HEMISPHERICAL CONCENTRATORS AND SPECTRAL FILTERS FOR PLANAR SENSORS IN DIFFUSE-RADIATION FIELDS

A dielectric hemisphere of refractive index N can act as an N-2 concentrator of isotropic diffuse radiation under appropriate conditions. We give an analytic expression for the gain of a concentrator of arbitrary radius, neglecting surface reflections, and numerical methods for calculating the gain when the surface transmissivity is an arbitrary function of incidence angle. The theory is applied to the design of multilayer spectral filters for hemispherical concentrators. When an appropriate wavelength shift is incorporated into the design process, an 11-layer, coupled-cavity spectral filter on the surface of a hemisphere of index 1.5 shows excellent bandpass performance with a concentrator radius as small as 3 times the sensor radius. This concentrator-filter combination shows a peak response of 97% of the ideal N-2 response at 950 nm, together with a FWHM of 55 nm.