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An analytical model for a shielding structure containing both bulk composite layers and planar metafilms (MFs) made of perfect electric conductors is presented, allowing for synthesis of shielding structures using the genetic algorithm (GA) optimization. MFs can be of two different types: patch or aperture. The frequency response, specifically, transmission (T ) and reflection (Γ ) coefficients in a plane-wave formulation, of any MF is calculated based on polarizabilities determined by the particular pattern geometry. T and Γ of a patch-type MF are derived using the generalized sheet transition conditions (GSTC) and the Babinet's duality principle is used for aperture-type MF to map the results from the complementary problem. T and Γ for a singlelayered MF are represented in a unified matrix form for any angle of incidence. T -matrix approach is used for getting T and Γ for a multilayered structure. Any MF buried in a host dielectric can be decomposed into three types of basic elements: a host composite slab, interface between media, and an MF inside the homogeneous host medium. Each basic element is described by a corresponding T -matrix, and the total T -matrix of the stack is the sequential product of the each individual T -matrix. T and Γ of the stack can be easily derived from the total T -matrix. If there are two or more MFs, the distance between them justifies the condition of neglecting higher-order evanescent mode interactions. Then the GA is applied to engineer a structure with the desired frequency response. It helps to choose the best geometry of MF patterns, thickness of layers, and appropriate constitutive parameters of each composite layer.

Abstract-Metasheet structures together with bulk composite dielectric layers can be used for antenna radomes, absorbers, and band gap structures. Transmission (T ) and reflection (Γ) coefficients for a plane wave incident at any angle upon a metasheet embedded in a dielectric layer are considered. These metasheets are either patch-type or an aperture-type, and they can be either singlelayered or multi-layered. To calculate T and Γ for a patch-type metasheet, a concise unified matrix approach is derived using the Generalized Sheet Transition Conditions (GSTC). The Babinet duality principle is utilized to get T and Γ for single-layered aperture-type metasheets (as complementary to the patch-type ones) at an arbitrary angle of incidence. The T-matrix approach is applied to calculate characteristics of multilayered metasheet structures containing a cascade of metasheets and dielectric slabs. In this paper, the minimum distance for neglecting higher-order evanescent mode interactions between the metasheets has been determined. Computed results based on the proposed analytical approach are compared with the full-wave numerical simulations. The analytical results are verified for satisfying the energy balance condition.