Green's Function for Fresnel Reflection?
- To: mathgroup at smc.vnet.net
- Subject: [mg100957] Green's Function for Fresnel Reflection?
- From: AES <siegman at stanford.edu>
- Date: Thu, 18 Jun 2009 20:46:59 -0400 (EDT)
- Organization: Stanford University
Can anyone point to a two-dimensional Green's Function for the classical Fresnel reflection problem of a linearly polarized infinite plane wave striking the planar interface between two unbounded half-spaces with different refractive indices? [This is admittedly a math-and-physics rather than Mathematica question; but there's an incredible level of mathematical smarts on this group, and I'd like to implement the answer in some extended Mathematica calculations.] Specific case of interest can be described as a y-polarized E field with k vector in the x,z plane; interface in the x,y (or y,z) plane; with wave going from higher to lower index half space so that TIR occurs above a critical angle, as treated using plane-wave analysis in every elementary optics or e-m theory text. A closed-form or special-function Green's function solution for a point source instead of an infinite plane wave would be extremely useful; and digging into Helmholtz/Weyl decomposition to derive something like this looks like very heavy going. Extension to point source located in higher-index planar slab between two lower-index half spaces (aka a planar waveguide) would be truly great.