Aberrationless effects of nonlinear propagation

Abstract

For nonlinear propagation, scaled complex ray tracing [Opt. Commun.119, 218 (1995)] in samples of Kerr media is accomplished in terms of four independent aberrationless effects: optical self-shortening, beam waist shift, waist width modification, and on-axis phase shift. A complex amplitude nonlinear modification is also introduced, and a symplectic nonlinear ABCD matrix is determined. All the aberrationless effects are self-consistently defined, and their dynamics are shown for focusing and defocusing nonlinearities, beam powers up to the self-trapped soliton or critical levels, and propagation ranges including those that contain a self-collapse point. The multidimensional nature of the analysis is indicated, and its relevance to pulse compression, Z-scan measurements, and higher-order mode propagation is outlined.