Statistical Modeling and Performance Characterization of Ultrashort Light Pulse Communication System Using Power-Cubic Optical Nonlinear Preprocessor

In this paper, we present an analytical approach in obtaining the probability density function (pdf) of the random decision variable Y, which is formed at the output of the power-cubic all-optical nonlinear preprocessor followed by the photodetector, with applications in ultrafast optical time-division multiplexing and optical code-division multiple-access systems. Our approach can be used to accurately evaluate the performance of ultrafast pulse detection in the presence of Gaussian noise. Through rigorous Monte Carlo simulation, the accuracy of the widely used Gaussian approximation of decision variable Y is refuted. However, in this paper, we show that the so-called log-Pearson type-3 (LP3) pdf is an excellent representation for the decision variable Y. Three distinguishable parameters of the LP3 pdf are obtained through an analytical derivation of three moments of the decision variable Y. Furthermore, toward a more realistic model, in addition to amplified spontaneous emission Gaussian noise, the effects of shot and thermal noises are also included. Finally, using the presented analytical approach, it is shown that the power-cubic preprocessor outperforms its quadratic counterparts, i.e., second-harmonic-generation and two-photon-absorption devices, in the high-power regime where shot and thermal noises can be neglected.