FDTD Simulation of a Double-Ridge Metal-Loaded Rectangular Waveguide

This article provides a comprehensive guide to calculating dispersion curves for fundamental and first higher-order modes in double-ridge metal-loaded rectangular waveguides using the Finite-Difference Time-Domain (FDTD) method. The implementation involves discretizing Maxwell's equations using central-difference approximations in both time and spatial domains, with special attention to boundary conditions at metal interfaces. Key algorithmic components include Yee's grid implementation for electromagnetic field staggering, perfect electric conductor (PEC) boundary handling for metal surfaces, and Fourier transform techniques for extracting modal frequencies from time-domain simulations. The waveguide design incorporates double ridges for enhanced mode control, requiring customized grid generation around ridge structures using staircase approximation methods. We analyze electromagnetic field distribution patterns and propagation characteristics through iterative field updates via update equations for E and H fields. Mode identification employs eigenvalue calculation from frequency-domain data transformed from time-domain signals using discrete Fourier transforms. The dispersion curve computation involves sweeping frequency points while monitoring field energy concentrations corresponding to specific modes. The code implementation utilizes parameterized waveguide geometry inputs, automated mode detection thresholds, and visualization routines for field patterns and dispersion plots. This approach enables researchers to accurately characterize waveguide mode behavior while understanding FDTD's numerical dispersion properties and stability constraints through Courant-Friedrichs-Lewy (CFL) condition maintenance.