a Schematic of light direction adjustment through grating diffraction, surface refraction, and angle magnification. In the first case, the grating adds a constant in-plane momentum component to the incident light independent of its incident angle. In the second case, upon surface refraction, the in-plane momentum component is conserved, but the output angle is scaled to the incident angle by Snell’s law. In the third case, for an ideal angle magnification, the device adds an in-plane momentum component to the incident light with a fixed scaling factor, and the input and output media are the same. b Illustration of a planar telescope consisting of two POEs for achieving angle magnification. Both POEs have spatially variant in-plane momentum. POE II compensates the spatially variant in-plane momentum of light added by POE I. Together, they work as a grating with adaptive periods according to the incident angle. p∥o in-plane momentum component of the output light, p∥i in-plane momentum component of the incident light, pm in-plane momentum component of the grating, M magnification factor, POE planar optical elements.
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