Recently a novel method has been proposed for the calculation of the scattering of an incoming electromagnetic wave by an arbitrarily shaped photonic crystal. The method rests on the representation of an arbitrary electromagnetic field inside a volume V by a fictitious surface current distribution along the boundary of this volume which acts as a source for a point response tensor for the medium. The validity of such a representation is rigorously proven.
The radiance arising from an anisotropically scattering illuminated stack of n slabs is calculated using the equation of radiative transfer. It appears to be unnecessary to calculate the radiance inside the material; including only the radiance at the boundary surfaces is sufficient to obtain the desired result. The novel method used for the solution of this problem leads immediately in a straightforward and systematic way to the known appropriate basic equations valid for the problem at hand, otherwise derived by ad hoc methods. A new simple set of linear equations for the radiance at the boundary surfaces is derived. This method applies equally well to similar problems with other geometries. Apart from this analytical derivation, this paper presents the results of the numerical solution of the set of equations that we obtained from the equation of radiative transfer, for n = 1. The results of the numerical calculations are compared with what is found in the literature and are found to give very good agreement.
We present a new method to calculate the scattering of light at the surface of a photonic crystal. The problem is solved in terms of virtual surface-current distributions and the calculation takes full advantage of the existing infmite-space plane-wave expansion method for obtaining the photonic band structure. Working with surface currents makes the calculations less-time consuming by means of reduction of the dimensionality in the problem. The method is tested and illustrated for semi-infmite two-dimensional photonic crystals of small and large dielectric contrast.
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