induce anartificial shift of the focal spots. The substrate planarity isl20 with l  0.6 mm, which is equivalent to 0.7lXRL.In addition, the stress caused by the mirror holder cancause deformations of several lXRL of amplitude. Wecreated a reference spherical wave front by diffractingthe laser beam with a 10 mm diameter pinhole placed at2.2 m from the sensor. The absolute SXRL wave frontis obtained by substraction of this reference wave fromthe laser wave front. A comparison of the positions of183901-2FIG. 1. Schematic representation of the experimental setupshowing an image of the lens array and corresponding imageof focal spots. The angle between the incident and reflectedbeams is 45±. The lighter parts of the image correspond to thebrighter part of the beam.the focal spots corresponding to the reference wave witha regular mesh clearly showed an increasing displacementof the focal spots from the beam center to the side,resulting from the increasing wave front slope on the sideof the spherical wave.Since the x-ray laser under study is fully coherent, thereis a unique phase relation between every point on the de-tector, and, consequently, the wave front shape can be re-constructed from the focal spot positions shown in Fig. 1.A program was developed to estimate each focal spot cen-troid with an accuracy of about 1022 pixels. The wavefront was subsequently reconstructed with a second pro-gram based on the algorithm written by Southwell [13].The phase in each point was calculated by using a Gauss-Seidel method, which has been chosen for its convergencespeed and its accuracy. The accuracy of the wave frontreconstruction is 1023lXRL.We have investigated the variation of the wave frontcharacteristics as a function of the argon pressure in thecapillary discharge laser channel. The results of mea-surements corresponding to discharge pressures of 200,420 (near the optimum for maximum laser power), and660 mTorr are shown in Fig. 2. The Shack-Hartmannwave front sensor allows the detection of aberration ampli-tudes of 1100 of the maximum peak. For all pressures, thewave front is nearly a divergent spherical wave with a cur-vature radius of almost 6.5 m. The wave front shape andradius are observed to be dominantly determined by beamrefraction in the discharge-pumped amplifier induced bythe radial electron density gradient in the capillary plasmacolumn [15]. It is also refraction that dominantly deter-mines the annular beam shape observed in Fig. 2a. Twogeneral trends are observed for each pressure: (i) Thewave front is smoother in the center of the beam; (ii) theamplitude of wave front defects decreases as the pressure isincreased (from 7lXRL rms at 200 mTorr, to 3lXRL rmsat 660 mTorr). The defects are evaluated by subtractingthe XRL wave front from a best-fit spherical wave front.This decrease in wave front aberration at increased pres-sure results from the smoother electron density gradients183901-2VOLUME 88, NUMBER 18 P H Y S I C A L R E V I E W L E T T E R S 6 MAY 2002FIG. 2. Wave front shape (left) and corresponding intensity distributions (right) for different discharge pressures [(a)– (c)]. Theradius of curvature of the wave front is 6.5 m. The annular shape of the beam at the lower pressures is due to increased refraction.and reduced refraction that are a consequence of reducedplasma column compression at the higher discharge pres-sures. The XRL shot-to-shot wave front stability was alsoinvestigated making several measurements for each pres-sure. The shot-to-shot wave front variation was determinedto be 0.22lXRL.The measured wave front characteristics discussedabove, which correspond to a 35 cm long capillary, wereused to simulate the intensity distribution of the laser beamat the focal spot of an f  50 mm diffraction-limitedoptic. Notice that if we had used only the measurementof the wave front shape the energy distribution in thefocal plane would have been inexact, as it results fromthe convolution of the wave front shape with the intensitydistribution in the beam. The energy distribution in thefocal plane was calculated for the three different pressuresat which the wave front and the corresponding intensitydistribution were measured. The results are shown inFigs. 