Interference of Polariton Waves in a Thin Film of CuCl: Additional Boundary Conditions and the Effect of Selective Pumping

Abstract

It is well known that, in a spatially dispersive medium which is described by a dielectric function with an explicit dependence on wave vector k, as well as frequency ω, ε (k, ω), an electromagnetic wave with a given frequency can propagate in several different modes, i.e., with various wavelengths. At the boundary of this medium, in touch with a non-spatially dispersive medium (vacuum for example), there arises a problem of so-called “Additional Boundary Conditions (ABC)”, since the number of the waves on both sides is, for a given frequency, larger than that of the Maxwell boundary conditions (MBC: Tangential components of E and H should be continuous.). This ABC problem, first noted by PEKAR [1], has attracted much attention for a long time from both theoretical and experimental points of view [2]. A study of interference pattern in a thin film has been considered to provide very useful information about such media. It is, however, only very recently that fine experimental results have become available [3, 4]. They provide a good chance to sensitively check the various ABC theories proposed so far. Especially in CuCl, further experiments with the use of pumping light have been carried out to obtain information as to how the upper and lower branch polaritons are produced and mutually correlated through ABC [4, 5]. These measurements have given rise to a new aspect of the ABC problem, and the theoretical interpretation of these pumping experiments is not yet established in spite of several proposals [6–8].