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Chauhan et al. Vol. 27, No. 4 /April 2010 /J. Opt. Soc. Am. B 619

Single-diffraction-grating and grism pulsecompressors

Vikrant Chauhan,* Pamela Bowlan, Jacob Cohen, and Rick Trebino

School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, Georgia 30332 USA*Corresponding author: vikrant@gatech.edu

Received November 23, 2009; accepted December 15, 2009;posted January 22, 2010 (Doc. ID 120330); published March 3, 2010

We introduce and demonstrate a simple, compact, and automatically aligned ultrashort-pulse compressor thatuses only a single diffraction element—a grating or a grism (a grating on a prism). This design automaticallyhas unity beam magnification and automatically contributes zero spatiotemporal distortions to the pulse, thusavoiding spatial chirp, angular dispersion, pulse-front tilt, and all other first-order spatiotemporal distortions.It is comprised of only three elements: a diffraction element, a corner cube, and a roof mirror. Half the size ofcomparable two-grating compressors, it can provide large amounts of negative group-delay dispersion withsmall translations of the corner cube. The device can operate on pulses with both large and small bandwidthsby varying the corner-cube position. Using a grism as the diffraction element, material dispersion up to thethird order can be compensated, and we demonstrated compensation for 10 m of optical fiber for 800 nmpulses. © 2010 Optical Society of America

OCIS codes: 320.1590, 320.5520.

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. INTRODUCTIONn ultrashort pulse lengthens in time as it propagates

hrough a dispersive medium, where lower frequencies ofight propagate faster than higher frequencies. This ef-ect, called group-delay dispersion (GDD), is undesirablen most applications, especially micromachining and mul-iphoton imaging, which thrive on the shortest possibleulses.Only a few approaches exist for compensating for GDD

nd hence shortening the pulse to its transform limit. Theost common is angular dispersion, which, independent

f its sign, always yields negative GDD [1]. Prisms [2],ratings, and grisms (a diffraction grating written on arism) [3] have been used. The amount of negative GDDs proportional to the square of the angular dispersionnd the distance traveled by the pulse after the dispers-ng component.

Although angular dispersion introduces the desiredegative GDD, angular dispersion itself is undesirable,nd it also introduces undesired spatiotemporal distor-ions, spatial chirp, and pulse-front tilt, and thus is notenerally useful by itself [4]. Useful pulse compressorsased on angular dispersion necessarily require four iden-ical dispersive components—the first to introduce angu-ar dispersion (and hence negative GDD), the second toompensate for the angular dispersion, and the third andourth to compensate for the spatial chirp after tworisms. A well-aligned pulse compressor, in principle, in-roduces negative GDD without the unwanted distortionsf residual angular dispersion and spatial chirp and alsoithout other spatiotemporal distortions, [4] such asulse-front tilt, which typically accompany angular dis-ersion and spatial chirp.Unfortunately, in practice, it is difficult to align—andaintained aligned—many of the commonly used com-

0740-3224/10/040619-6/$15.00 © 2

ressors because these multiple dispersive elements muste identical and have identical incidence angles. A simplemall variation in the input beam pointing direction isnough to introduce significant amounts of the variouspatiotemporal distortions.

Consider the original four-prism pulse compressor (Fig.). If aligned correctly, the net result is just the addition ofegative GDD to the pulse. However, unless the elementsave precisely the same composition and apex angles andre positioned at precisely the same incidence angles,ome residual angular dispersion, spatial chirp, andulse-front tilt will occur in the output pulse [5]. WhileDD tuning in a prism compressor can occur via simplerism translation or more complex variation in the prismeparations, in grating or grism compressors, GDD ad-ustment requires the more complex variation in the sepa-ations between the first two and last two elements,hich must be maintained as equal. Worse, in prism,rating and grism designs, wavelength tuning requiresdjusting and maintaining identical incidence angles ofll four components. As a result, four-element pulse com-ressors are prohibitively cumbersome devices to use inractice.Compressors have generally been simplified to two

omponents by placing a periscope after the second ele-ent and folding the beam back through the first two el-

ments (see Fig. 2). This design halves both the complex-ty and the size of the device, but the difficulty of

aintaining equal angles of the two dispersive elementsnd the inability to readily tune GDD in grating andrism designs remain problematic.

