Macroscopic electromagnetic theory of resonant dielectrics

Abstract

The application of the macroscopic Maxwell equations to the resonant interaction of electromagnetic radiation and dielectric crystals consisting of molecules coupled via retarded dipole fields is investigated. The macroscopic fields are defined by space averaging over volume elements of linear dimensions $\Delta$ satisfying $a\ll \Delta \ll \lambda$, where $a$ is the intermolecular separation and $\lambda$ the wavelength in vacuo. The essential point of our method is the direct derivation from the microscopic equations of a constitutive relation for a finite dielectric, taking proper account of the radiation reaction terms and avoiding the use of an expansion in powers of the molecular polarizability. The results lead to a simple interpretation of the expressions for the internal fields derived by Vlieger along similar lines, and verify the validity of the standard equations of dispersion theory to all points inside the medium a distance $\Delta$ away from the surface. The transmission and scattering of radiation at or near a molecular resonance by media of over-all extent small and large compared to the wavelength are discussed for sphere and slab geometries, and the effective natural linewidths are calculated. The limits of validity of the constitutive relation are discussed, and the existence of frequency regions where the macroscopic description breaks down due to the appearance of large spatial variations in the dipole moments is pointed out. As an example of such "antiresonant" behavior and of the role played by the higher-order radiation-damping terms, the scattering of light from two interacting molecules is treated in detail. In the absence of sufficiently strong dissipative damping, the occurrence of antiresonance is predicted to be a general phenomenon giving rise to large oscillations in the scattering cross section even in the presence of spatial dispersion in a narrow region around the frequency where the expression for the macroscopic index of refraction diverges.