Compensation of Kerr self-focusing using negative phase shifts from the cascade quadratic nonlinearity

Summary form only given. When an intense beam propagates through a Kerr nonlinear medium, the beam´s transverse intensity profile generates a corresponding phase profile through,the intensity-dependent refractive index. The positive phase resulting from the Kerr nonlinearity (B-integral) underlies a number of physical processes, including whole-beam and small-scale self-focusing (SSSF). Self-focusing limits the peak power attainable by high energy lasers and amplifiers. We show in numerical simulation and experiment that negative Kerr-like phase shifts from cascade quadratic processes can compensate for the effects of SSSF, and cancel B-integral. We consider a two-stage system where an unchirped beam with transverse intensity modulation is incident on a Kerr medium, which generates positive phase and beam distortion due to SSSF. In the second stage, the distorted beam propagates through a quadratic medium, arranged to cancel the Kerr phase.