Qubit Lattice Algorithm Simulations of the Scattering of a Bounded Two Dimensional Electromagnetic Pulse from an Infinite Planar Dielectric Interface

Qubit lattice algorithm (QLA) simulations are performed for a two-dimensional (2D) spatially bounded pulse propagating onto a plane interface between two dielectric slabs. QLA is an initial value scheme that consists of a sequence of unitary collision and streaming operators, with appropriate potential operators, that recover Maxwell equations in inhomogeneous dielectric media to second order in the lattice discreteness. For the case of total internal reflection, there is transient energy transfer into the second medium due to the evanescent fields as the Poynting unit vector of the pulse is rotated from its incident to reflected direction. Because of the finite spatial extent of the pulse, a self-consistent Goos-Hanchen-type displacement along the interface is found without imposing any explicit interface boundary conditions on the fields. For normal incidence. the standard Fresnel coefficients are recovered for appropriately averaged QLA fields. Energy is conserved at all times to seven significant figures.