PHYSICAL REVIEW SPECIAL TOPICS - ACCELERATORS AND BEAMS 12, 033501 (2009)

Theoretical and experimental study of passive spatiotemporal shaping of picosecond pulses

A. K. Sharma,* T. Tsang, and T. Rao Instrumentation Division, Brookhaven National Laboratory, Upton, New York 11973, USA (Received 29 September 2008; published 24 March 2009) We report the results of theoretical and experimental studies on passive spatiotemporal shaping of cw mode-locked picosecond laser pulses for driving the photocathode of a high-brightness, high-current energy recovery linear accelerator. The temporal pulse shape is modified using birefringent crystals, while a refractive optical system is used to generate a flattop spatial beam profile. An optical transport system is designed and implemented to deliver the flattop pulse onto a photocathode sited 9 m away from the shapers. The alignment tolerances on the beam shaper and the temporal pulse stacker have been studied both theoretically and experimentally. The experimental results agree well with theoretical simulations.

DOI: 10.1103/PhysRevSTAB.12.033501 PACS numbers: 42.25.Lc, 42.15.Eq, 42.60.Jf, 29.25.Bx

grammable dispersive filter, commercially known as I. INTRODUCTION DAZZLER, has successfully shaped laser pulse in the Shaping the spatial (transverse) and the temporal (lon- picosecond regime [18], its use proved limited for low gitudinal) profiles of beams is highly energy laser pulses operating at a repetition rate up to a desirable for several scientific research and industrial ap- few kHz. Therefore, passive pulse stacking techniques are plications, such as producing low-emittance photoelec- commonly used to temporally shape energetic MHz-repe- trons for accelerators [1–3], high- tition-rate picosecond laser pulses [19–24]. Such pulse [4], optical parametric amplifiers [5], laser micromachin- stackers can be built either using a conventional delay ing [6], and terahertz generation [7]. Energy recovery line [19–21] or a set of appropriately oriented birefringent linear accelerators (ERL) employ photoinjectors to deliver crystals [22–24]. The basic underlying process of pulse high current and low-emittance electron beam. To mini- stacking is the same in both schemes and requires inter- mize the electron emittance, the laser pulse shape and ferometric alignment precision. Conventional delay lines beam profiles are often shaped other than Gaussian that generally consist of several optical elements, such as [1–3]. The high-current ERL being built at Brookhaven polarizers, wave plates, beam splitter, and reflectors, often National Laboratory [3] requires flattop transverse and are difficult to align and stabilize to this degree of preci- longitudinal profile with pulse duration of 60 ps for sion. On the other hand, using birefringent crystals for low charge ( < 1:4nC) and 120 ps for high charge pulse stacking [22–24] is relatively simple, providing sta- ( > 5nC) operations. ble pulse shaping, though with limited parametric flexibil- Schemes to obtain spatiotemporal flattop laser pulses [8] ity. Likewise, the spatial beam profile may be shaped using for low-emittance photoinjectors were demonstrated at either an inverse-Gaussian transmittive filter [25] or dif- SPring8 [9], DESY [10], LCLS [11], and EUROFEL fractive elements [26,27] to control optical transmission in [12]. Temporal shaping of femtosecond laser pulses is the radial direction. However, a passive aspheric refractive/ mostly achieved by modulating the amplitude and phase reflective optical shaping system [28–30] is simple, and in the spectral domain [13,14] using optical devices such as robust, offering high optical transmission. a spatial modulator. Longer duration (nanosecond) In this paper, we present our theoretical and experimen- laser pulses can be directly shaped by an electro-optic tal studies with a passive temporal and spatial beam shaper modulator [15,16]. Although these powerful pulse shaping using 10 ps laser pulses. Since the photoinjector of an techniques can deliver arbitrary pulse shapes, they all have accelerator is typically located many meters away from certain limitations that include spatiotemporal distortions, the laser room, we designed and built an optical beam and limited optical power handling capabilities. Further- transport system to deliver the spatiotemporal shaped more, spectral modulation is impractical for picosecond ‘‘beer-can’’ laser beam onto a photocathode positioned at 9m light pulses because of its narrow spectral width; often a from the beam shaper. Our experimental results feedback system and a converging algorithm are required compared favorably with our theoretical calculations. to generate the desired laser shape [17]. Further, direct electro-optical modulation on picosecond light pulses is II. THEORY OF TEMPORAL PULSE SHAPING also not feasible because of circumscribed bandwidth of We begin by describing the underlying physical princi- the electronic systems. Although an acousto-optic pro- ple of the birefringent-crystal-based passive pulse stacker, and then we present our theoretical calculation to deter- *[email protected] mine the temporal profile of the shaped laser pulse.

