Green's functions for Maxwell's equations: application to spontaneous emission |
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Authors: | Wijnands F Pendry J B Garcia-Vidal F J Bell P M Roberts P J Moreno L Marti´n |
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Institution: | 1. Condensed Matter Theory Group, The Blackett Laboratory, Imperial College, Prince Consort Road, London, SW7 2BZ, UK 2. Defence Research Agency, St Andrew's Road, Great Malvern, Worcs, WR14 3PS, UK 3. Instituto de Ciencia de Materiales (Sede B), Universidad Auto′noma de Madrid, 280049, Madrid, Spain
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Abstract: | We present a new formalism for calculating the Green's function for Maxwell's equations. As our aim is to apply our formalism
to light scattering at surfaces of arbitrary materials, we derive the Green's function in a surface representation. The only
requirement on the material is that it should have periodicity parallel to the surface. We calculate this Green's function
for light of a specific frequency and a specific incident direction and distance with respect to the surface. The material
properties entering the Green's function are the reflection coefficients for plane waves at the surface. Using the close relationship
between the Green's function and the density of states (DOS), we apply our method to calculate the spontaneous emission rate
as a function of the distance to a material surface. The spontaneous emission rate can be calculated using Fermi's Golden
Rule, which can be expressed in terms of the DOS of the optical modes available to the emitted photon. We present calculations
for a finite slab of cylindrical rods, embedded in air on a square lattice. It is shown that the enhancement or suppression
of spontaneous emission strongly depends on the frequency of the light.
This revised version was published online in November 2006 with corrections to the Cover Date. |
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