A Heat-Equation Approach to Mixed Ray and Modal Representations of Green's Functions for ∇2 + κ2


  • Herbert Kurss


A Green's function G for ∇2 + κ2 is interpreted essentially as a Laplace transform of a Green's function H for ∇2 - ∂/∂t. The Laplace integral is evaluated by selecting a mixing parameter T and representing H by rays in (0, T) and modes in (T, ∞). This procedure enables one to systematize, simplify, and extend the scope of the technique originated by Ewald (1916). As an illustration, G for a parallel-plate wave guide is detailed.