1098-4402=09=12(3)=033501(9) 033501-1 Ó 2009 The American Physical Society A. K. SHARMA, T. TSANG, AND T. RAO Phys. Rev. ST Accel. Beams 12, 033501 (2009)

Birefringent crystals [31] have two axes, the ordinary known as an a-cut crystal. The linearly polarized laser and extraordinary (o and e) oriented along the x and y axes, beam impinges on the -cut crystal at an angle of incidence shown in Fig. 1(a), with refractive index no and ne, re- with its polarization direction lying at an angle to the spectively. The crystal, of length d, is referred to as -cut o-axis. The component of the electric field whose polar- crystal when the xy plane makes an angle with the normal ization is along the o (e) direction propagates with velocity to the face of the crystal. When equals 90 , the crystal is corresponding to the refractive index no (ne) at an angle o

FIG. 1. (Color) (a) Left: Schematic diagram illustrating input and output pulse polarization and right: schematic diagram illustrating relevant angles, path length Lo and Le for o and e rays for -cut birefringent crystal. (b) Schematic depicting a sequence of eight replica pulses with alternate orthogonal polarizations. The optic axis is shown by thin lines on the surface of each crystal. The polarization of the laser pulse is depicted by the double arrow shown in each crystal. The notation S, P represents s-polarization and p-polarization, respectively. Polarizations a and b depict the linear polarizations oriented at þ45, and 45 relative to the y axis of the Cartesian coordinate system. (c) Simulated temporal pulse shapes from eight replica pulses of identical polarization with zero chirp (red line), linear chirp with a spectral phase of 17:5ps2=rad2 (green line), and 22 ps2=rad2 (blue line). All replica pulses are separated by a temporal delay of 15 ps. The intensity of eight replica pulses (scaled by half for clarity) is also depicted (black line). (d) Simulated temporal pulse and the intensity of eight replica pulses. The differential static phase between interfering pulses is set at 0 (magenta line), =2 (black line), 0 and =2 at alternate positions (green line).

