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 - <p style="text-align: justify;">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).</p>