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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.


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