A Semi-Analytical Approach for the Design of Reconfigurable All-Dielectric Metagratings With Phase-Change Material Constituents

We present a semi-analytical approach, based on a volume-integral equation method employing entire-domain expansion functions, for the calculation of the transmission response of all-dielectric two-component metagratings embedded in air. The presented approach can efficiently treat metagratings with high permittivity inclusions by taking a sufficient number of basis functions representing the electric field within the inclusions. A particular strength of this method is that it is able to delineate the transmission contributions of the individual available Bragg diffracted channels. We utilize the capabilities of this method to design metagratings for reconfigurable beam splitting which relies on the high-refractive index shift between amorphous and crystalline phases of newly developed dielectric phase-transition alloys. We further analyze the salient characteristics of Fano features present in the transmission responses of the crystalline-state metagrating and discuss the pertinent principles to guide the design of related practical systems for beam splitting. These principles further underline the need for transmission information within each Bragg channel and hence the merit of the semi-analytical approach presented here.