Light pulse propagation through a dielectric slab. I. Retarded integral equations and their local finite-difference solution
Abstract
We describe the propagation of a nonresonant light pulse normally incident on a thin dielectric slab using an integral-equation approach to electromagnetism. This emerges naturally from the microscopic picture of the material as made of polarizable atoms, confined within the material vacuum volume by their bonding interactions, each responding to the input radiation pulse as well as to the re-radiated pulses of the other atoms to which it is causally connected. The retarded integral equations are shown to be exactly equivalent to a local wave equation coupled to an auxiliary Lorentz-oscillator equation, which we solve numerically with a finite-difference time-domain scheme. For a slab thick enough that the front- and back-surface reflections are temporally separated, the front-surface reflectivity extracted from the simulation agrees with the Fresnel formula to within 1 percent, and the back-surface echo appears at exactly the expected round-trip delay. For a slab thinner than one optical cycle, the multiply-reflected wavelets overlap and interfere, and a full space-time map of the field directly visualizes the build-up of thin-film-like interference in the time domain. The material parameters used here are illustrative rather than fitted to measured data, and the numerical scheme is verified by an explicit grid-convergence study. In a companion paper (Paper II) the retarded integral equations are solved directly, without the local reformulation, and the two independent numerical solutions are shown to agree.
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BibTeX
@misc{reali2026light,
title = {{Light pulse propagation through a dielectric slab. I. Retarded integral equations and their local finite-difference solution}},
author = {Giancarlo Reali},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29336},
eprint = {2610.29336},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29336},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Light pulse propagation through a dielectric slab. I. Retarded integral equations and their local finite-difference solution
AU - Giancarlo Reali
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.29336
UR - https://arxiv.org/abs/2610.29336
AB - We describe the propagation of a nonresonant light pulse normally incident on a thin dielectric slab using an integral-equation approach to electromagnetism. This emerges naturally from the microscopic picture of the material as made of polarizable atoms, confined within the material vacuum volume by their bonding interactions, each responding to the input radiation pulse as well as to the re-radiated pulses of the other atoms to which it is causally connected. The retarded integral equations are shown to be exactly equivalent to a local wave equation coupled to an auxiliary Lorentz-oscillator equation, which we solve numerically with a finite-difference time-domain scheme. For a slab thick enough that the front- and back-surface reflections are temporally separated, the front-surface reflectivity extracted from the simulation agrees with the Fresnel formula to within 1 percent, and the back-surface echo appears at exactly the expected round-trip delay. For a slab thinner than one optical cycle, the multiply-reflected wavelets overlap and interfere, and a full space-time map of the field directly visualizes the build-up of thin-film-like interference in the time domain. The material parameters used here are illustrative rather than fitted to measured data, and the numerical scheme is verified by an explicit grid-convergence study. In a companion paper (Paper II) the retarded integral equations are solved directly, without the local reformulation, and the two independent numerical solutions are shown to agree.
ER -