Abstract
Abstract The generalized Snell’s law dictates that introducing a phase gradient at the interface of two media can shape incident light and achieve anomalous reflection or refraction. However, when the introduced phase gradient is realized via the scattering of nanoparticles in the metasurfaces, this law needs to be modified; certain conditions need to be met when the law is established. We present the conditions for establishing the “generalized Snell’s law of refraction” in all-dielectric metasurfaces under the incidence of different polarized light. These conditions can provide theoretical bases for the subsequent design of high-efficiency beam deflection metasurfaces. The relationship between the highest achievable anomalous refraction efficiency and the number of nanoparticles within one period of the metasurface is also summarized. In addition, the generalized refraction should not depend on the polarization states of incident light; however, the previous realization conditions of anomalous refraction were sensitive to the polarization states. Thus, conditions for establishing the polarization-independent generalized Snell’s law of refraction in all-dielectric metasurfaces are presented.
Highlights
Conventional optical devices rely on the phase shifts accumulated during the propagation of light to shape light beams [1]
The generalized refraction should not depend on the polarization states of incident light; the previous realization conditions of anomalous refraction were sensitive to the polarization states
It should be emphasized that, because the metasurfaces are composed of nanopillars whose Jones matrix is a linear birefringent, unitary matrix, the responses of the metasurfaces to different polarized light vary; the metasurfaces shape different polarized light in different manners
Summary
Conventional optical devices rely on the phase shifts accumulated during the propagation of light to shape light beams [1]. A basic function of metasurfaces is the realization of light beam deflection (i.e., to reflect or refract incident light to the desired direction). In 2011, Yu et al [1] proposed generalized laws of reflection and refraction and showed that anomalous reflection can be observed when metallic antennas on silicon within one period of the metasurface array have a linear phase change along the interface. In 2020, Rousseau et al [7] reported that the above-mentioned generalized laws of refraction and reflection have to be modified to describe the propagation of light through metasurfaces composed of diffractive elements. They theoretically proved that generalized reflection or refraction can only be
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