Evaluation of diffraction loss in prism light guides by finite-difference time-domain field modeling

Prism light guides are hollow dielectric tubes that use prismatic facets to guide light by means of total internal reflection. An unresolved problem has been to determine the magnitude of loss caused by diffraction in prism light guides. Neither experimental measurement nor an analytical solution has yet been achieved, so we attacked the problem numerically, in two steps. First, we found a way to represent such a transitionally invariant three-dimensional system as an equivalent two-dimensional problem. Second, we employed the finite-difference time-domain algorithm, with periodic boundary conditions, to yield a computation problem of manageable size. We found that the diffraction-induced transmissivity of a prism light guide wall is of the order of the wavelength divided by the prism size-a result that has encouraging practical implications.