Consider a plane wave incident on a multilayered planar anisotropic structure composed of conventional materials and metamaterials and surround by two half-spaces. In this paper, we aim to prove three theorems which indicate a kind of duality in these structures. Assume an arbitrarily polarized plane wave obliquely incident on the structures. Theorem 1: Assume that an arbitrarily polarized plane wave is obliquely incident on the structure. Now each layer is filled with by dual media according to the interchanges DPS ↔ DNG and ENG ↔ MNG. Then, the reflection (R) and transmission (T) coefficients of the structure become the complex conjugates of their counterparts. Consequently, the reflected power and transmitted power from the structure are the same for the two dual cases of anisotropic media. Theorem 2: If the interchanges DPS ↔ DNG and ENG ↔ MNG are made in all the layers except in the half spaces on the two sides of the multilayer structure (which is more realizable), then the reflection coefficients become complex conjugates and the reflected power remains the same. Theorem 3: If the structure is backed by a perfect electric conductor and the media interchanges DPS ↔ DNG and ENG ↔ MNG are made in the layers, then the reflection coefficients of the two dual structures become complex conjugates of each other, and the reflected powers are equal. Independent of wave frequency, the number of layers, their thickness, and the type of polarization, these theorems hold true in case of any change in any of these conditions. In the last section, some examples are provided to verify the validity of the proposed theorems.
Mohammad Mahdi Salary,
"A Duality Between Metamaterials and Conventional Materials in Multilayered Anisotropic Planar Structures," Progress In Electromagnetics Research M,
Vol. 32, 13-25, 2013. doi:10.2528/PIERM13041107
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