Includes bibliographical references (page 957).A soft-x-ray Mach-Zehnder interferometer configuration that makes use of the time delay introduced by diffraction gratings to conduct single-shot measurements of the linewidth of soft-x-ray laser amplifiers is proposed and analyzed. The scheme was experimentally demonstrated in the near-IR region of the spectrum by measurement of the mode separation of a semiconductor laser. A symmetric configuration with compensated time delays that can be implemented for plasma diagnostics and for evaluating soft-x-ray optics is also discussed

Chilla, Juan L. A.

Marconi, Mario C.

Martinez, Oscar E.

Rocca, Jorge J.

English

A soft-x-ray Mach-Zehnder interferometer configuration that makes use of the time delay introduced by diffraction gratings to conduct single-shot measurements of the linewidth of soft-x-ray laser amplifiers is proposed and analyzed. The scheme was experimentally demonstrated in the near-IR region of the spectrum by measurement of the mode separation of a semiconductor laser. A symmetric configuration with compensated time delays that can be implemented for plasma diagnostics and for evaluating soft-x-ray optics is also discussed

Chilla, Juan L. A., author

Martinez, Oscar E., author

Rocca, Jorge J., author

Marconi, Mario C., author

Optical Society of America, publisher

Mountain Scholar (Digital Collections of Colorado and Wyoming)

