Far-Field Perfect Imaging with Time-Modulated Gratings

Abstract

We study the capabilities of time-modulated diffraction gratings as imaging devices. It is shown that a time-dependent but transversally homogeneous slab can be used to make a perfect image of an object in the far-field, since all the evanescent modes couple to propagative time-diffracted orders. It is found that, if the image to be obtained is axially symmetric, it can be recovered by measuring the time signal at a single point, without the need to perform a spatial scan, so that time gratings can act as well as single-pixel imaging devices. In the case of having an object without axial symmetry, the time grating can be combined with a spatial grating, and then the full image can be recovered again with a measurement at a single point. We apply the theory of compressive sensing to optimize the recovery method, and numerical examples are provided. We show, therefore, that time-modulated gratings can be used to perfectly recover the image of an object in the far-field and after measuring at a single point in space, making them a promising approach to superresolution and ultrafast imaging.