Novel metamaterial surfaces from perfectly conducting subwavelength corrugations

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Motivated by the numerical experiments carried out in [S. C. Yurt, A. Elfrgani, M. I. Fuks, K. Ilyenko, and E. Schamiloglu, IEEE Trans. Plasma Sci., 44(2016), pp. 1280-1286], we apply an asymptotic analysis to show that corrugated waveguides can be approximated by smooth cylindrical waveguides with an effective metamaterial surface impedance. We show that this approximation is in force when the period of the corrugations is subwavelength. Here the metamaterial delivers an effective anisotropic surface impedance and imparts novel dispersive effects on signals traveling inside the waveguide. These properties arise from the subwavelength resonances inside the corrugations. For sufficiently deep corrugations, the metamaterial waveguide predicts backward wave propagation. In this way we may understand backward wave propagation as a multiscale phenomenon resulting from local resonances inside subwavelength geometry. Our approach is well suited to numerical computation, and we provide a systematic investigation of the effect of corrugation geometry on wave dispersion, group velocity, and power flow.

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SIAM Journal on Applied Mathematics

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