A recently introduced single-prism pulse compressorolved all of the alignment issues by reducing the numberf dispersive elements to one and permitting easy GDDuning by simple translation of a corner cube [6] (see Fig.

010 Optical Society of America

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620 J. Opt. Soc. Am. B/Vol. 27, No. 4 /April 2010 Chauhan et al.

). The beam quadruple-passes the prism, using the cor-er cube to retroreflect the beam back to the prism andimultaneously invert it (so the prism need not be in-erted). Corner cubes are extremely accurately manufac-ured, so the dispersion added on the second (fourth) passs equal and opposite to that in the first (third) pass. Theevice continues to use a (less critically aligned) roof mir-or between the second and third passes through therism (i.e., on the other side of it, as in two-prism com-ressors), where beam inversion is not appropriate andlignment is not as critical. Translating the corner cubearies the beam propagation distance between the prismasses and effectively tunes the GDD over a large range.ecause the device tunes by varying the propagation dis-

ance between prism passes, it has the additional advan-age that it can simultaneously accommodate both largend small bandwidths by simply changing the distance.his is a great advantage over two- and four-prism de-igns, which must use a fixed prism separation and whichune by moving a prism into and out of the beam, and soannot accommodate large and small bandwidths unlessignificant additional realignment is performed.

Fig. 1. (Color online) Conven

Fig. 2. (Color online) Two-prism pulse compressor.

Prism-based compressors, however, have limits on theagnitude of negative GDD that can be introduced. Since

iffraction gratings and grisms are much more dispersivehan prisms, grating and grism compressors can provideuch larger amounts of negative GDD, approximately 2

rders of magnitude more than prism compressors for theame-size device.

So here we introduce single-grating and single-grismompressors based on this single-dispersive-component/orner-cube design. Single-grating (aberration-free) com-ressor designs [7] and devices based on the use of twooof mirrors have been introduced previously but do notchieve such alignment ease, and the use of corner cubesas not been mentioned in earlier work on grating orrism compressors, to the best of our knowledge. Usually,uch compressors are used in chirped pulse amplification,here tuning of group-delay dispersion is not as impor-

ant.Our analysis of spatiotemporal distortions, however,

hows that all previous grating and grism designs are

four-prism pulse compressor.

ig. 3. (Color online) Schematic diagram of single-prism pulseompressor.

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Chauhan et al. Vol. 27, No. 4 /April 2010 /J. Opt. Soc. Am. B 621

rone to them. After following careful alignment steps,uch a compressor or stretcher is best left untouched, andnput beam wander must be minimized. It is important toote that the magnitude of the undesired spatiotemporalistortions scales with the amount of GDD added by theompressor. Therefore, conventional compressor designsequire even higher alignment precision when a highlyispersive element like a grating or a grism is used.In our single-dispersive-element/corner-cube design,

he use of the corner cube succeeds in achieving maxi-um accuracy for cancellation of all first-order spatiotem-

oral distortions, including angular dispersion, pulse-ront tilt, and spatial chirp. In our design, tuning theDD involves simply translating the corner cube, and

uning the wavelength involves simply tuning the gratingngle. It also automatically achieves unity beam magnifi-ation. In addition, the corner cube causes the input beamo track the output beam; so, even if the compressor isumped, it remains aligned. And due to the double-assing of the path, it is also half the size of analogouswo-grating or two-grism devices. Finally, unlike currentrating and grism designs, the same device can be usedor a much larger bandwidth by simply restricting the cor-er cube distance.As mentioned above, nearly all materials exhibit posi-

