An Axially Graded Index LEns (AGILE) is provided. Such optical elements can provide optical concentration in excess of the free-space brightness theorem limit, because of the increased refractive index at the output of the concentrator compared to the input. Optical contact (i.e., no intervening low index material) between the AGILE and the absorbing element (or an optical source) can be employed to ensure no loss of brightness at the interface between the AGILE and the absorbing element (or source). Although solar cell concentration is a significant application of this technology, there are various other applications, such as increasing the efficiency of optical emission, and providing transmissive optical windows that include optically cloaked regions.