Dispersion of nonlinearity in subwavelength waveguides: derivation of pulse propagation equation and frequency conversion effects

Description of pulse propagation in waveguides with subwavelength features and high refractive index contrasts requires an accurate account of the dispersion of nonlinearity due to the considerable mode profile variation with the wavelength. The corresponding model derived from asymptotic expansion of Maxwell equations contains a complicated network of interactions between different harmonics of the pulse, and therefore is not convenient for analysis. We demonstrate that this model can be reduced to the generalized nonlinear Schrödinger-type pulse propagation equation under the assumption of factorization of the four-frequency dependence of nonlinear coefficients. We analyze two different semiconductor waveguide geometries and find that the factorization works reasonably well within large wavelength windows. This allows us to utilize the pulse propagation equation for the description of a broadband signal evolution. We study the mechanism of modulational instability induced by the dispersion of nonlinearity and find that the power threshold predicted by the simple model with three interacting harmonics is effectively removed when using pulses, while the efficiency of this process grows for shorter pulse durations. Also, we identify the effects of geometrical and material dispersion of nonlinearity on spectral broadening of short pulses in semiconductor waveguides.