Modeling nonlinear optical phenomena in silicon-nanocrystal composites and waveguides

Abstract

A high demand in relation to simple propagation equations describing nonlinear optical phenomena in silicon-nanocrystal composites is caused by the impracticality of solving Maxwell’s equations while treating thousands of silicon nanocrystals in the composites individually. Recently, we derived such equations for the case of two optical fields using a number of simplifying assumptions (Rukhlenko 2013 Opt. Express 21 2832–46). In particular, we neglected the effects of cross-phase modulation and cross-two-photon absorption due to the interaction between waves of different frequencies, set equal different kinds of mode-overlap factors, and assumed a uniform effective mode area for both fields regardless of their polarizations. Also, it was assumed that the fields interact inside a highly birefringent silicon-nanocrystal waveguide, which provides tight lateral confinement of its propagating modes and ensures the absence of phase matching between them. Here we abandon these approximations and generalize the coupled-amplitude equations for the case of an arbitrary number of quasi-monochromatic optical fields interacting through the third-order nonlinear polarization of silicon nanocrystals. We derive two sets of equations enabling one to study theoretically the anisotropy of such effects as Raman amplification, four-wave mixing, and wavelength conversion—one for unbounded silicon-nanocrystal composites and the other for different kinds of silicon-nanocrystal waveguides—and provide an overview of the material parameters entering these equations.