Modeling Parametric Processes in Few-Mode Semiconductor Optical Amplifiers

Few-mode semiconductor optical amplifiers (FM SOAs) allow more than one transverse modes to propagate inside of the waveguide region. They are useful in optical signal processing of distinct spatial mode signals when applied to spatial division multiplexing in an optical fiber communication. A model for FM SOAs including carrier rate and coupled-mode equations, which govern linear and nonlinear effects, is derived for the first time. The model reveals two distinctions of parametric process in FM SOAs through carrier gratings. First, the carrier gratings with transverse variation patterns provide unique mode selectivity, which only allows efficient interaction between certain modes. This mode selectivity is summarized as a parallelogram rule, a simple method to find the interacting modes and categorize them. Second, degenerate four wave mixing (FWM) via static carrier grating diffraction distinguishes itself from other types of FWMs for the highest wave interaction efficiency. Theoretical analysis and numerical simulation show that optical signal processing based on the degenerate FWM features high power efficiency, broadband operation, phase sensitivity, and mode selectivity. The processing can be done either in the spatial mode domain or in the frequency domain, or by combing them together. These features bestowed by the introduction of spatial degree of freedom, make FM SOAs promising in optical signal processing.