Dynamical characteristics of electromagnetic field under conditions of total reflection

TL;DR

This paper analyzes the spatial distribution and behavior of electromagnetic energy, momentum, and spin near a reflective interface, emphasizing the Minkowski momentum framework and its implications for optical field manipulation.

Contribution

It provides explicit expressions for electromagnetic dynamical characteristics at total reflection interfaces using Minkowski momentum, including novel insights into spin and momentum components orthogonal to the plane of incidence.

Findings

Discontinuities in energy, helicity, and momentum at the interface.

Continuous spin components parallel to the interface.

Regular field characteristics with no singularities in the decomposition.

Abstract

The dynamical characteristics of electromagnetic fields include energy, momentum, angular momentum (spin) and helicity. We analyze their spatial distributions near the planar interface between two transparent and non-dispersive media, when the incident monochromatic plane wave with arbitrary polarization is totally reflected, and an evanescent wave is formed in the medium with lower optical density. Based on the recent arguments in favor of the Minkowski definition of the electromagnetic momentum in a material medium [Phys. Rev. A 83, 013823 (2011); 86, 055802 (2012); Phys. Rev. Lett. 119, 073901 (2017)], we derive the explicit expressions for the dynamical characteristics in both media, with special attention to their behavior at the interface. Especially, the "extraordinary" spin and momentum components orthogonal to the plane of incidence are described, and the canonical (spin - orbital) momentum decomposition is performed that contains no singular terms. The field energy, helicity, the spin momentum and orbital momentum components are everywhere regular but experience discontinuities at the interface; the spin components parallel to the interface appear to be continuous, which testifies for the consistency of the adopted Minkowski picture. The results supply a meaningful example of the electromagnetic momentum decomposition, with separation of spatial and polarization degrees of freedom, in inhomogeneous media, and can be used in engineering the structured fields designed for optical sorting, dispatching and micromanipulation.