Conditions for establishing the “generalized Snell’s law of refraction” in all-dielectric metasurfaces: theoretical bases for design of high-efficiency beam deflection metasurfaces

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.