WFl(1nvited) 8:30am-9:00am zyxwvutsrqpo Compensation of self-focusing using the cascade quadratic nonlinearity Kale Beckwitt('), Frank W. Wise('), Liejia Qian(2), Larry A. Walker 11(3), and Edesly Cant~-Said(~) zyxw (l) Department of Applied Physics, Cornell University, Ithaca, zyxwv NY 14853 607-255-9956 (phone), 607-255-7658 (fax), kb778wrnell.edu (email) (2)Shanghai Institute of Optics and Fine Mechanics, PO Box 800-211, Shanghai 201800, China 86-21-5953-4890 (phone), 86-21-5952-8812 (fax), liejia@hotmail.com (email) (3) Clark-MXR, Inc., 7300 West Humn River Dr., Dexter, MI 48130 734-426-2803 (phone), 734-426-6288 (fax) Abstract: zyxwvutsrq We demonstrate theoretically and experimentally the compensation of positive Kerr phase shifts with negative phases generated by cascade quadratic processes. Experiments show correction of small-scale and whole-beam self-focusing, and self-phase modulation. When an intense beam propagates through a third-order nonlinear medium, its intensity profile generates a corre- sponding phase profile through the intensity-dependent refractive index. The phase shift resulting from the electronic Kerr nonlinearity underlies a number of physical processes, including whole-beam (WBSF) and small-scale self- focusing (SSSF) in space [l], and self-phase modulation (SPM) in time [2]. Since self-focusing limits the peak power attainable by high energy lasers and amplifiers, and SPM underlies the need to use pulse stretching in regenerative amplifiers (RAs) [3], a means of compensating these effects is desirable. Self-focusing and SPM in materials with zyxwvutsrq n2 > 0 arise from nonlinear phase shifts ( a ; ; , = (27r/X) nddz, so one can utilize a material with real or effective zyxwvutsrq n2 < 0 for compensation. One way to generate such a compensating phase is through the negative nonlinear refractive index present in semiconductors. GaAs wafers were used to suppress the effects of self-focusing [4], and to cancel the B-integral [5]. However, this approach has the disadvantages inherent to semiconductors: high loss due to two-photon absorption and relatively low damage threshold. Recently, the phase shifts generated by cascading x(~) processes in quadratic nonlinear media have garnered attention because they can be large in magnitude, have controllable sign, and are proportional to intensity in the limit of large phase mismatch between the fundamental (FH) and second-harmonic (SH) waves [6]. It has been shown that cascade phase shifts can compensate the B-integral in a fiber amplifier [SI. Here we show in numerical simulation and experiment that negative phase shifts from cascade quadratic processes can effectively compensate the effects of self-focusing. We demonstrate compensation of both SSSF and WBSF in the propagation of femtosecond pulses in bulk fused silica. In addition, we show cancellation of the B-integral from a picosecond Tisapphire amplifier with pulse energies zyxwvut N 6 orders of magnitude greater than demonstrated in [8]. As in [7] we model the system with the coupled wave equations for the FH and SH fields in a medium with zyx x@) and x(~) nonlinearity. Fig. 1 shows the results of numerical simulations performed under conditions typical of a mJ-pulse energy RA. In the absence of compensation, a beam with transverse intensity modulation (Fig. l(a)) traverses a piece of x(~) material which produces (aNL N K and increases the spatial intensity modulation (Fig. l(b)). With compensation, the intensity profile is smoothed compared to the uncompensated case (Fig. l(c)). zyxw y (arb. units) Fig. 1. Simulated transverse intensity profile (a) at input with seeded intensity modulation, (b) after propa- gation through 6 cm of fused silica, (c) with optimal compensation, and (d) overcompensating Kerr phase. Experimentally, we observe self-focusing after propagating the output of a Ti:sapphire RA (A, = 800 nm, ~ W H M = 150 f s, E M 600 pJ/pulse) through 6 cm of fused silica. Fig. 2 shows the experimental beam profiles. At low intensity, we observe linear propagation through the fused silica (Fig. 2(a)). At high intensity (10 = 23 GW/cm2, ipNL 1.1~) we observe both WBSF (narrowing of the beam profile) and SSSF (increased modulation depth between the noise peaks and background) (Fig. 2(b)). To compensate self-focusing, a 2.5 cm long BBO crystal is inserted into the beam path immediately before the fused silica. As a control experiment, we orient the BBO so that only the Kerr 0-7803-7105-4/01/$10.0002001 IEEE 439