033501-2 THEORETICAL AND EXPERIMENTAL ... Phys. Rev. ST Accel. Beams 12, 033501 (2009) P p^ I t t ak t ( e) to the face normal. In general, the directions of where k, kð Þ, and function kð Þ¼ i¼0;1;2;3... i ð kÞ propagation vector k, and the Poynting vector differ; the are, respectively, the polarization unit vector, intensity, and e ray deviates from the e wave by the walk-off angle , and temporal phase for the kth pulse, !o is the central angular propagates at an angle e þ . The electric field of both frequency, and k is the relative delay between kth and replica pulses are given as E1 ¼ Eo cosðÞ and E2 ¼ (k þ 1)th pulse. In the phase function ðtÞ, parameters a0 Eo sinðÞ, where Eo is the electric field of the incident and a1, respectively, are the static and linear temporal pulse. phase, and the higher order terms represent pulse chirp of We calculate the temporal delay between the two replica the corresponding orders. We express the intensity profile pulses using the diagram shown on the right side in of the stacked pulse as Fig. 1(a),as IstackðtÞ¼EstackðtÞEstackðtÞ 0 jnoLo neLej t ¼ t t ¼ ; X2n X2n X2n d o e c (1) ¼ Ijðt jÞþ ðp^ j:p^ kÞ j¼1 j¼1 k¼1; t t kÞj where o and e are the propagation time, respectively, for qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi o e n0 the pulse and pulse, e is the refractive index along the I ðt ÞI ðt Þ direction of propagation of the e wave, c is the speed of j j k k light, and Lo, Le are their geometrical propagation dis- cosfjðt jÞkðt kÞg: (6) tances, expressed as The first term in Eq. (6) is the sum of intensities of the d Lo ¼ OA þ AB ¼ þ d½tanðe þ Þtano sin individual replica pulses. The second term represents the coso interpulse interference that is governed by the polarization d sequence (p^ j:p^ k) and the phase difference [jðtÞkðtÞ] Le ¼ OC ¼ ; (2) cosðe þ Þ between pulses containing static and time-varying terms. Equation (6) suggests that the final temporal pulse profile 0 where sin ¼ no sino ¼ ne sine and can be controlled by the amplitude, the temporal delay, n n phase, and the polarization sequence of the individual 0 o e ne ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (3) replica laser pulses. For a sequence of pulses with alternate 2 2 ½ne cosðe þ Þ þ½no sinðe þ Þ polarizations, as depicted in Fig. 1(b), p^ j:p^ k ¼ 1 for j þ k ¼ even; andp^ j:p^ k ¼ 0 for j þ k ¼ odd. When the de-  2 2  lays between all interfering pulses are much larger than the sin2ðe þ Þðno neÞ ¼ tan1 : 2 n cos 2 n sin 2 pulse width of the incident laser, they do not overlap f½ e ð e þ Þ þ½ o ð e þ Þ g significantly and so the contribution from their interference (4) is negligible. For a sequence of pulses with identical polar- izations, they all interfere with each other, so that p^ j:p^ k ¼ The beam walk-off will cause the two pulses to emerge in 1 for all j and k. different directions, which must be minimized. This can be For ultrashort pulses with inherently large spectral band- achieved by assuring that the laser beam is incident per- width, the time-varying phase (i.e., pulse chirp) also affects fectly normal to the optic axis on an ideal a-cut birefrin- the shape of the output pulse. The polarization sequence of gent crystal where o and e equal 0, and Lo and Le the laser pulses is important for controlling interpulse equal d. interference. While a chirped pulse sequence of alternate Therefore, two replica pulses with various amplitude polarizations minimizes interpulse interference [9,20], a and temporal delay may be generated from a single bire- chirp-free pulse sequence of identical polarizations can fringent crystal. We can extend this discussion to a stack of synthesize a specific laser pulse shape with full coherence birefringent crystals, as depicted in Fig. 1(b). In general, a characteristics [10,21]. stack of n birefringent crystals will generate 2n replica To illustrate the effect of pulse chirp on the final shape of pulses. The temporal profile of the stacked pulse can be the pulse, we first considered a chirp-free Gaussian laser determined from the cumulative electric field that can be pulse having FWHM pulse duration of 10 ps, and then we written as the sum of electric fields of individual laser added pulse chirps and delays to the eight pulse sequence pulses as X to examine the quality of the shaped pulse for different EstackðtÞ¼ EkðtÞ polarization sequences. Figure 1(c) depicts the simulated k¼1:2n temporal pulse shapes from eight replica pulses of identical X qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi polarization with zero chirp (red line), a linear chirp with a i ! t t p^ I t e ½ oð k1Þþ kð k1Þ; 2 2 ¼ k kð k1Þ spectral phase of 17:5ps=rad (green line), and with n k¼1:2 22 ps2=rad2 (blue line). All replica pulses are separated (5) by a temporal delay of 15 ps. The black line in Fig. 1(c)

