Radiation pressure and the linear momentum of light in dispersive dielectric media

Masud Mansuripur

doi:10.1364/opex.13.002245

Abstract

We derive an exact expression for the radiation pressure of a quasi-monochromatic plane wave incident from the free space onto the flat surface of a semi-infinite dielectric medium. In order to account for the total optical momentum (incident plus reflected) that is transferred to the dielectric, the mechanical momentum acquired by the medium must be added to the rate of flow of the electromagnetic momentum (the so-called Abraham momentum) inside the dielectric. We confirm that the electromagnetic momentum travels with the group velocity of light inside the medium. The photon drag effect in which the photons captured in a semiconductor appear to have the Minkowski momentum is explained by analyzing a model system consisting of a thin absorptive layer embedded in a transparent dielectric.

Highlights

In a previous paper [1] we showed that the momentum density p of a plane electro-magnetic wave inside a dispersionless dielectric medium may be expressed as the average of the Minkowski and Abraham momentum densities [2], namely, p = 1⁄4 Real (E × H*)/c2 + 1⁄4 Real (D × B*)
The first term is the Abraham momentum density of the field, while the second term is the mechanical momentum density imparted to the medium. (If the coefficient of the second term were 1⁄2 instead of 1⁄4, the total momentum density p would have been equal to the Minkowski momentum.) The electromagnetic and mechanical momenta of the light inside the dielectric are not decoupled from each other
This fact is better appreciated if one observes, for instance, that the same beam of light, upon emerging into the free-space at the exit facet of a dielectric slab, recovers its total initial momentum by re-converting the mechanical momentum to electromagnetic momentum [1]

Summary

Introduction

For simplicity’s sake, we assume that the entrance and exit facets of the dielectric slab are anti-reflection coated, upon transmission, the emerging beam’s momentum will be identical to the momentum it possessed before entering the slab; in other words, the (partial) conversion of the beam’s momentum into mechanical form that takes place while the beam passes through the slab, is fully reversed when the beam leaves the slab and returns to the free space Another example of the “connectedness” of the electromagnetic and mechanical momenta was provided in [6], where the radiation pressure on a dielectric wedge and its surrounding liquid was found to arise from the total momentum of the beam as opposed to, say, from one or the other of its constituents. To resolve the discrepancy between the theory and certain experiments in which the light appears to possess the Minkowski momentum, we propose a model system for analyzing the photon drag effect observed in certain bulk semiconductors

Superposition of two plane waves in free space

Superposition of two plane waves in a dielectric medium

The photon drag effect