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Linear-Operator Theory for Inhomogeneous Omega Planar Waveguides

Topa, A.

Linear-Operator Theory for Inhomogeneous Omega Planar Waveguides, Proc Progress in Electromagnetics Research Symp. - PIERS, Stockholm, Sweden, Vol. 1, pp. 1 - 1, August, 2013.

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The omega medium has been first proposed in, as a new type of artificial bianisotropic
media. An omega medium consists of small omega-shaped microstructures printed onto a
dielectric substrate and then stacked. An incident electric field induces both electric and
magnetic polarization on such printed elements. Omega media are nonchiral, since these
polarization vectors are perpendicular to each other. This distinctive feature of omega media
implies that the orientation of the doping elements in the host isotropic medium cannot be
random but must be parallel to a unique preferred direction.
In this paper, a linear-operator formalism for the analysis of inhomogeneous omega planar
waveguides is presented. Using the theory of linear operators, the problem of guided
electromagnetic wave propagation is reduced to an eigenvalue equation related to a 2×2 matrix
differential operator. Based on the transverse electromagnetic field equations an eigenvalue
problem is then obtained. For each eigenvalue the corresponding eigenfunction represents a
transverse mode function of the waveguide. Hence, the orthogonality properties of these
eigenfunctions can be used to represent the electromagnetic field as a superposition of mode
functions, as long as completeness is guaranteed.
A complete spectral representation for the electromagnetic field of planar multilayered
waveguides inhomogeneously filled with omega media is obtained. Using the concept of adjoint
waveguide, general bi-orthogonality relations for the hybrid modes (either from the discrete
or from the continuous spectrum) are derived.
In order to have a complete field representation in open omega waveguides, these relations
are of utmost importance when choosing an appropriate set of mutually orthogonal radiation
modes. One should note that this linear-operator formalism is applicable to multilayered planar
waveguides with inhomogeneous layers. However, in the case of homogeneous layers the
general formalism reduces to an algebraic 2×2 coupling matrix eigenvalue problem.