033501-3 A. K. SHARMA, T. TSANG, AND T. RAO Phys. Rev. ST Accel. Beams 12, 033501 (2009) depicts the intensity of the eight replica pulses. We esti- III. EXPERIMENT mated that the intensity modulation in the plateau of the shaped pulse is 14% (rms), 0:5% (rms), and 6% A commercial diode-pumped cw mode-locked Nd:va- (rms), respectively, for the three cases. Although this nadate laser oscillator (Cheetah-X from Time Bandwidth modulation can be reduced to 0.5% for an optimally Products Inc.) was used. It delivered s-polarized laser chirped pulse, it increases further with larger pulse chirp. pulses at 532 nm with an average power of The intensity modulation for a pulse sequence with alter- 2.5 Watts at a repetition rate of 81.25 MHz. The pulse nate polarization [9] increases by an order of magnitude for duration was measured to be 10 ps FWHM by using an the same set of parameters. In contrast, for a pulse se- autocorrelator. The beam waist diameter was measured to quence wherein the first half has identical polarization and be 1.3 mm with an ellipticity of 0:97 and a beam diver- is orthogonal to that of the second half [23], the intensity gence of 0:15 mrad using a CCD camera (model Data modulation can be minimized to <2% (rms) using crystal Ray WinCamD). Figure 2 illustrates the experimental thickness in the ratio of 1:2:3:68 instead of 1:2:4 that setup. The laser beam was first split into two using a generally is used in a pulse stacker [1,24]. 50% beam splitter, passed through two delay lines (arms) In an optimally chirped pulse to get flattop pulse a time- and then recombined and focused on a type II second bandwidth product of 0.490 is obtained, which is slightly harmonic crystal [potassium dihydrogen phosphate larger than that of a chirp-free Gaussian laser pulse (0.441). (KDP)] for auto- and cross-correlation measurements. In By controlling the pulse chirp, different temporal shapes one arm of the cross correlator, we positioned a stack of YVO C ; C ; C can be generated from a single birefringent crystal, such as three 4 birefringent crystals ð 1 2 3Þ in decreasing thicknesses of 24, 12, and 6 mm. These crystals were bell-shaped and triangular-shaped pulses. In such an ar- rangement, two replica pulses initially chirp-free of equal mounted on rotational stages (0.5 accuracy) with inde- amplitude and identical polarization is employed. Their pendent horizontal and vertical tilt adjustments to obtain temporal delay is set to 1.5 times the initial pulse width. variable amplitudes and static phase of the various replica The pulse chirp is adjusted to yield a time-bandwidth pulses. A half-wave plate and polarizer were placed after product of 0.517 and 0.576, respectively, for bell- and the stack enabled us to rotate the polarization of the output triangular-shaped pulses. beam to match that of the reference pulse on the other arm. In our experimental study, the laser pulses are nearly The half wave plate, polarizer, beam splitter, and the mirror M3 were mounted on flip mounts, allowing the shaped chirp-free. Therefore, the effect of pulse chirp can be beam to be directed either to the cross-correlation mea- ignored in our simulations. We employed three a-cut yt- surement or to the photocathode. The front and back trium orthovanadate (YVO4) crystals (i.e. n ¼ 3) of suit- crystal surfaces of each birefringent crystal are antireflec- able thickness, thus generating a total of eight pulses tion coated at the wavelength of 532 nm with a measured separated by an equal relative temporal delay of insertion loss of <0:5% per optical surface. The overall 1:1ps=mm calculated from the measured birefringence transmission of the three YVO4 crystals is 62%, yielding of 0.33. In the simulation we considered an initially 1 an intrinsic absorption loss of 0:116 cm . chirp-free Gaussian laser pulse of duration of 10 ps Because of the nonzero optical absorption, thermal ex- (FWHM) at a wavelength of 532 nm. The total material 0:008 15 ps2 0:0119 ps2 pansion of the crystals and the temperature dependence of dispersion was calculated as and , their birefringence lead to a time dependent variation of o e respectively, for the and ray, which is negligible for differential phase shifts among replica pulses. Hence, the 10 ps pulses. Therefore, we ignored the effect of pulse chirp on pulse shaping in Eq. (6). For a sequence of eight replica pulses with alternate polarizations, we considered six interference regions with a differential phase between interfering pulses, represented by p1 to p6 [Fig. 1(d)]. Adjacent pulses of identical polarization contribute to such interference. This figure depicts the intensity of eight individual replica pulses and the total intensity of the stacked pulse for different values of static phases. For differential static phases of either zero or =2, we obtain a flattop pulse. However, in both cases the rise and fall time differ. At other values of static phases, strong intensity modulations in the plateau of the flattop pulse are expected, as depicted in Fig. 1(d) for a specific case of p1;p3;p5 ¼ =2, and p2;p4;p6 ¼ 0. Such a static phase arises because FIG. 2. (Color) Schematic of the experimental setup and the of unequal path length traversed by the o pulse and e pulse cross correlator. The beam splitter BS, mirror M3, wave plate in each crystal as a result of the tilt of the crystal plane. W, and polarizer P are mounted on flip mounts.

