Windows into non-Euclidean spaces

Abstract

Two microlens arrays that are separated by the sum of their focal lengths form arrays of micro-telescopes. Parallel light rays that pass through corresponding lenses remain parallel, but the direction of the transmitted light rays is different. This remains true if corresponding lenses do not share an optical axis (i.e. if the two microlens arrays are shifted with respect to each other). The arrays described above are examples of generalized confocal lenslet arrays, and the light-ray-direction change in these devices is well understood [Oxburgh et al., Opt. Commun. 313, 119 (2014)]. Here we show that such micro-telescope arrays change light-ray direction like the interface between spaces with different metrics. To physicists, the concept of metrics is perhaps most familiar from General Relativity (where it is applied to spacetime, not only space, like it is here) and Transformation Optics [Pendry et al., Science 312, 1780 (2006)], where different materials are treated like spaces with different optical metrics. We illustrate the similarities between micro-telescope arrays and metric interfaces with raytracing simulations. Our results suggest the possibility of realising transformation-optics devices with micro-telescope arrays, which we investigate elsewhere.