Thresholds of transverse instabilities arising from the mutual interaction of counterpropagating waves in a slab of Kerr medium without any cavity or mirror feedback are calculated from first principles, allowing for the effects of diffusion on the longitudinal index grating and for the field polarization. It is shown that the amplitude and polarization instabilities decouple in the linear limit under rather general conditions. Static polarization instabilities may have lowest threshold for finite transverse wave vector or on axis, depending on the Kerr constants. Analytic expressions are presented for the latter case. Numerical simulations show hexagon formation, consistent with related experiments.

Date Published: 16 December 1992
PDF: 14 pages
Proc. SPIE 1840, Transverse Patterns in Nonlinear Optics, (16 December 1992); doi: 10.1117/12.131800

Published in SPIE Proceedings Vol. 1840:
Transverse Patterns in Nonlinear Optics
Nikolay N. Rosanov, Editor(s)