033501-4 THEORETICAL AND EXPERIMENTAL ... Phys. Rev. ST Accel. Beams 12, 033501 (2009)

FIG. 3. (Color) Cross correlation recorded every 10 min over a 4 h period, demonstrating the short and long term stability, (thick black line) a deconvoluted pulse, (red line) theoretical pulse; and (thin black line) autocorrelation of the incident laser pulse.

crystals were left to reach thermal equilibrium ( 1 hour) The walk-off angle () calculated using Eq. (4) was prior to the alignment process. We found this stabilization 0:1 per degree deviation from the normal incidence of procedure was critical in routinely yielding a reproducible an input laser beam for an ideal a-cut crystal. The corre- flattop pulse. The alignment of the crystals was carried out sponding change in temporal delay, for a 24 mm long in the following manner: first, the optic axis of all three YVO4 crystal, is 5.6 fs, which is negligible compared to YVO4 crystals were oriented along the same direction to the total propagation delay of 26.4 ps. Even for a perfect obtain a maximum delay between the two replica pulses, normal incidence, an imperfect cut of the crystal will entail measured as 45:4ps. Then, the optic axis of the subse- a beam walk-off. We observed no distortion of the beam’s quent crystals was rotated by 45 with respect to the spatial profile at 9maway from the pulse stacker, in- previous one to generate eight replica pulses of equal dicating that the effect of any error in the crystal cut is amplitudes and alternate polarizations. We obtained a negligible. near flattop pulse profile with FWHM duration of Using thinner crystals will enable us to better shape 53 ps, with a rise and fall time of 10 ps as dictated femtosecond light pulses, and will enhance overall trans- by the initial pulse width. The calculated intensity modu- mission. For picosecond light pulses, crystals with a lower lation over the flattop region was 9% (rms). Figure 3 loss coefficient must be used. Since the spectral transmis- depicts the experimental cross correlations, the corre- sion of the YVO4 crystal is limited from 500 nm to sponding deconvoluted shape of the laser pulse, and its 5000 nm, for temporal shaping in the UV spectral regime theoretically calculated shape for a static phase of =2 [9], birefringent crystals such as -BBO (barium beta between all interfering pulses. The experimental cross borate) [9] and quartz should be employed. correlation agrees reasonably well with theoretical calcu- lations. The flattop temporal profile was recorded every IV. SPATIAL BEAM PROFILE SHAPING AND 10 min over 4 h of continuous operation, demonstrating its BEAM TRANSPORT short and long term stability in a standard laboratory environment. We obtained a spatial flattop beam using a commercial We minimized the intensity modulations in the plateau refractive beam shaper ( shaper, Newport Corporation of flattop pulse by carefully adjusting the horizontal and Model GBS-AR14 [32]) consisting of two fused silica vertical tilts of each crystal such that the differential static plano-convex aspheric lenses, arranged with their convex phase was constant between the interfering pulse; this surfaces facing each other. We optimized the shaper at its occurs when incident angle nears zero. This sensitive operation of 532 nm by setting the separation procedure can be simplified by placing a polarizer before between aspheric lenses at 149.8 mm. To match the opti- the last crystal to avoid interference between near-adjacent mum input beam size at the refractive beam shaper, the laser pulses; however, this addition reduces the output input laser beam was magnified by using a 3.5X beam power by half. We note that, by adjusting the tilt angle of expander, consisting of a plano-concave and a plano- each crystal, we can vary the phase shifts among the pulse convex lens of focal length 100 and þ350 mm, respec- replicas. Such additional fine control confers the ability to tively. We used ZEMAX, an optical design software, to generate arbitrary replica pulse shapes with different am- simulate the beam profiles at the input and output of the plitudes, temporal delays, and time-varying phases (i.e., shaper, to investigate the alignment tolerance, and to chirp). study the image-relay system for beam transport.