ive GDD (second-order dispersion) and also third-orderispersion (TOD) at wavelengths near 800 nm. It is wellnown that prism and grating compressors designed toompensate for a given amount of GDD cannot indepen-ently compensate for TOD. While materials nearly allave a positive TOD-to-GDD ratio, grating compressorslways have a negative TOD-to-GDD ratio, so compensa-ion of large amounts of GDD using a grating compressorctually exacerbates the TOD, thus yielding a highly dis-orted pulse in time. Prism-based compressors have theorrect sign for this ratio but not the correct magnitude,nd they lack ratio tuning and only offer a relativelymall amount of GDD compensation. A grism [3,8] com-ressor of conventional design can address this issue, buturrent designs have the same limitations as conven-ional grating and prism designs because they consist ofultiple dispersive elements and cannot be easily tuned

or varying amounts of GDD. A single-grism pulse com-ressor, on the other hand, is automatically aligned forero spatiotemporal distortions and can compensate foroth GDD and TOD simultaneously.In this work, we extend the single-dispersive-element

ompressor concept to grating and grism compressors.oth of these devices have all of the above advantagesnd, in addition, our single-grism pulse compressor com-ensates for material dispersion up to the third order.nd using it, we demonstrated fourth-order limited-ispersion compensation for a 30 nm bandwidth,00 nm wavelength pulse that had propagated through0 m of optical fiber.

. SINGLE-DISPERSIVE-ELEMENT PULSEOMPRESSORSur single-diffraction-grating pulse compressor uses only

hree elements: a reflection grating, a corner cube, and aoof mirror. The input beam diffracts off the reflection

rating and impinges on to the corner cube, which ret-oreflects this angularly dispersed beam antiparallel tohe one incident on it, with the spatial order of colors re-ersed (see Fig. 4). This inverts the beam on the secondass and causes a sign reversal of the angular dispersionntroduced by the grating relative to that of the first pass.herefore, after the first two passes, the angular disper-ion in the beam is compensated, as required. A roof mir-or reverses the beam path at a different height whileaintaining the same order of colors in the dispersed

eam. The last two passes thus remove both the spatialhirp and pulse front tilt while doubling the magnitude ofDD, as required.The single-grism design follows directly from the ear-

ier single-prism compressor [5], and the single-gratingesign mentioned in the previous section. We replaced therating in the single-dispersive-element design with a re-ection grism as shown in Fig. 5. The grism used in thisxperiment is a right-angled SF2 glass prism with a 600roove-per-mm reflection grating glued to its base. The in-ut beam is incident on the face of the grism, which is or-hogonal to the grating. It then undergoes total internaleflection at the diagonal face of the grism and finally ex-ts the diagonal face of the grism after it diffracts off therating. The beam path in each pass through the grism is

ig. 4. (Color online) Schematic diagram of single-grating pulseompressor.

ig. 5. (Color online) Schematic diagram for single-grism pulseompressor.

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622 J. Opt. Soc. Am. B/Vol. 27, No. 4 /April 2010 Chauhan et al.

epicted on the top of the grism with a dashed line (seeig. 5). After the first pass, the beam is reflected back onto

he grism using a corner cube. As in the single-prism de-ign [5], the corner cube functions as a retroreflector andbeam inverter, and the device functions analogously to

he single-prism and single-grating designs. At the correctngle of incidence, however, the output pulse thus ob-ained has negative GDD and negative TOD in the correctatio to cancel out material dispersion to the third order,nd it has no spatiotemporal distortions.

. MODELING AND SIMULATION. Single-Grating Pulse Compressor

. Unity Beam Magnificationhe corner cube very accurately retroreflects the beam, sohe exit angle after the first pass is equal to the incidencengle for the second pass. An analytical calculation usingostenbauder matrices [9] shows that the spatial magni-cation of the beam for each pass is:

M1 = −sin �

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sin �

sin �= M4, �1�

here � and � are the diffracted and incidence angles ofhe beam measured from the grating surface (not the nor-al to it), the definitions of the angles in Kostenbauder’s

aper. Therefore, the total magnification of this device islways unity. The above calculation also applies to angu-ar magnification.

