Laplace-transform-based method to calculate back-reflected radiance from an isotropically scattering half-space

We present a method to determine the back-reflected radiance from an isotropically scattering half-space with matched boundary. This method has the advantage that it leads very quickly to the relevant equations, the numerical solution of which is also quite easy. Essentially, the method is derived from a mathematical criterion that effectively forbids the existence of solutions to the transport equation which grow exponentially as one moves away from the surface and deeper into the medium. Preliminary calculations for infinitely wide beams yield results which agree very well with what is found in the literature.

Calculation of the radiance distribution at the boundary of an isotropically scattering slab

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.

On the existence of non-radiating frequencies in the radiation from a stochastic current distribution

The theory of non-radiating stochastic current distributions is developed within the framework of first-order coherence theory of electromagnetic fields. Necessary and sufficient conditions for non-radiating current correlations are derived. A class of non-radiating stochastic current distributions is constructed. In contrast to these results, it can be shown that any non-trivial field correlation given on an arbitrary surface radiates

Coherence effects in propagation through photonic crystals

We have analytically studied how a partially coherent quasi plane wave is affected by a photonic crystal structure including a grating. The analysis is presented for spatial and temporal cases showing the possibility to determine the coherence characteristics of the pulse.