TY - JOUR T1 - 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 AU - Vahala , George AU - Vahala , Linda AU - Ram , Abhay K. AU - Soe , Min JO - Communications in Computational Physics VL - 1 SP - 22 EP - 38 PY - 2023 DA - 2023/02 SN - 33 DO - http://doi.org/10.4208/cicp.OA-2022-0034 UR - https://global-sci.org/intro/article_detail/cicp/21423.html KW - Unitary algorithms, qubits, Maxwell equations, pulse propagation. AB -

The effect of the thickness of the dielectric boundary layer that connects a material of refractive index $n_1$ to another of index $n_2$ is considered for the propagation of an electromagnetic pulse. A qubit lattice algorithm (QLA), which consists of a specially chosen non-commuting sequence of collision and streaming operators acting on a basis set of qubits, is theoretically determined that recovers the Maxwell equations to second-order in a small parameter $\epsilon.$ For very thin but continuous boundary layer the scattering properties of the pulse mimics that found from the Fresnel discontinuous jump 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 thicker one finds deviations away from the discontinuous Fresnel conditions and eventually one approaches the expected WKB limit. However there is found a small but unusual dip in part of the transmitted pulse that persists in time. Computationally, the QLA simulations still recover the solutions to Maxwell equations even when this parameter $\epsilon → 1.$ On examining the pulse propagation in medium $n_1 , \epsilon$ corresponds to the dimensionless speed of the pulse (in lattice units).