Abstract

Using parallel computers, we numerically study the propagation of beams in a quadratically nonlinear medium with a square law transverse distribution of the index of refraction, as in a graded index optical fiber. A symmetrized split-step beam propagation method is used to solve the coupled differential equations in the paraxial approximation. We show that in the range of moderate intensities, a periodic solution for the fundamental beam resulting from the superposition of many linear modes is only weakly perturbed. The second harmonic transverse profile, however, is generally nonperiodic and usually exhibits a ring structure. The single-mode solution becomes generally unstable, and periodic changes of the transverse intensity profile emerge.

© 1992 Optical Society of America