This research focuses on the exact electromagnetic analysis of various double negative (DNG) metamaterial structures. The boundaries of these structures are coordinate surfaces of the elliptic cylinder coordinate system. Four structures are considered: (1) the elliptic cylinder, (2) a semielliptical cavity flush mounted under an aperture; (3) a quarter elliptic channel at the corner between two metallic walls; and, (4) a multilayered elliptical cylinder. All these structures are made of or filled with DNG metamaterial. Inside a DNG metamaterial both permittivity and permeability are negative resulting in a negative index of refraction. These two-dimensional boundary-value problems are solved exactly, in the frequency domain, when the primary field is either a plane wave of arbitrary polarization and direction of incidence or an electric or magnetic line source. The electromagnetic fields in the various regions and the incident fields are expressed in terms of infinite series of elliptic-cylinder wave functions, involving products of radial and angular Mathieu functions. Numerical results shown to clarify the effect of DNG metamaterials in these geometries.
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