3a–3c. The most notable changes are observed in theintensity distribution at the foot of the beam, and are a re-sult of the wave front improvement at the higher pressures[from 7lXRL rms at 200 mTorr in Fig. 3a to 3lXRL rmsat 660 mTorr in Fig. 3c]. At the pressure of 660 mTorr,the focal spot diameter is estimated to be approximately0.3 mm, and increases in size as the pressure is reducedreaching 0.7 mm at a pressure of 200 mTorr. Of particularinterest are the results of Fig. 3b, corresponding to thenearly optimum laser operating pressure of 420 mTorr atwhich laser pulse energies approaching 1 mJ can be gen-erated. At this pressure the distribution exhibits a strongpeak that includes 70% of the total laser beam energy in a183901-30.5 mm focal spot. The focal spot is estimated to be only5 times larger than the area of a diffraction-limited beam,corresponding to an intensity of about 4 3 1013 W cm22assuming one reflecting surface with 50% reflectivity.In contrast, significantly shorter capillary lengths wereobserved to result in a much larger focal spot. Figure 4shows the energy distribution in the focal plane for an18 cm long capillary discharge operated at 420 mTorr. Inthis case, the energy is spread out over a surface area ofabout 70 3 70 mm2, with large secondary peaks causedby strong aberrations on the SXRL wave front. About 5%of the total energy in the beam is focused onto a 4 mmdiameter focal spot. This result is in good agreement witha previous focusing experiment [16], where 3% of thebeam energy was focused onto a 2 mm diameter focalspot. At the time of the experiment, it was not possibleto perform the same measurement but for the longestcapillary due to the need to sample the focal spot withan accuracy of typically 0.03 mm. The improvement ofthe focusing characteristics of the beams generated by thelonger capillaries is a result of the spatial filtering inducedby beam refraction in the capillary. This effect is alsoresponsible for the previously observed enhancement ofthe degree of spatial coherence with capillary length.In summary, we have measured for the first time theabsolute electromagnetic field of a soft x-ray laser. Asoft x-ray Shack-Hartmann sensor was used to gather ina single shot the data required for the reconstruction ofthe electromagnetic field corresponding to a capillary dis-charge soft x-ray laser. The results suggest it should bepossible to focus the output of capillary discharge lasers183901-3VOLUME 88, NUMBER 18 P H Y S I C A L R E V I E W L E T T E R S 6 MAY 2002FIG. 3. Simulated beam intensity distributions of the laserbeam of a 35 cm long capillary discharge at the focal spot ofan f  50 mm diffraction-limited optics for three different dis-charge pressures. The figure shows zooms of the foot of thefocal spot. The ratio between peak and foot amplitude 120is selected to be the same in all cases.onto near diffraction-limited spots, achieving unprece-dented soft x-ray power densities. The use of thistechnique to obtain detailed knowledge of the electromag-netic field distribution of different tabletop short wave-length sources will allow their improvement for use in anew variety of applications ranging from phase contrastimaging a beam focusing onto submicron focal spots.183901-4FIG. 4. Simulated beam intensity distribution of the laser beamproduced by an 18 cm long capillary discharge at the focal spotof an f  50 mm diffraction-limited optics for a discharge pres-sure of 420 mTorr.This work was supported by the National Science Foun-dation, the U.S. Department of Energy, Chemical Sciences,Geosciences and Biosciences Division of the Office ofBasic Energy Sciences, and by the contract NSF/CNRSNo. 9153. We also acknowledge support from the W. M.Keck Foundation.[1] C. A. Larabell, D. Yager, and M. Meyer-Ilse, in Proceed-ings of the Sixth International Conference on X-ray Mi-croscopy, Berkeley, 1999, edited by W. Meyer-Ilse, T. War-wick, and D. Attwood (American Institute of Physics, NewYork, 2000), p. 107.[2] S. Hüfner, Photoelectron Spectroscopy (Springer-Verlag,Berlin, 1996), 2nd ed.[3] A. L’Huillier and Ph. Balcou, Phys. Rev. Lett. 59, 56(1987).[4] Z. Chang et al., Phys. Rev. Lett. 79, 2967 (1997).[5] A. Rundquist et al., Science 280, 1412 (1998).[6] B. R. Benware et al., Phys. Rev. Lett. 81, 5804 (1998).[7] J. Dunn et al., Phys. Rev. Lett. 84, 4834 (2000).[8] R. Smith et al., Phys. Rev. A 59, R47 (1999).[9] L. B. Da Silva et al., Phys. Rev. Lett. 74, 3991 (1995).[10] Ph. Zeitoun et al., Nucl. Instrum. Methods Phys. Res.,Sect. A 416, 189 (1998).[11] Y. Liu et al., Phys. Rev. A 63, 033802 (2001).[12] D. Attwood, in Soft X-rays and Extreme Ultraviolet Radi-ation: Principles and Applications (Cambridge University,Cambridge, England, 2000), p. 318.[13] W. H. Southwell, J. Opt. Soc. Am. 70, 8 (1980).[14] H. Medecki, E. Tejnil, K. Goldberg, and J. Bokor, Opt.Lett. 21, 1526 (1996).[15] C. H. Moreno et al., Phys. Rev. A 58, 1509 (1998).[16] B. R. Benware et al., Opt. Lett. 24, 1714 (1999).183901-4

Electromagnetic-field distribution measurements in the soft s-ray range: full characterization of a soft x-ray laser beam

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Electromagnetic-field distribution measurements in the soft s-ray range: full characterization of a soft x-ray laser beam

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