Multimode analysis of compound parabolic concentrators with flat absorber.

We introduce the concept of the reflection mode in the analysis of data generated by ray tracing for the study of the overall optical behavior of compound parabolic concentrators (CPC's) for beam radiation. The light ray paths in two classical CPC cavities with a flat absorber, full and truncated, were simulated by a system of two recurrent series derived for this purpose. The optical behavior of the cavities is summarized by two sets of functions, P(k)(θ(i)) and S(k)(a, θ(i)), each with an infinite number of terms, that depends on the incident angle θ(i) and on the aperture position a traversed by a light ray. These functions satisfy general properties of symmetry, inclusion, and convergence, either in the angular or in the spatial domains of the aperture and absorber. The use of those functions for calculating the angular acceptance, local and average optical efficiency, and flux density distribution is illustrated. Applications to the design of gaps are also discussed. Although this method of analysis is exemplified for the classical CPC's, the properties and applications of these functions are likely to extend to other types of nonimaging concentrators.