033501-5 A. K. SHARMA, T. TSANG, AND T. RAO Phys. Rev. ST Accel. Beams 12, 033501 (2009)

FIG. 4. (Color) Simulated and measured beam profiles. (a) Left: ZEMAX simulated ray diagram for the shaper (vertical scale expanded by 10X); right: schematic of the image-relay system. (b) Left to right: ZEMAX simulated beam profiles of the Gaussian input beam, output flattop beam at 10 cm, at 9 m without image-relay lens, and at 9 m with image-relay lens. (c) Corresponding measured beam profiles.

Simulations of the beam transport suggested that a flat- the beam transport system, while Fig. 4(b) shows the top laser beam is prone to diffraction and strong diffraction simulated beam profiles of the input beam, the output rings appears in the laser beam profile over long propaga- beam, output beam freely propagated to a 9 m, and finally, tion distances. The depth of focus, that is, the distance over the output beam image relayed to a distance of 9 m from which flattop profile does not develop diffraction rings, the shaper. Figure 4(c) illustrates the corresponding was 50 cm for this configuration. Typically, the photo- experimental beams’ profiles. With a beam diameter of injector of an accelerator is located 3–10 m away from the the input at 4.7 mm, the shaper produces laser room. Therefore, in addition to obtaining a flattop a high-quality flattop beam profile with a diameter of spatial beam profile, there must be an optical beam trans- 6.5 mm FWHM. Figure 5 depicts the central horizontal port system to deliver the flattop beam onto the photo- line scan of the output spatial beam’s profile at 10 cm from cathode. Accordingly, we designed a Keplerian image- the shaper and the corresponding beam profiles from relay magnifier/demagnifier system consisting of two iden- ZEMAX simulation. The agreement between them is good. tical plano-convex lenses with focal length of 2:25 m At 10 cm from the shaper and at 9 m from the image- separated by 4:50 0:01 m. Figure 4(a) depicts the ZEMAX relay system, we measured the intensity modulations in the simulated ray diagram of the shaper and the schematic of spatial profile as 7% (rms) and 10% (rms), respec-

FIG. 5. (Color) Horizontal line scan of the output spatial beam profile of Fig. 4 at 10 cm from the shaper: (black line) experimental profile, (blue line) corresponding ZEMAX simulation.

033501-6 THEORETICAL AND EXPERIMENTAL ... Phys. Rev. ST Accel. Beams 12, 033501 (2009) tively, over the flat region. Despite there being many mum beam diameter the tolerance on the input beam size is mirrors and lenses in the image-relay system, the flattop 60 m. These tolerances also dictate the acceptable beam profile remained almost undistorted. The measured beam pointing error of an input laser beam. Presently, the optical transmission of the shaper was 92%. beam pointing error is 25 rad per degree change in the The angular misalignment (or tilt) and laser beam de- environmental temperature. The shaper requires a near 2 center (or beam lateral offset) relative to the axis of TEM00 input beam profile with a M parameter close to 2 shaper may distort the output profile. Using ZEMAX we unity. In our case, the M parameter of the laser oscillator determined and verified experimentally these tolerances as output is less than 1.1 as specified by the laser manufac- 9 mrad tilt angle and 0:38 mm decenter. Figure 6(a) turer. However, for high-power solid-state systems with a displays the simulated and experimental beam profiles at master oscillator and power amplifier, it often is difficult to propagation distances of 10 and 45 cm from the shaper. achieve a near TEM00 spatial beam profile. Therefore, an The experiment agrees well with simulation. The inferred all-fiber based high-power laser system may be preferable tolerances in the beam decenter and tilts are, respectively, to solid-state . 20 m and 0:5 mrad. Similarly, at the 4.7 mm opti-

FIG. 6. (Color) Spatial beam profile at 10 and 45 cm away from the shaper at different alignment conditions: (a) ZEMAX simulation; (b) corresponding experimental profiles.

