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 travelingwave semiconductor optical amplifiers in the subcarrier multiplexing CATV transmission system can be calculated by expressing the output power P o of the amplifiers with the Taylor series of the input optical power P i and specifying the various order derivatives of P o with respect to P i , the solutions to the rate equations of the amplifiers have been derived, and the analytical expressions of the various order derivatives of P o with respect to P i have been obtained and simulated numerically by selecting typical amplifier parameters.