We present the operation of a one-way nonlinear mirror, where the image is formed by the process of difference frequency generation on one and the same side of the metasurface, independently of the object location on the left or right. The imaging principle is based on the generalized law of refraction. Regularly, an image of a source, produced by such a deeply subwavelength layer of a nonlinear material, is expected to form on both sides of the surface with a nearly equal efficiency. This symmetric two-side generation is a consequence of the lack of phase-matching constraints within the subwavelength-thin medium. The use of a nanostructured medium allows for control of the generation directionality via interference of the multipolar partial waves produced by the nonlinear response of nanoelements comprising the metasurface. Such interference can result in suppression of the generated field on one side of the metasurface. The approach proposed here allows for a nonreciprocal directionality where this side, additionally, remains unchanged independently of the source location. The approach does not require asymmetry of the nanoelement geometry. Rather, it relies on the existence of shared pathways inducing electric and magnetic multipolar moments in the nanoelement via a nonlinear interaction These pathways allow controlling the phase of both electric and magnetic, nonlinearly produced, multipolar modes by a single (electric or magnetic) vector of the fundamental field of a given frequency. Reversing the direction of that fundamental field thus results in a simultaneous phase switch of both electric and magnetic, nonlinearly produced, multipolar modes, preserving the generation direction.
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