Three-dimensional ideal concentrators for distant sources

Abstract

Ideal radiation concentrators suitable for distant localized sources are investigated. In all such concentrators, the maximal time-averaged concentration achieved for a distant point source which spends equal time in every direction of the solid acceptance angle ω is π/ω. A necessary requirement for ideality for distant localized sources in that ω has the same magnitude and uniform shape across the entire entrance aperture of the concentrator (this is not required of maximal concentrators of isotropic diffuse radiation). Peak concentration in terms of the magnitude of ω is found to be closest to the derived limit of (2π/ω) 2 in linear, extreme asymmetrical concentrators, which achieve a peak concentration of 2/tan(ω/4). Limits of performance for ideal transformers having an exit solid angle of less than 2π steradians are derived. Refractive concentrators are discussed and ideal linear refractive transformers are shown to be impossible.