July 1, 1996 / Vol. 21, No. 13 / OPTICS LETTERS 955Soft-x-ray interferometer for single-shotlaser linewidth measurementsJuan L. A. Chilla and Jorge J. RoccaDepartment of Electrical Engineering, Colorado State University, Fort Collins, Colorado 80523Oscar E. Martinez and Mario C. MarconiDepartamento de Fı́sica, Universidad de Buenos Aires, 1428 Buenos Aires, ArgentinaReceived January 23, 1996A soft-x-ray Mach–Zehnder interferometer configuration that makes use of the time delay introduced bydiffraction gratings to conduct single-shot measurements of the linewidth of soft-x-ray laser amplifiersis proposed and analyzed. The scheme was experimentally demonstrated in the near-IR region of thespectrum by measurement of the mode separation of a semiconductor laser. A symmetric configuration withcompensated time delays that can be implemented for plasma diagnostics and for evaluating soft-x-ray optics isalso discussed.  1996 Optical Society of AmericaThere is significant interest in the measurement ofthe linewidths of soft-x-ray lasers and their varia-tion with amplif ication, because of the linewidths’fundamental importance to gain, radiative transport,and amplifier performance.1,2 The profile of unam-plified plasma lines is the result of Doppler broaden-ing, Stark broadening, and collisional rates and canalso be inf luenced by effects such as plasma turbu-lence.3 Radiation transport also can strongly inf lu-ence the line profile, as reabsorption broadens the line.In the case of amplified lines the line profiles nar-row as a function of plasma length in the nonsatu-rated amplification regime, and they can rebroadenlater as the amplification saturates if the intrinsicprofiles of the lines are dominated by inhomogeneousbroadening. These measurements are, however, dif-ficult to perform, because of the very high resolutionrequired, typically Dlyl , 1024. Recently the f irstlinewidth measurements of amplified soft-x-ray laserlines were performed at Lawrence Livermore NationalLaboratory.2 In those experiments the line profiles ofsome of the soft-x-ray laser lines pumped by the Novalaser facility were measured with a sophisticated high-resolution grazing-incidence spectrograph, with a dis-tance of more than 8.5 m between the laser plasma andthe detector plane. Although such instruments have aresolution of approximately 30 000, their cost and sizecan make them inaccessible to many of the smaller re-search groups currently involved in the development ofcompact tabletop soft-x-ray laser sources.4 – 7The high intensity of soft-x-ray lasers makes itpossible to perform high-resolution line profile mea-surements by use of interferometric techniques.Interferometric techniques have been widely usedto measure the linewidths of visible lasers. How-ever, interferometric measurement of line profilesin the soft-x-ray regime is signif icantly more diff i-cult. A soft-x-ray interferometer that uses thin-filmmultilayer beam splitters has been implemented atLawrence Livermore National Laboratory and hasbeen demonstrated in the diagnostics of dense laser-0146-9592/96/130955-03$10.00/0created plasmas.8 Recently a linewidth measurementof the neonlike yttrium x-ray laser was performedinterferometrically; the decay of the contrast of theinterference fringes was measured as a function ofthe detuning of the length of one of the arms of theinterferometer for a sequence of soft-x-ray laser shots.9In this Letter we propose and investigate a novelsoft-x-ray interferometer design that takes advan-tage of the time delay introduced by diffractiongratings to conduct single-shot measurements ofthe soft-x-ray laser line profiles. The lateral de-lay introduced by gratings was previously used forthe construction of single-shot autocorrelators forthe measurement of ultrashort pulses.10 The newtype of compact (, 1 m in length) Mach–Zehnderinterferometer that we propose has a resolutionof 90 000 when constructed with 5-cm-wide grat-ings of 600 groovesymm. It has the advantagesof allowing one to perform line profile measurementsin a single shot and of not requiring the use ofsophisticated x-ray beam splitters. It also can beconstructed with off-the-shelf gratings, in which allthe ref lections are at grazing incidence, with the con-sequent high throughput without the need of specialcoatings. A visible Mach–Zehnder interferometerthat uses gratings as beam splitters has been used totest f ine-ground surfaces at grazing incidence.11 Thedesign of a soft-x-ray Smartt interferometer that usesa grating to improve efficiency was recently discussedby Bokor et al.12The layouts of two possible conf igurations of the pro-posed interferometer are depicted in Fig. 1. Both con-figurations (a and b) consist of two f lat gratings (G1and G2) acting as beam splitters in a Mach–Zehnderarrangement. In both cases the beams are redirectedby ref lections in mirrors (M1–M4) so that after diffrac-tion on the second gratings they emerge collinearly andthe astigmatism of the system is compensated. Theinterference pattern produced can be recorded in a two-dimensional CCD detector. One can obtain interfer-ence fringes in any desired density and parallel to the 1996 Optical Society of America956 OPTICS LETTERS / Vol. 21, No. 13 / July 1, 1996Fig. 1. Proposed Mach–Zehnder interferometer conf igu-rations with gratings G1 and G2 acting as beam splitters.Configurations a, with compensated delay, and