Nonlocal Theory of Radiation-Matter Interaction: Boundary-Condition-Less Treatment of Maxwell Equations

Abstract

Based on the separability with respect to position variables of the susceptibility for a finite system, we have developed a formulation which solves Schri:idinger and Maxwell equations selfconsistently. The case of linear response is' described in detail. As a manifestation of the selfconsistency between the two equations, the appearance of radiative damping rate with correct magnitude has been demonstrated for a two-level atom in vacuum. § 1. Introduction 225 The interaction of electromagnetic (EM) radiation with matter has been studied in various aspects for quite a long time. The relevant phenomena range, in the scale of wavelength, from rf wave (NMR, for example) to gamma ray (Mossbauer effect): They are related with the absorption, reflection, transmission, propagation, refrac-tion, scattering, diffraction, emission, etc. of EM wave in linear and nonlinear manner. For the theoretical treatment of these phenomena, we need Schrodinger equation for the description of matter and Maxwell equations in classical or quantized form for radiation field. When the Maxwell equations are treated in classical form, this is called semiclassical treatment of radiation-matter interaction. Though it has a certain limitation, the semiclassical treatment can be appliedto most of the phenomena mentioned above. For the treatment of the interaction of EM radiation with solids, it is usual to employ a susceptibility function to describe the solid, and solve the Maxwell equations containing that susceptibility as an integral kernel. In doing so, we must consider the boundary conditions (BC) arising from the shape of the sample in question. However, we do not consider BC's in treating microscopic systems such as an atom or small molecule. This would mean that the use of BC(s is in general not compulsory, although we are so much accustomed to it. In this respect, there has been a long debated problem of additional boundary condition (ABC) in relation with exciton polaritons in semiconductors or insulators, where the nonlocal nature of the medium allows the existence of two or more eigenmodes of the coupled exciton-EM radiation. After the long history of the ABC problem,r>-4 > we now have a recipe to derive the appropriate form(s) of ABC(s) from a microscopic model of the medium including the details of the surface. 5 >-s> Another form of the microscopic solution of the ABC problem has been given as an ABC-free formulation, 9 >-n> where one needs