Analytical Model of Four-Wave Mixing in Semiconductor Optical Amplifier

Abstract

The four-wave mixing process in pump-probe configuration requires the solutions of propagation equations of the three pulses: pump, probe and conjugate simultaneously. Since the pump power is much larger than the other pulses, this makes the differential equation of pump not coupled with the other equations, hence it can be solved alone. In this paper, we consider that the differential equation of pump is linear by assuming that the amplifier is divided into small sections to be the power change through each section is too small. Solving the resulting pump equation requires calculating the integrated gain, where the integrated gain is calculated after each section numerically by an iterative equation that was derived. Simultaneously, the solution of the probe and conjugate equations were also calculated after each section, where a simple recursive formula was found. Finally, the conversion efficiency will be calculated, where the present analysis agrees very well with the numerical solution.