The effect of the thickness of the dielectric boundary layer that connects amaterial of refractive index n1 to another of index n2 is considered for the propagation of an electromagnetic pulse.A qubit lattice algorith...
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The effect of the thickness of the dielectric boundary layer that connects amaterial of refractive index n1 to another of index n2 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 theMaxwell equations to second-order in a small parameterǫ.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√n2/*** the boundary layer becomes thicker one finds deviations away from the discontinuous Fresnel conditions and eventually one approaches the expectedWKB *** there is found a small but unusual dip in part of the transmitted pulse that persists in ***,the QLA simulations still recover the solutions to Maxwell equations even when this parameterǫ→*** examining the pulse propagation in medium n1,ǫcorresponds to the dimensionless speed of the pulse(in lattice units).
A Dyson map explicitly determines the appropriate basis of electromagnetic fields which yields a unitary representation of the Maxwell equations in an inhomogeneous medium. A qubit lattice algorithm (QLA) is then deve...
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A Dyson map explicitly determines the appropriate basis of electromagnetic fields which yields a unitary representation of the Maxwell equations in an inhomogeneous medium. A qubit lattice algorithm (QLA) is then developed perturbatively to solve this representation of Maxwell equations. A QLA consists of an interleaved unitary sequence of collision operators (that entangle on lattice-site qubits) and streaming operators (that move this entanglement throughout the lattice). External potential operators are introduced to handle gradients in the refractive indices, and these operators are typically non-unitary but sparse matrices. By also interleaving the external potential operators with the unitary collide-stream operators, one achieves a QLA which conserves energy to high accuracy. Some two dimensional simulations results are presented for the scattering of a one-dimensional (1D) pulse off a localized anisotropic dielectric object.
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