Linear-Operator Formalism in the Analysis of Omega Planar Layered Waveguides

A complete spectral representation for the electromagnetic field of planar multilayered waveguides inhomogeneously filled with omega media is presented. The problem of guided electromagnetic propagation is reduced to an eigenvalue equation related to a 2 ´ 2 matrix differential operator. 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. For the special case of homogeneous layers the linear operator formalism is reduced to a simple 2 ´ 2 coupling matrix eigenvalue problem. Finally, as an example of application, the surface and the radiation modes of a grounded omega slab waveguide are analyzed.

Authors:

• António L. Topa

Keywords:

• Metamaterials
• linear operators
• omega media
• layered waveguide
• orthogonality relations

References:

[1] N. Engheta and M. M. I. Sadaoun, "Novel pseudochiral or W -medium
and its applications," Proc. Conf. PIERS-91, Cambridge, MA, p. 339,
July 1991.
[2] A. Priou (Ed.), Bianisotropic and Bi-Isotropic Media and Applications,
EMW Publishing, Cambridge, 1994 - Ch. 10: A. Toscano and L. Vegni,
"Electromagnetic waves in planar pseudochiral structures," pp. 181-
218.
[3] J. Mazur and D. Pietrzak, "Field displacement phenomenon in a
rectangular waveguide containing a thin plate of a W -medium," IEEE
Microwave Guided Lett., vol. 6, pp. 34-36, Jan. 1996.
[4] C. R. Paiva and A. M. Barbosa, "A linear-operator formalism for the
analysis of inhomogeneous biisotropic planar waveguides," IEEE Trans.
Microwave Theory Tech., vol. 40, pp.672-678, Apr. 1992.
[5] A. L. Topa, C. R. Paiva, and A. M. Barbosa, "New biorthogonality
relations for inhomogeneous biisotropic planar waveguides," IEEE
Trans. Microwave Theory Tech., vol. 42, pp. 629-634, Apr. 1994.
[6] A. D. Bresler, G. H. Joshi, and N. Marcuvitz, "Orthogonality properties
for modes in passive and active uniform waveguides," J. Appl. Phys.,
vol. 29, pp. 794-799, May 1958.
[7] B. Friedman, Principles and Techniques of Applied Mathematics. New
York: Wiley, 1956.
[8] A. L. Topa, C. R. Paiva, and A. M. Barbosa, "NRD directional couplers
using omega media," in Proc. NATO Advanced Research Workshop:
Metamaterials for Secure Information and Communication
Technologies, Cairo, Egypt, February 2010.