Waveguide optimization for dielectric media variation based on the FDTD method and the Monge-Kantorovich mass transfer problem

An efficient methodology is developed to analyze 3-D waveguide structures when their dielectric permittivity parameters are unknown or under optimization. Mainly, the configuration is numerically solved for a set of predetermined permittivity values through a time-domain (herein the FDTD) technique at least twice, depending on the desired accuracy. Finally, using a mass transfer problem formulation, the desired fields are rigorously evaluated for a broader range of values, as substantiated by several results.