volume | PIER Journals

Abstract

The Floquet-Bloch theorem allows waves in infinite, lossless periodic media to be expressed as a sum of discrete Floquet-Bloch modes, but its validity is challenged under the realistic constraints of loss and finite extent. In this work, we mathematically reveal the existence of Floquet-Bloch modes in the electromagnetic fields sustained by lossy, finite periodic layered media using Maxwell's equations alone without invoking the Floquet-Bloch theorem. Starting with a transfer-matrix representation of the electromagnetic field in a generic layered medium, we apply Fourier transformation and a series of mathematical manipulations to isolate a term explicitly dependent on Floquet-Bloch modes. Fourierdomain representation of the electromagnetic field can be reduced into a product of the Floquet-Bloch term and two other matrix factors: one governed by reflections from the medium boundaries and another dependent on layer composition. Electromagnetic fields in any finite, lossy, layered structure can now be interpreted in the Fourier-domain by separable factors dependent on distinct physical features of the structure. The developed theory enables new methods for analyzing and communicating the electromagnetic properties of layered metamaterials.

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Dr. Kenneth J. Chau

Dr. Mohammed H. Al Shakhs

Prof. Peter Ott