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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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