Cutoff wavenumbers of eccentric circular metallic waveguides

Cutoff wavenumbers k_nm are determined analytically for an eccentric circular metallic waveguide. Separation of variables technique is used for the solution. For small eccentricities kd, where d is the distance between the axes of the cylinders, cosine and sine laws are used instead of the translational addition theorem, in order to satisfy the boundary conditions at the surface of the outer cylinder. Keeping terms up to the order (kd)² exact, analytical expressions of the form k_nm(d) = k_nm(0)[1+g_nm(k_nmd)²+O(k_nmd)⁴] are obtained for the cutoff wavenumbers of the waveguides, where k_nm(0) corresponds to the coaxial geometry, with d = 0. Both transverse magnetic and transverse electric modes are considered. Numerical results are given for all types of modes and for various values of the parameters. The method used here is an alternative of the one using the translational addition theorem, in the case of small eccentricities.