Abstract
Recently there has been a large interest in achieving metasurface resonances with large quality factors. In this article, we examine metasurfaces that comprised a finite number of magnetic dipoles oriented parallel or orthogonal to the plane of the metasurface and determine analytic formulas for their resonances’ quality factors. These conditions are experimentally achievable in finite-size metasurfaces made of dielectric cubic resonators at the magnetic dipole resonance. Our results show that finite metasurfaces made of parallel (to the plane) magnetic dipoles exhibit low quality factor resonances with a quality factor that is independent of the number of resonators. More importantly, finite metasurfaces made of orthogonal (to the plane) magnetic dipoles lead to resonances with large quality factors, which ultimately depend on the number of resonators comprising the metasurface. In particular, by properly modulating the array of dipole moments by having a distribution of resonator polarizabilities, one can potentially increase the quality factor of metasurface resonances even further. These results provide design guidelines to achieve a sought quality factor applicable to any resonator geometry for the development of new devices such as photodetectors, modulators, and sensors.
Highlights
A large variety of optical behaviors, such as flat lenses, beam converters, Huygens’ sources, and holograms,[1,2,3,4,5,6,7,8,9,10,11,12] can be obtained using metasurfaces, or two-dimensional arrays of subwavelength resonators
We investigate a finite-size metasurface of cubic all-dielectric resonators at the magnetic dipole resonance in the second section, reporting the distribution of dipole moments along the array that will be necessary for the analytical portion of this work
We develop analytical formulas to compute the resonance Qs of finite-size metasurfaces composed of magnetic dipoles
Summary
A large variety of optical behaviors, such as flat lenses, beam converters, Huygens’ sources, and holograms,[1,2,3,4,5,6,7,8,9,10,11,12] can be obtained using metasurfaces, or two-dimensional arrays of subwavelength resonators. We investigate a finite-size metasurface of cubic all-dielectric resonators at the magnetic dipole resonance, reporting the distribution of dipole moments along the array that will be necessary for the analytical portion of this work. Theory of Qs of finite metasurfaces with uniform distribution of dipole moments Consider the finite array of orthogonal (to the plane) magnetic dipoles in Figure 4(a) or of parallel magnetic dipoles, with periods dx and dy along the x and y directions, respectively. The approximate theory based on perfect magnetic conductor side walls for a lossless dielectric cubic resonator gives the resonant frequency for the first transverse mode rbaffiffisffiffiffieffiffidffiffiffiffiffioffiffiffinffiffiffiffiffitffiffihffiffiffieffiffiffiffiffitffirffiffiaffiffiffinffiffiffiscendental equation kzc 1⁄4
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