Appendix C: Green's function for the paraxial equation

Abstract

There is a difference in the definitions of the Green's functions for the Helmholtz equation and the paraxial equation. This difference is removed by the introduction of an appropriate excitation constant for the solution obtained from the Helmholtz equation. Then, the paraxial approximation of the exact solution found from the Helmholtz equation is the same as the paraxial approximation deduced from the paraxial equation.