. Wavelength Tuning of the Single Grating Pulseompressornce this device is set up to operate at a particular wave-

ength, it is easy to tune for other wavelengths. As is evi-ent from the figure (see Fig. 4) shown above, lookingrom the top, the grating is rotated counterclockwise ifavelength is decreased and clockwise for longer wave-

engths. The beam path in the device does not change inither case. Therefore, this device can be tuned for a dif-erent wavelength by rotating just one knob, which ro-ates the only grating used.

. No Spatiotemporal Distortionsgain, using the Kostenbauder matrix formalism, it isasily deduced that the beam emerging from the single-rating compressor has zero pulse-front tilt, zero spatialhirp, and zero residual angular dispersion. Since, asentioned, the corner cube retroreflects the beam, the

xit angle after the first pass is the same as the incidencengle for the second pass. Therefore, the compressor isuto-aligned to introduce zero distortions, independent ofhe incidence angle of the beam.

K = KgratingKspaceKgratingKmirrorKgratingKspaceKgrating . �2�

The calculated Kostenbauder matrix [Eq. (2)] showshat added spatial chirp K1,4, angular dispersion K2,4, andulse front tilt K1,3 are all zero. The GDD, K3,4, is nega-ive, as required.

. Negative Group-Delay Dispersionhe analytical result for GDD using the Kostenbauderatrix formalism is exactly the same as that obtained by

ifferentiating the phase introduced by a grating com-ressor [Eq. (3)].

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here � is diffraction angle measured from the gratingormal, b is the path length inside the compressor, andhe grating groove spacing is d.

. Single-Grism Pulse Compressore also used Kostenbauder matrices to model the single-

rism pulse compressor. The matrix for each pass throughhe grism can be obtained by treating it as a composite op-ical element composed of a tilted air-glass interface, a re-ection grating, and another tilted glass-air interface. Us-

ng the matrix for each grism pass, the Kostenbauderatrix for the compressor is given as

Kc = KgrismKspaceKgrismKmirrorKgrismKspaceKgrism . �4�

The elements of the calculated matrix [Eq. (4)] that cor-espond to spatiotemporal distortions are found to be allero. The calculated Kostenbauder matrix shows that thepatial magnification Kc 1,1 and angular magnificationc 2,2 are unity. Spatial chirp Kc 1,4, angular dispersionc 2,4, and pulse front tilt Kc 1,3 are all zero. And again,DD Kc 3,4 is negative, as required. This shows that there

s fundamentally no spatial chirp, residual angular dis-ersion, or pulse front tilt in the output of this device.ince the pulse travels equal distances inside the cornerube, the spatial chirp introduced in the first two passess completely removed in the last two passes in the com-ressor. Therefore, there is no mismatch in the angle ofncidence for the first two and last two passes of the pulsehrough the grism. This ensures that the angular disper-ion is completely cancelled in the compressor.

. EXPERIMENT. Group Delay Dispersion

n our experiments, a transform-limited pulse from a KMabs Ti:sapphire oscillator centered at 825 nm with aWHM bandwidth of 30 nm was stretched using theingle-grating pulse compressor. The corner cube consistsf silver coated mirrors and has an angular tolerance of 3rc seconds. The angle of incidence of the input beam is2 degrees from the grating normal and the grating has aroove density of 600 lines/mm. The phase introduced byhe compressor was measured using spatially encoded ar-angement for temporal analysis by dispersing pair ofight E-fields (SEA TADPOLE) [10,11] and a polynomialt returned the GDD for varying separation of the cornerube and the grating (Fig. 6). The measured values ofDD were then plotted with the corner cube separation.he variation was found linear and in very good agree-ent with the simulations from the previous section.Similarly, the dispersion introduced into the output

ulse by the single-grism pulse compressor was also mea-ured using SEA TADPOLE. The input pulse was cen-

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Chauhan et al. Vol. 27, No. 4 /April 2010 /J. Opt. Soc. Am. B 623

ered at 800 nm with a bandwidth of 30 nm. The inci-ence angle was fixed at 8.4 degrees from the grismurface normal. The GDD introduced by the compressort each grism-corner cube separation is plotted below (seeig. 7).

