Coupled-Mode Theory of an Irregular Waveguide with Impedance Walls Aleksandr V. Maksimenko 1 & Vitalii I. Shcherbinin 1 & Viktor I. Tkachenko 1,2 Received: 9 January 2019 /Accepted: 2 April 2019/ # Springer Science+Business Media, LLC, part of Springer Nature 2019 Abstract The eigenvalue problem is solved for a longitudinally inhomogeneous waveguide with impedance walls. The cross-section method is applied to reduce the problem to an infinite set of ordinary differential equations for amplitudes of basis modes. As a numerical example, a tapered metallic cavity of currently available THz gyrotron is considered. The combined effect of mode coupling (conversion) and ohmic wall losses on electromagnetic properties of the gyrotron cavity is considered and discussed. Keywords Eigenvalue problem . Coupled-mode theory . Irregular waveguide . Surface impedance . Gyrotron 1 Introduction Wave propagation along a longitudinally inhomogeneous waveguide is an issue of crucial importance for many technological applications. For any kind of waves (electromagnetic, acoustic, elastic etc), the use of such a guiding structure is impracticable without knowledge of wave reflection, attenuation, and conversion, which are due to waveguide non-uniformities, low fabrication tolerance, wall roughness, and losses. The desired wave characteristics can be determined by solving the eigenvalue problem for the longitudinally inhomogeneous waveguide. Because of the coupling between basis modes in such waveguide, this problem cannot be easily solved both analytically and numerically, even though the waveguide walls are assumed to be ideal (smooth and lossless). A review of available methods of attacking this problem can be found, for example, in [1–4]. Of even more complicated form is the eigenvalue problem for a waveguide with non-ideal walls. Often for such waveguide, the boundary conditions can be Journal of Infrared, Millimeter, and Terahertz Waves https://doi.org/10.1007/s10762-019-00589-x * Aleksandr V. Maksimenko maksimenko.mcme@gmail.com 1 National Science Center BKharkiv Institute of Physics and Technology^ of National Academy of Science of Ukraine, 1 Akademicheskaya St., Kharkiv 61008, Ukraine 2 V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv 61022, Ukraine