Abstract

Spatial and temporal instabilities are known to occur when light propagating in a Kerr medium is modulated spatially and temporally respectively. The simultaneous presence of diffraction and dispersion in nonlinear media give rise to spatiotemporal instabilities. The analysis in this previous research accounted for GVD in the slowly varying envelope approximation (SVEA). However, the self- focusing of femtosecond pulses is not adeequately described by the SVEA in dispersive media. This work deals with the theoretical analysis of spatiotemporal instabilities of femtosecond pulses propagating in a nonlinear medium. More specifically, we investigate space-time focusing effects on those instabilities including up to fourth order dispersion and considering the wavevector k(Ω) series expansion keeping terms of O(Ω²), instead of O(Ω) as in reference (1) to obtain, where v_gis the group velocity, β₂the group velocity dispersion, k₀the propagation constant and k_T= $\sqrt[]{k_x^{\text{2}}+k_y^{\text{2}}}$ with k_x, k_yand k_zas the cartesian components of k.The new terms represent a coupling between GVD and diffraction. Following along the lines of reference (3), investigation of the instability is based on a linear stability analysis around a quasi-homogeneous-stationary solution of the wave equation by inserting.

© 1995 IEEE