. Measurement of Spatiotemporal Distortions

. Spatial Chirphe spatial chirp in the output pulse from the single-rating compressor and the single-grism compressor waseasured experimentally using an imaging spectrometer

12]. The beam to be examined was dispersed in the direc-ion of one of the beam’s spatial coordinates, which wasrthogonal to the one in which the beam was expected toave some spatial chirp, i.e., the dimension in which an-ular dispersion is introduced by the grating or the grism.he spatiospectral plot below shows that there was noeasurable spatial chirp in the output beam from the

ingle grating pulse compressor. The spatial-chirp rho pa-ameter [13] calculated from the spatiospectral plothown (Fig. 8) gave a value of 0.05, which is at the detec-ion limit of our device. We obtained the same result forhe single-grism pulse compressor.

. Angular Dispersion and Pulse-Front Tilthe two compressors do not introduce any pulse-front tiltr residual angular dispersion in the beam. It can behown easily that residual angular dispersion, if presentn the beam, will cause some spatial chirp to occur afterropagating some distance after the compressor. There-ore, for measuring angular dispersion, a good check is to

ig. 6. (Color online) Variation of GDD versus distance iningle-grating pulse compressor.

ig. 7. (Color online) GDD versus distance in single-grism pulseompressor.

easure the spatial chirp at two different locations alonghe beam path after the beam exits the pulse compressor.ur measurements confirmed that there was no residualngular dispersion introduced by the two compressors.ecause there are only two independent (and six depen-ent) first-order spatiotemporal distortions, the absencef two of them simultaneously, that is, angular dispersionnd spatial chirp, guarantees that there is no pulse-frontilt in the beam either. Therefore, there are no (first-rder) spatiotemporal distortions introduced by the singlerating and the single grism pulse compressors.

. Third-Order-Dispersion Compensationo demonstrate third-order-dispersion compensation, aulse from a Ti:sapphire oscillator at a center wavelengthf 805 nm was stretched using a 10 m long optical fiber.he input pulse incident on the fiber had a FWHM pulseidth of 90 fs and a spectral bandwidth of 30 nm as mea-

ured by a Swamp Optics GRENOUILLE. The spectralhase of the pulse after the fiber and before the compres-or was also measured using SEA TADPOLE (see Fig. 9).

ig. 8. Spatiospectral plot revealing the lack of spatial chirp inhe compressor output after four beam passes, indicated by theack of tilt in this plot. The minor structure and the fringes atight are due to a stray reflection also entering the spectrometernd hence are of no significance.

ig. 9. (Color online) Spectrum and spectral phase before andfter the compressor.

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624 J. Opt. Soc. Am. B/Vol. 27, No. 4 /April 2010 Chauhan et al.

fiber collimator attached to the end of this fused silicaptical fiber collimated the beam, which then served ashe input to the single-grism pulse compressor. The colli-ated beam was incident upon the grism at an angle of 8°

rom the grism surface normal. The curvature of thehase being monitored using SEA TADPOLE decreaseds the corner cube was translated further from the grism.fter removing the second-order phase, minor adjust-ents in the incidence angle and corner-cube position

ielded an almost flat-phase output pulse. The measuredpectrum and the spectral phase of the output are shownelow (Fig. 9). The spectral phase of the output pulsehows that the dispersion introduced by the optical fiberas completely removed up to and including the third or-er. Additionally, the compressor works for both horizon-al and vertical polarizations. Neither the metal cornerube nor the roof mirror rotates the polarization of theeam, so the output beam maintains the same polariza-ion as the input. However, gratings and grisms have dif-erent diffraction efficiencies for the two orthogonal polar-zations, so use of an intermediate polarization wouldield some polarization rotation.

