Trapping dynamics in nonlinear wave scattering by local guiding defects

We study numerically the trapping dynamics of nonlinear waves scattered by local guiding photonic centers with normal eigenmodes which are embedded in uniform nonlinear Kerr waveguides. The linear and nonlinear scattering from a local defect may be treated from either a wave optics approach or a ray optics approach. The former provides a better understanding of the wave dynamics while the latter enables one to perform quasi-analytical estimates of the extent of trapping in a given structure. In the presence of a single-site multi-mode local scattering center, power may localize in a certain normal mode of the center, or periodically oscillate between different normal modes. The degree of trapping and mode of localization can be controlled as function of both the input power and the angle of incidence. With multi-site local scattering centers, the trapping dynamics are strongly dependent on the degree of coupling between the neighboring sites. In the scattering by a local multi-site defect with strongly coupled adjacent sites, two possibilities for nonlinear trapping arise. At intermediate nonlinear powers, periodic tunneling of power between adjacent sites and their normal modes is observed. At highly nonlinear powers, but still within experimental feasibility, the radiation can become strongly localized in a single site. The scattering and trapping dynamics are also described in the context of nonlinear Fabry-Perot etalons, as a function of the local defect's refractive index.