Analytic theory of coherent cross-gain modulation in semiconductor travelling-wave amplifiers

We report a simple analytic solution to the problem of cross amplitude-phase modulation in nonlinear two-wave mixing, under the approximation of constant saturating power. The results are applied to travelling-wave semiconductor laser amplifiers where the linewidth enhancement factor inevitably leads to amplitude-phase coupling and asymmetric energy transfer. Our solution is used to obtain the transmission gain of each beam, the spectral profile and the amplifier input-output characteristics. Limits are established as to the applicability of the analytic solution, by comparison with numerical solutions to the related full four-wave mixing problem.