. CONCLUSIONSe have demonstrated single-dispersive-element com-

ressors using a grating and a grism. They are easilyligned, automatically distortion free, one-fourth or halfhe size of previous equivalent compressors, and they canasily be tuned for the operating wavelength and varyingmounts of GDD, and, with the grism device, for GDD-to-OD ratio. The use of a grating as the dispersive element

mproves the ability to compensate for GDD by more thann order of magnitude compared to any prism compressor5], while the single-grism pulse compressor should be ofreat utility when compensation for large amounts of ma-erial dispersion up to and including the third order be-omes necessary, for example, in fiber delivery of ul-rashort pulses.

CKNOWLEDGMENTShe authors are grateful for support from the Georgia Re-

earch Alliance and the National Science Foundation

NSF) Small Business Innovation Research grant53-9595.

EFERENCES1. R. L. Fork, O. E. Martinez, and J. P. Gordon, “Negative dis-

persion using pairs of prisms,” Opt. Lett. 9, 150–152 (1984).2. Z. Bor and B. Racz, “Group velocity dispersion in prisms

and its application to pulse compression and travelling-wave excitation,” Opt. Commun. 54, 165–170 (1985).

3. S. Kane and J. Squier, “Grism-pair stretcher-compressorsystem for simultaneous second and third-order dispersioncompensation in chirped-pulse amplification,” J. Opt. Soc.Am. B 14, 661–665 (1997).

4. S. Akturk, X. Gu, P. Gabolde, and R. Trebino, “The generaltheory of first-order spatiotemporal distortions of Gaussianpulses and beams,” Opt. Express 13, 8642–8661 (2005).

5. K. Osvay, A. P. Kovacs, Z. Heiner, G. Kurdi, J. Klebniczki,and M. Csatari, “Angular dispersion and temporal changeof femtosecond pulses from misaligned pulse compressors,”IEEE J. Sel. Top. Quantum Electron. 10, 213–220 (2004).

6. S. Akturk, X. Gu, M. Kimmel, and R. Trebino, “Extremelysimple single-prism ultrashort-pulse compressor,” Opt. Ex-press 14, 10101–10108 (2006).

7. M. Lai, S. T. Lai, and C. Swinger, “Single-grating laserpulse stretcher and compressor,” Appl. Opt. 33, 6985–6987(1994).

8. J. J. Field, C. G. Durfee, J. A. Squier, and S. Kane,“Quartic-phase limited grism-based ultrashort pulseshaper,” Opt. Lett. 32, 3101–3103 (2007).

9. A. G. Kostenbauder, “Ray-pulse matrices: a rational treat-ment for dispersive optical systems,” IEEE J. QuantumElectron. 26, 1148–1157 (1990).

0. P. Bowlan, P. Gabolde, A. Schreenath, K. McGresham, S.Akturk, and R. Trebino, “Spatially resolved spectral inter-ferometry,” in Frontiers in Optics, OSA Technical Digest(CD) (Optical Society of America, 2006), paper FThM1.

1. P. Bowlan, P. Gabolde, A. Schreenath, K. McGresham, andR. Trebino, “Crossed-beam spectral interferometry: asimple, high-spectral-resolution method for completelycharacterizing complex ultrashort pulses in real time,” Opt.Express 14, 11892–11900 (2006).

2. X. Gu, S. Akturk, and R. Trebino, “Spatial chirp in ultrafastoptics,” Opt. Commun. 242, 599–604 (2004).

3. P. Gabolde, D. Lee, S. Akturk, and R. Trebino, “Describingfirst-order spatiotemporal distortions in ultrashort pulsesusing normalized parameters,” Opt. Express 15, 242–251

(2007).