b, with non-compensated delay, are shown.plane of the system by introducing a slight inclina-tion in the perpendicular direction. On incidence upongrating G1, the x-ray laser beam is diffracted into dif-ferent orders. By properly choosing the incidence an-gle and blaze of the grating, one can ensure that mostof the incoming energy is split evenly between the zeroand the first diffraction orders.As can be readily shown with geometric considera-tions, light diffracted in the f irst order acquires atransverse-position-dependent delay. In the sim-plest conf iguration depicted in Fig. 1a, there is oneref lection in each branch. The consequent inversionexperienced by the beams compensates for the de-lays introduced by G1 and G2. One can adapt thisconfiguration to conduct plasma diagnostics or totest soft-x-ray optics by introducing the sample intothe optical path of one branch and using the otherbranch as a reference. In the second configurationthe delays introduced by the gratings are not com-pensated. When additional inversion (ref lection) isintroduced into the first-order branch of the interfer-ometer the delays introduced by both gratings addup, so that the interfering beams have a relativedelay that depends on the transverse position on thedetector. An extra ref lection is also necessary in thezero-order branch (Fig. 1b) because of the low spatialcoherence of existing x-ray lasers. Any vertical (outof the plane of the page) cross section will show thetypical oscillatory behavior of two interfering lightbeams, but the visibility of the fringes will dependon the horizontal (in-plane) position on the detector.Close to the center of the beam, where both paths areequal, the visibility will be maximum, and toward theedges of the detector the visibility will drop becauseof the finite coherence length (inverse linewidth) ofthe laser source. The line profile can be obtained asthe Fourier transform of the delay dependence of thevisibility of the fringes.13 If several laser lines areemitting, their effect will be evident as modulations inthe delay dependence of the visibility. All the spec-tral information is obtained in a single shot of thelaser. The calibration of the path difference Dz of thesystem is given by Dz ­ 2xlysd cos gd, where x denotesthe distance measured on the detector plane, d is thegroove spacing, and g is the incidence angle on the f irstgrating. A conservative estimate of the resolution isobtained when we require that the visibility decay to1ye of its maximum value within the range of delayof the system. The resulting resolution depends onthe grating size a and is given by Dlyl ­ dyspad.Because of the inverse Fourier relationship, the spatialresolution of the detector does not limit the resolutionbut instead puts a limit on the maximum linewidthobservable with the interferometer.To demonstrate the feasibility of the aparatus,experiments were conducted in the near-IR regionof the spectrum by use of a vertical-cavity surface-emitting laser diode,14 which could be adjusted to emitin two modes of similar amplitude. Using standard1-in. s2.54 cmd gratings of 600 groovesymm made itpossible to measure the spectral separation of themodes of the available laser, but the spectral widthof the individual modes was not resolved because of, 1-m coherence length. Interferograms were ob-tained for both the compensated (Fig. 2a) and thenoncompensated (Fig. 2b) conf igurations by the use ofcollimated beams of approximately 3 mm FWHM. Ascan be seen from Fig. 2a, the visibility of the fringes isroughly constant across the entire pattern, droppingonly toward the edges of the illuminated region.The interferogram shown in Fig. 2b was obtainedwith the configuration depicted in Fig. 1b and showsa transverse-position dependence caused by the delayintroduced by the gratings. The dark and the lightregions of the interferogram can be seen to alternate asthe visibility of the fringes is modulated as a function ofthe position on the detector. The transverse-positionperiod of the visibility, 1.25 mm, translates into a delayof 1.94 mm after the measured central wavelength of0.856 mm and the incidence angle of 48.7± are takeninto account. This delay corresponds to a spectralseparation of s0.377 6 0.018d nm, which is in excellentagreement with the independently measured emissionspectrum of the laser, which gave a separation ofs0.371 6 0.010d nm.For measurement of the linewidths of soft-x-raylasers, consideration also has to be given to their poorspatial coherence. Radiation going through differentFig. 2. Interferograms obtained from a multimode laserdiode with a, the conf iguration in Fig. 1a, where the visi-bility of the fringes is roughly constant across the pattern,and b, with the configuration in Fig. 1b. The visibility ofthe fringes oscillates with a period corresponding to thespectral separation of the modes.July 1, 1996 / Vol. 21, No. 13 / OPTICS LETTERS 957arms of the interferometer after splitting at the f irstgrating should fall upon points on the plane of the de-tector that are within the coherence distance, which inexisting x-ray lasers can be ,100–200 mm at distancesof 2–3 m from the laser source.9 Factors contributingto difference paths in both arms are the dispersion ofdifferent frequencies in the gratings at f irst order andthe lateral magnification experienced by the beam asit goes through the f irst-order branch of