Numerical method for calculating spontaneous emission rate near a surface using Green’s functions
We present a novel computational approach for calculating spontaneous emission in the presence of a surface of a material slab. The only requirement on the material is that it should have periodicity parallel to the surface. The spontaneous emission rate is calculated using Fermi’s golden rule, which can be described in terms of the classical Density of States (DOS). The DOS can in turn be expressed in terms of the Green’s function. We calculate the Green’s function for light of a specific frequency and a specific incident direction and distance with respect to the surface and then integrate over all incident directions. The only information required from the material, is the reflection coefficients for plane waves at the surface. With our method we reproduce results of an analytical calculation for a semi-infinite homogeneous dielectric. We also present new results for a slab of cylindrical dielectric rods embedded in air on a square lattice.
KeywordsReflection Coefficient Spontaneous Emission Mesh Point Transfer Matrix Method Surface Distance
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