Evaluation of addition coefficients introduced by the addition theorems for vector spherical harmonics is one of the most intractable problems in electromagnetic scattering by multi-sphere systems. The derivation of the analytical expressions for the addition coefficients is lengthy and complex while the computation of the addition coefficients is annoyingly time-consuming even with the reasonably fast computers available nowadays. This paper presents an efficient algorithm for calculating addition coefficients which is based on the recursive relations of scalar addition coefficients. Numerical results from the formulation derived in this paper agree with those of previous published results but the algorithm proposed here reduces the computational time considerably. This paper also discusses the strengths and limitations of other formulations and numerical techniques found in the literature.

We have proposed a highly scattering optical transmission (HSOT) polymer for use as a high efficiency light source medium. This polymer contains specified internal microscopic heterogeneous structures for controlling light-transmission properties. An LCD backlighting system having a new light pipe made of this polymer has twice the brightness of the conventional one. A light scattering phenomenon inside the HSOT polymer was quantitatively analyzed by a ray tracing simulation based on the Mie scattering theory and the Monte Carlo method. The illumination of the backlight which is optimized by using the simulation program has enough uniformity of intensity and color because of specified multiple light scattering phenomena inside the HSOT polymer. We propose the new backlighting system having fewer components and twice efficiency of the conventional one.