PHYSICAL REVIEW SPECIAL TOPICS - ACCELERATORS AND BEAMS 12, 033501 (2009) Theoretical and experimental study of passive spatiotemporal shaping of picosecond laser 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 ultrashort pulse laser 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-harmonic generation 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 light 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 À45 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 À 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 à IstackðtÞ¼EstackðtÞEstackðtÞ 0 jnoLo À neLej t ¼ t À t ¼ ; X2n X2n X2n d o e c (1) ¼ Ijðt À 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 À ÞI ðt À 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 À jÞkðt À 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 d½tanð e þ Þtan o sin individual replica pulses. The second term represents the cos o interpulse interference that is governed by the polarization d sequence (p^ j:p^ k) and the phase difference [jðtÞkðtÞ] Le ¼ OC ¼ ; (2) cosð e þ Þ between pulses containing static and time-varying terms. Equation (6) suggests that the final temporal pulse profile 0 where sin ¼ no sin o ¼ ne sin e 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 cosð e þ Þ þ½no sinð e 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.