The Effect of the Width of the Incident Pulse to the Dielectric Transition Layer in the Scattering of an Electromagnetic Pulse — A Qubit Lattice Algorithm Simulation (Communications in Computational Physics, 2023)
The effect of the thickness of the dielectric boundary layer that connectsa material of refractive index $n_1$ to another of index $n_2$ is considered for the propagationof an electromagnetic pulse. A qubit lattice algorithm (QLA), which consists of a specially chosen non-commuting sequence of collision and streaming operators acting ona basis set of qubits, is theoretically determined that recovers the Maxwell equations tosecond-order in a small parameter $ε.$ For very thin but continuous boundary layer thescattering properties of the pulse mimics that found from the Fresnel discontinuousjump conditions for a plane wave - except that the transmission to incident amplitudes are augmented by a factor of $\sqrt{ n_2/n_1}.$ As the boundary layer becomes thickerone finds deviations away from the discontinuous Fresnel conditions and eventuallyone approaches the expected WKB limit. However there is found a small but unusualdip in part of the transmitted pulse that persists in time. Computationally, the QLAsimulations still recover the solutions to Maxwell equations even when this parameter $ε → 1.$ On examining the pulse propagation in medium $n_1, ε$ corresponds to thedimensionless speed of the pulse (in lattice units).