Transverse modulation instability of vector optical beams in quadratic nonlinear media

A full vector formalism of coupled fundamental second-harmonic waves is used to analyze transverse modulation instability of plane-wave eigenstates in quadratically nonlinear optical media. The unperturbed eigenstates are constrained to balance their nonlinear phase mismatch to be equal to the linear phase mismatch. The existence of significant cross-phase modulation, which results in significant gain in all spatial-frequency ranges in both the focusing and the self-defocusing regimes, is demonstrated. It is also shown that the gain curves are significantly different at low and high input powers because of competition between birefringence and pure cross-phase modulation-induced gain. (C) 1997 Optical Society of America.