Chapter 2.3.2 - The Theory of Light Scattering in Continuous Dielectric Media

Abstract

This chapter proposes the theory of light scattering in continuous dielectric media. The Ewald-sphere construction is universal in scattering theory and has been widely used, particularly in X-ray scattering and electron diffraction. In many cases, a long-lived excitation (quasi-particle), A, that only couples significantly to a small energy range of the same excitation exists. In such cases, an energy-independent A is obtained with a small complex part and a “single-mode” theory is proposed. If this excitation describes a locally conserved variable then its lifetime would increase with wavelength and a “hydrodynamic” mode is introduced. For such modes at energies sufficiently large compared with the inverse lifetime, an expansion of lA, can be made in powers of the wave vector. The energy dependence giving rise to the real poles, however, can be described by analytic continuation of the function into a second sheet of the complex plane.