Gaussian-mode analysis of waveguide-enhanced Kerr-type nonlinearity of optical fibers and photonic wires

The Gaussian approximation of waveguide modes is used to analyze a Kerr-type nonlinearity of an optical fiber. This analysis gives physical insights into the behavior of the optimal transverse size of a waveguide providing the maximum enhancement of nonlinear-optical processes as a function of the core-cladding refractive-index step and the radiation wavelength. We show that, for the maximum enhancement of nonlinear-optical processes in a fiber where only the core is nonlinear, the effective mode area needs to be slightly larger than its minimum value. In the case of fused-silica fibers, the maximum enhancement of nonlinear-optical processes is achieved with fiber core diameters that are less than the radiation wavelength.