Abstract
Rectangular waveguides containing inhomogeneous metamaterials with graded refractive-index profiles have potential applications in bending waveguides and radiation-enhanced antennas, and accurate eigenvalue solutions are prerequisite. Commonly used commercial electromagnetic solvers such as HFSS, COMSOL, and CST could not efficiently calculate the eigenvalues of waveguides containing graded refractive-index dielectrics. In this paper, an accurate and efficient semianalytical method based on the modal expansion has been proposed to solve these waveguides. The proposed method has been employed to calculate the eigenvalues, including the cutoff wavenumbers and dispersion relations, for metamaterials with various graded refractive-index profiles. Calculated results are then validated by comparison, using commercial solver HFSS, which indicates the superiority of the proposed method in accuracy and efficiency. Below-cutoff backward wave propagation is observed in waveguides filled with graded refractive-index metamaterials, which provides a new approach for waveguide miniaturization.
Highlights
Rectangular waveguides filled with inhomogeneous dielectrics are the most fundamental guided wave structures [1] to realize various functional microwave devices, such as filters [2]; couplers [3]; dividers [4]; and substrate integrated waveguides (SIWs) [5, 6]. e overall performances of such devices strongly depend on the guided wave propagation properties of the waveguides
From the waveguide modal theory presented in the previous section, a specific code that can compute the eigenvalues of a rectangular waveguide filled with a graded-index composite right-handed and left-handed material (CRLHM)
It should be noted that HFSS cannot set the spatially dependent dielectric parameters, and the discretization and convergence analysis must be conducted in the simulation of graded-index metamaterials. e technique proposed in this paper can be employed for arbitrary inhomogeneity analysis
Summary
Rectangular waveguides filled with inhomogeneous dielectrics are the most fundamental guided wave structures [1] to realize various functional microwave devices, such as filters [2]; couplers [3]; dividers [4]; and substrate integrated waveguides (SIWs) [5, 6]. e overall performances of such devices strongly depend on the guided wave propagation properties of the waveguides. Commercial electromagnetic simulation software, including HFSS, COMSOL, and CST, are based on the full-wave numerical methods, such as the finite element method (FEM), the finite-difference time-domain (FDTD), the method of moments (MoM), and the boundary element method (BEM) [15, 16] These electromagnetic solvers have powerful analysis capabilities, they require a very long calculation time and a large amount of computer memory for structures containing complex inhomogeneous dielectrics. An accurate semianalytical method based on a one-dimensional modal expansion theory has been proposed to calculate the eigenvalues of rectangular waveguides filled with CRLHM having graded refractive-index profiles.
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