Abstract
We theoretically investigate a metal-to-insulator transition in artificial two-dimensional (2D) crystals (i.e., metasurfaces) of tightly coupled closed-ring resonators. Strong interaction between unit resonators in the metasurfaces yields the effective permittivity highly dependent on the lattice spacing of unit resonators. Through our rigorous theory, we provide a closed form of effective permittivity of the metasurface and reveal that the permittivity possesses a Lorentzian-type resonant behavior, implying that the transition of the effective permittivity can arise when the lattice spacing passes a critical value.
Highlights
Metal-to-insulator transition is an essential physical phenomenon in crystal solids as it results in drastic changes in electrical and optical responses of materials [1,2,3]
When resonators are capacitively coupled to each other with a deep subwavelength lattice spacing, we find that the metal-to-insulator transition occurs when the lattice spacing exceeds a critical value
When structural parameters are varied continuously, we observe that the change of refractive index from pure imaginary to real, or metal-to-insulator transition, occurs when the denominator passes zero, or when the gap size gx exceeds the critical value gt, which is determined by λ2 d3y
Summary
Metal-to-insulator transition is an essential physical phenomenon in crystal solids as it results in drastic changes in electrical and optical responses of materials [1,2,3]. In artificial crystals, such as three-dimensional metamaterials and two-dimensional metasurfaces, the notion of transition can be extended in the context of an effective medium theory. We clarify the underlying physical mechanism of the phase transition in terms of light transmission in metasurfaces through two competing transmission channels.
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