Tracing optical force fields within graded-index media

Abstract

The mechanical interaction between light and graded index media (both isotropic and anisotropic) is presented from the geometrical optics (GO) perspective. Utilizing Hamiltonian equations to determine ray trajectories combined with a description of the Lorentz force exerted on bound currents and charges, we provide a general method that we denote ‘force tracing’ for determining the direction and magnitude of the bulk and surface force density in arbitrarily anisotropic and inhomogeneous media. This technique provides the optical community with machinery which can give a good estimation of the force field distribution in different complex media, and with significantly faster computation speeds than full-wave methods allow. Comparison of force tracing against analytical solutions shows some unusual limitations of GO, which we also illustrate.