We develop a detailed theory of the transverse instabilities that can occur as two laser beams intersect in a nonlinear Kerr medium. Our analysis of the interaction includes all the various sources of nonlinear phase shifts of the interacting fields as well as the mutual interaction of the two pump waves. In general, the interaction gives rise to a four-sidemode process. The couplings among the sidemodes arise from three distinct interactions of modulational instability, two-beam-excited (TBE) conical emission, and nonlinear Bragg diffraction. Modulational instability and TBE conical emission are shown to exhibit exponential spatial gain. The value of this gain is higher for the case in which both processes contribute than in the cases in which the two processes occur singly. Nonlinear Bragg diffraction is shown to be a spatially stable process by itself. However, in the presence of the other two processes this process provides an additional nonlinear phase shift that changes the direction of maximum growth of the instability. In none of the cases does the maximum growth occur for perfect linear phase matching.
© 1993 Optical Society of America
Original Manuscript: March 29, 1993
Published: December 1, 1993
Martti Kauranen, Alexander L. Gaeta, and C. J. McKinstrie, "Transverse instabilities of two intersecting laser beams in a nonlinear Kerr medium," J. Opt. Soc. Am. B 10, 2298-2305 (1993)