Dielectric slab reflection/transmission as a self-consistent radiation phenomenon

TL;DR

This paper presents a self-consistent radiative approach to analyze wave reflection and transmission through a dielectric slab, offering an exact, boundary-condition-independent solution that emphasizes physical transparency and mathematical elegance.

Contribution

It introduces a novel self-consistent integral equation framework for dielectric slab reflection, avoiding boundary condition guesswork and providing a more physically transparent solution.

Findings

Exact cancellation of interior fields demonstrated.

Integral equation approach yields constructive buildup of reflected/transmitted fields.

Framework confirms Ewald-Oseen extinction without traditional boundary conditions.

Abstract

We revisit the electromagnetic problem of wave incidence upon a uniform, dissipative dielectric slab of finite thickness. While this problem is easily solved via interface field continuity, we treat it under the viewpoint of radiative self-consistency, with interior current sources gauged by ohmic/polarization comparisons against those of the exterior medium. Radiative self-consistency yields an integral equation over the slab field giving a fully constructive buildup of the reflected/transmitted contributions, without any need for implicit determination via boundary conditions. Solution steps lead to an exact cancellation of the interior field, and bring in still other contributions of a reference medium variety, required to balance the incoming excitation. Such balancing provides the linear conditions for slab field determination. This two-step solution provides evidence of Ewald-Oseen extinction, even though the analytic framework here differs from the proofs available. We solve the balancing equations by vector manipulation without determinants, and then offer a boundary value confirmation in the special case of perpendicular incidence. In an appendix, we allow the the upper/lower half spaces to differ, the upper serving as reference and remote launch site of the incoming excitation. Effective currents now exist both within the slab and throughout an entire half space, necessitating a provision for cross-talk between slab and the radiating half space. The appendix provides an accelerated presentation of these generalized features, but stops short of an explicit field solution by reason of algebraic inflation. All logical details are however displayed in plain view. The self-consistency program is far more elegant and physically far more satisfying than the prevailing method of scattered fields guessed as to their structure and then fixed by boundary conditions.