Kinematic wave theory

Abstract

In the kinematic theory of wave propagation (e. g. geometrical optics) a quantity J is needed in the calculation of wave intensity either through transport equations or the principle of conservation of wave action. This quantity is a spatial Jacobian with respect to a parameter space and represents a volume element convected with the rays. To avoid its direct computationas a Jacobian, derived ray equations are obtained whose solutions lead to alternative ways of calculating J . This approach is specialized to cases involving Snell’s law (with cylindrical and spherical as well as planar symmetry) and non-dispersive propagation. The behaviour of the theory under Lorentz transformations is shown.