Theory of Phase and Amplitude Bunching in Traveling Wave Interactions

A solution is given for the parametric interaction of two traveling waves (νk, k) and (ω, k) where (vk, k) ≫ (ω, k). The strong pump wave at frequency νk is not affected but modulates the index of refraction for the weak wave at ω. The solution is for an arbitrary initial time dependence of the weak wave and can describe a large change in the fractional bandwidth of the modulatecl wave. If the phase velocities ν and ω/k are equal, the cycles of the high-frequency wave bunch together in every other half-cycle of the modulation wave and draw apart in the alternate lialf-cycles. This strong phase branching is accompanied by strong amplitude modulation that is found to have the same x and t dependence as the instantaneous frequency. © 1973, IEEE. All rights reserved.