Transformation of waves defined by hyperbolic variational principles

Abstract

In this chapter we consider the geometrical optics of waves defined by linear differential equations or systems. In the linear theory, waves of different kinds (say, longitudinal and oblique waves) usually propagate independently. However, in nonhomogeneous media a transformation (or ‘conversion’) of waves of different kinds is typical at certain interior points of the domain. This ‘interior scattering’ of waves also occurs in homogeneous media (Hamilton’s conical refraction in crystals). However, the geometry of the interior scattering in generic nonhomogeneous media is rather different from the geometry of Hamilton’s conical refraction, as will be seen below¹.