Reflection and transmission of plane unbounded electromagnetic waves at an absorbing–nonabsorbing interface with numerical calculations for an ocean–air interface

Abstract

The problem of how plane unbounded electromagnetic waves in an absorbing medium are reflected and transmitted at an interface between an absorbing medium and a nonabsorbing medium is a problem of much current interest. In this paper, we will present a Maxwellian boundary-type solution to this problem in which the forms of the E and H components are determined from Maxwell's equations and the boundary conditions, and the radiant fluxes, represented by the Poynting vector, evaluated in both media. From these radiant fluxes, it is possible to determine the forms of the radiant flux flow lines and to see how the propagation characteristics differ in the two media. In the second medium, we again find, as in total internal reflection [A. I. Mahan and C. V. Bitterli, Appl. Opt. 17, 509 (1978)], that inhomogeneous nontransverse waves appear, whose planes of constant phase are normal to the refracted rays and whose planes of constant amplitude are parallel to these refracted rays. Because of these inhomogeneous waves, the second medium, although nonabsorbing under more familiar conditions, now exhibits refractive indices and absorption coefficients, which are functions of the more conventional optical constants and the angle of incidence, and new laws for reflection and transmission appear along the interface for both polarizations. These equations have been applied specifically to an ocean-air interface for a frequency of 100 Hz, and extensive calculations were carried out in which the radiant fluxes and their associated radiant flux flow line forms were determined along the interface and at other points outside the interface for both polarizations under steady state, time changing, and time average conditions. The radiant flux flow lines in the air above the ocean take the forms of up and over radiant fluxes, some of which are trapped above the interface and the remaining flow lines come out of the interface and return to the interface. These ideas are extensions of our earlier work on total internal reflection and show how the radiant fluxes and their associated flow lines in the second medium can be changed markedly by simply making the incident medium absorbing.