033501-7 A. K. SHARMA, T. TSANG, AND T. RAO Phys. Rev. ST Accel. Beams 12, 033501 (2009)

Beams of different sizes on the photocathode can be then is expanded to a beam size of 4:7mmon to the obtained by placing an image relay cum shaper. As Fig. 7(a) shows, significant spatial fringes are with magnification factor other than unity or a beam– observed in the former arrangement, while the latter con- magnifier/demagnifier and unit magnification image-relay figuration yielded a relatively undistorted spatial flattop system after the shaper. With a 2X beam demagnifier the profile. The emergence of the spatial fringes with larger shaper’s depth of focus was reduced from 25 cm to beam size on the birefringent crystals may be attributed to 15 cm. The flattop beam profile was also imaged onto the small walk-off angle between all the interfering beams, the photocathode using a single imaging lens; however, to nonzero piezoelectric coefficient of the crystals [30,33], then the output beam was not collimated. or to the optical rotatory dispersion effect [34]. However, because our 10 ps laser pulses have a narrow spectral V. SPATIOTEMPORAL (THREE-DIMENSIONAL) bandwidth ( 0:4 A), we expect a negligible contribution SHAPING from optical rotatory dispersion. Although such modula- tion on the spatial intensity profile is undesirable, it was The spatiotemporal shaping has been achieved by cas- minimized to 15% (rms) over the plateau region in the cading the temporal pulse shaper and the shaper to- latter approach, as depicted in Fig. 7(b). Nevertheless, the gether. Because, the shaper has a limited depth of smaller beam size may limit the intensity range of the laser focus that can affect the cross-correlation measurements, pulses due to the damage to the crystals. we first employed temporal pulse shaping, followed by the Finally, the spatiotemporally shaped beam was image beam expander, spatial beam shaping, and finally used an relayed to 9 m; the profile is shown in Fig. 7(c). This final image-relay beam transport system (Fig. 2). Although, the output beam profile resembles the input but with a little beam expander can be positioned either before or after the additional spatial distortion. Figure 7(d) illustrates the temporal pulse shaper, we found that the latter configura- reconstruction of the beer-can shaped spatiotemporal tion was best for assuring high-quality spatiotemporal pulse, wherein the color represents the pulse intensity at shaping. different locations on the envelope of the flattop pulse Figure 7 depicts the spatial beam profiles recorded at shown in Figs. 3 and 7(b). 10 cm from the shaper for two different optical arrange- ments. In the first case, the laser beam is expanded to a beam size of 4:7mmand then incident on the temporal VI. CONCLUSION pulse stacker followed by the spatial shaper. In the latter We have presented our theoretical and experimental case, the output of the laser oscillator, with a beam size of studies on the spatial beam profile and temporal pulse 1:3mm , is incident on the temporal pulse stacker and shaping of picosecond laser pulses. We employed a set of birefringent crystals for temporal pulse shaping, and a commercial refractive beam shaper for spatial beam shap- ing. A three-dimensional flattop beam is generated by cascading these two passive devices together. We devel- oped an optical image-relay system to transport the final 3D flattop laser pulse to the photocathode located 9 m away. We theoretically studied the critical parameters to maximize the successful operation of the spatiotemporal shaper, and verified them experimentally. Tolerances to various misalignments were quantified. We obtained good agreement between our experimental results and theoretical simulations.

ACKNOWLEDGMENTS We acknowledge the technical support of John Walsh and William Smith. This work was supported by U.S. Department of Energy under Contract No. DE-AC02- 98CH10886.

FIG. 7. (Color) Spatial beam profiles at 10 cm away from the shaper with beam expander positioned: (a) before the pulse [1] I. V.Bazarov, D. G. Ouzounov, B. M. Dunham, S. A. stacker; (b) after the pulse stacker; (c) same as (b) but image Belomestnykh, Y.Li, X. Liu, R. E. Meller, J. Sikora, and relayed to 9m; (d) reconstructed beam envelope of the spa- C. K. Sinclair, Phys. Rev. ST Accel. Beams 11, 040702 tiotemporal shaped beer-can light pulse profile. (2008).

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