the interfero-meter. A simple ray-tracing analysis shows that ra-diation detuned from the central frequency by Dl andpropagating at an angle Dw arrives at points on the de-tector separated by a distance Dx, given byDx ­ Dl√z cos2 gcos2 u1 2zd!2 Dw z√1 2cos2 gcos2 u!,where u is the diffracted angle from the first grating,z is the distance between the gratings, and zd is thedistance from the second grating to the detector. Forthe system to work properly Dx should be smaller thanthe coherence distance of the source. For a grazingincidence configuration cos u . cos g, and the f irstterm is dominated by the dispersion after the secondgrating, which is minimized because the detector islocated as close as possible to the grating. The samerelation between the angles makes the expression inparentheses in the second term close to unity, and thusthe only way of minimizing the second term is by usinga fairly well-collimated beam. A beam divergenceof approximately 0.2 mrad would be required for aninteferometer with 50-cm spacing between gratings.This can be achieved by means of a curved mirrorbetween the soft-x-ray laser and the interferometer.Below we present the design of the proposed in-terferometer for measurement of the linewidth of the46.9-nm laser line of neonlike argon. Such a tran-sition is of interest in relation to the recent obser-vation of large amplification in a discharge-createdplasma.4 Following the previous discussion, a resolu-tion of close to 50 000 can be attained with a standardgrating of 5 cm in size and 300 groovesymm. If theincidence angle is chosen to be 86±, the calibration re-sults in 405 mm of delay per millimeter on the detectorfor a total delay range of 1.4 mm on the 3.5-mm-wideilluminated area. Radiation with Dlyl ­ 5 3 1025 at46.9 nm would produce in that width fringes with visi-bility decaying to e22 to both sides of the central maxi-mum. For maximum fringe visibility the blaze of thegrating should be 1.6±. The dimensions of the inter-ferometer are determined by the size of the folding mir-rors. Because of the grazing incidence angles and themagnification experienced by the first-order branch,the mirrors have a minimum required size of 32 cm.The total size of the instrument is nevertheless com-pact, and the interferometer can be constructed in avacuum chamber of ,75 cm 3 15 cm.In summary, we propose a new type of Mach–Zehnder interferometer that makes use of thetransverse-position-dependent delay introduced bydiffraction gratings to conduct linewidth measure-ments on soft-x-ray lasers in a single shot. Thetransverse-position-dependent delay introduced bythe gratings can be compensated for use of the in-terferometer for plasma diagnostics and testing ofhigh-quality optics. The proposed interferometerdesign was analyzed theoretically, with the beamdivergence and spatial coherence taken into account,and was experimentally demonstrated in the IR regionof the spectrum with a diode laser of known spectralcharacteristics.This research was supported by National Sci-ence Foundation grant ECS-9401952 and FundaciónAntorchas proyecto A13218y1. The support of the Col-orado Advanced Technology Institute for collaborationwith Hyperfine (Boulder, Colo.) is also acknowledged.O. E. Martinez and M. C. Marconi are members ofthe staff of the Consejo Nacional de InvestigacionesCientı́ficas y Técnicas de la República Argentina.References1. J. A. Koch, B. J. MacGowan, L. B. Da Silva, D. L.Matthews, J. H. Underwood, P. J. Batson, and S.Mrowka, Phys. Rev. Lett. 68, 3291 (1992).2. J. A. Koch, B. J. MacGowan, L. B. Da Silva, D. L.Matthews, J. H. Underwood, P. J. Batson, R. W. Lee,R. A. London, and S. Mrowka, Phys. Rev. A 50, 1877(1994).3. H. R. Griem, Plasma Spectroscopy (McGraw-Hill, NewYork, 1964).4. J. J. Rocca, V. Shlyaptsev, F. G. Tomasel, O. D.Cortazar, D. Hartshorn, and J. L. A. Chilla, Phys. Rev.Lett. 73, 2192 (1994).5. B. Lemoff, G. Y. Yin, C. L. Gordon III, C. P. J. Barty,and S. E. Harris, Phys. Rev. Lett. 74, 1574 (1995).6. P. V. Nickles, M. Schmurer, M. P. Kalashnikov, I. Will,W. Sanders, and V. N. Shlyaptsev, Proc. SPIE 2520,373 (1995); A. Morozov, L. Polansky, and S. Suckewer,Proc. SPIE 2520, 373 (1995).7. S. Basu, P. L. Hagelstein, and J. G. Goodberlet, Appl.Phys. B 57, 303 (1993).8. L. B. Da Silva, T. W. Barbee, Jr., R. Cauble, P. Celliers,D. Ciarlo, S. Libby, R. A. London, D. Matthews, S.Mrowka, J. C. Moreno, D. Ress, J. E. Trebes, and A.Wan, Phys. Rev. Lett. 74, 3991 (1995).9. P. Celliers, F. Weber, L. B. Da Silva, T. W. Barbee, Jr.,R. Cauble, A. S. Wan, and J. C. Moreno, Opt. Lett. 20,1907 (1995).10. R. Wyatt and E. E. Marinero, Appl. Phys. 25, 297(1981).11. P. Hariharan, Opt. Eng. 14, 257 (1975).12. J. Bokor, K. A. Goldberg, H. Medecki, R. Beguiristain,K. Jackson, D. T. Attwood, G. E. Sommargren, R.Hostetler, and J. P. Spallas, presented at the OpticalSociety of America Annual Meeting, Portland, Ore.September 10–15, 1995.13. M. Born and E. Wolf, Principles of Optics, 2nd ed.(Pergamon, Oxford, 1964).14. J. L. A. Chilla, B. Benware, M. E. Watson, P. Stanko,J. J. Rocca, C. Wilmsen, S. Feld, and R. Leiberguth,IEEE Photon. Technol. Lett. 7, 449 (1995).

Soft-x-ray interferometer for single-shot laser linewidth measurements

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Soft-x-ray interferometer for single-shot laser linewidth measurements

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