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Transient fields in oblique scattering from an infinite planar dielectric interface -- a qubit lattice simulation

Min Soe, George Vahala, Linda Vahala, Efstratios Koukoutsis, Abhay K. Ram, Kyriakos Hizanidis

TL;DR

This work develops a Dyson-map–based, unitary representation of Maxwell equations for inhomogeneous dielectrics and applies a qubit lattice algorithm (QLA) to simulate time-dependent oblique scattering at a planar dielectric interface. By formulating $i \frac{\partial \mathcal{U}}{\partial t} = \mathbf{W}^{-1/2} \mathbf{M} \mathbf{W}^{-1/2} \mathcal{U}$ with $\mathcal{U} = \mathbf{W}^{1/2} \mathbf{u}$, the method achieves energy-conserving evolution and is amenable to quantum encoding through linear combinations of unitaries (LCUs) for non-unitary terms. The simulations reveal that, for subcritical oblique incidence, transmitted pulses acquire shorter wavelengths and exhibit Goos-Hanchen–like wavefront structures, with the detailed pattern depending on the incidence direction and pulse width; results extend prior normal-incidence and total-internal-reflection studies to oblique, bounded pulses. Overall, the work demonstrates the viability of second-order, energy-conserving QLA for transient Maxwell dynamics in heterogeneous media and outlines a path toward fully unitary quantum Maxwell solvers via LCUs.

Abstract

An initial value algorithm is utilized to examine the time dependent evolution of the electromagnetic fields arising from oblique scattering of bounded pulses from an infinite planar dielectric interface. Since the qubit lattice algorithm (QLA) is almost fully unitary, one finds excellent conservation of electromagnetic energy. Various Gaussian envelope pulses are considered in regimes where the incident angle is below that needed for total internal reflection. While the reflected pulse retains its overall Gaussian shape, the transmitted pulse exhibits a combination of a Gaussian envelope along with Huygen-like emitted wave fronts from the collision point of the initial pulse with the infinite dielectric interface. The strength of these Huygen wavefronts depends on the width of the incident pulse.

Transient fields in oblique scattering from an infinite planar dielectric interface -- a qubit lattice simulation

TL;DR

This work develops a Dyson-map–based, unitary representation of Maxwell equations for inhomogeneous dielectrics and applies a qubit lattice algorithm (QLA) to simulate time-dependent oblique scattering at a planar dielectric interface. By formulating with , the method achieves energy-conserving evolution and is amenable to quantum encoding through linear combinations of unitaries (LCUs) for non-unitary terms. The simulations reveal that, for subcritical oblique incidence, transmitted pulses acquire shorter wavelengths and exhibit Goos-Hanchen–like wavefront structures, with the detailed pattern depending on the incidence direction and pulse width; results extend prior normal-incidence and total-internal-reflection studies to oblique, bounded pulses. Overall, the work demonstrates the viability of second-order, energy-conserving QLA for transient Maxwell dynamics in heterogeneous media and outlines a path toward fully unitary quantum Maxwell solvers via LCUs.

Abstract

An initial value algorithm is utilized to examine the time dependent evolution of the electromagnetic fields arising from oblique scattering of bounded pulses from an infinite planar dielectric interface. Since the qubit lattice algorithm (QLA) is almost fully unitary, one finds excellent conservation of electromagnetic energy. Various Gaussian envelope pulses are considered in regimes where the incident angle is below that needed for total internal reflection. While the reflected pulse retains its overall Gaussian shape, the transmitted pulse exhibits a combination of a Gaussian envelope along with Huygen-like emitted wave fronts from the collision point of the initial pulse with the infinite dielectric interface. The strength of these Huygen wavefronts depends on the width of the incident pulse.
Paper Structure (5 sections, 18 equations, 5 figures, 1 table)

This paper contains 5 sections, 18 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Maxwell Equations in Dyson Variables
  3. QLA for Eq. \ref{['eqA6']}
  4. QLA Simulations for Oblique Angle Scattering by a Plane Dielectric Interface
  5. Summary and Conclusions

Figures (5)

  • Figure 1: Evolution of the magnetic field $H_z(x,y) > 0$ for incident angle $\theta = 25^o < \theta_c$ for two different pulse shapes. $n_1=1 \text{(left side)} \rightarrow n_2=2 \text{(right side)}$. Notation: Fig 1(b.56) in the text refers to Fig. 1b (thin long pulse) at time t = 56k.
  • Figure 2: Evolution of the magnetic field $H_z(x,y) > 0$ for incident angle $\theta = 25^o < \theta_c=30^o$ for two different pulse shapes. $n_1=2 \text{(left side)} \rightarrow n_2=1 \text{(right side)}$. Notation: Fig 2(a.76) in the text refers to Fig. 2a (burst) at time t = 76k.
  • Figure 3: Evolution of the magnetic field $H_z(x,y) > 0$ for incident angle $\theta = 25^o < \theta_c=30^o$ for a finite pulse. $n_1=2 \text{(left side)} \rightarrow n_2=1 \text{(right side)}$.
  • Figure :
  • Figure :