Analytical expressions of the various derivatives of the output power of the semiconductor optical amplifiers with respect to the input power

Based on the physical fact that the nonlinear distortions induced by the tr aveling-wave semiconductor optical amplifiers in the subcarrier multiplexin g CATV transmission system can be calculated by expressing the output power Po of the amplifiers with the Taylor series of the input optical power Pi and specifying the various order derivatives of Po with respect to Pi, the solutions to the rate equations of the amplifiers have been derived, and th e analytical expressions of the various order derivatives of Po with respec t to Pi have been obtained and simulated numerically by selecting typical a mplifier parameters.