MATLAB Analysis of 2D TE Plane Wave Scattering by a Metallic Cylinder

In electromagnetic field and wave analysis, studying the scattering characteristics of plane waves incident on metallic cylinders represents a classical problem. This article demonstrates how to implement 2D Transverse Electric (TE) wave scattering analysis for metallic cylinders using MATLAB. ### Fundamental Theory When a TE plane wave (with electric field perpendicular to the incident plane) illuminates a perfect electric conductor cylinder, surface currents are induced, generating scattered fields. Based on Maxwell's equations and cylindrical boundary continuity conditions, the solution can be obtained through separation of variables. The scattered field can be expanded as a superposition of cylindrical waves, where each term relates to Bessel and Hankel functions. ### Implementation Approach Parameter Configuration: Define incident wave frequency, metallic cylinder radius, computational domain size, and spatial resolution. In TE mode, the electric field has only a z-component while the magnetic field contains radial and angular components. MATLAB implementation typically begins with defining physical parameters like `freq = 2.4e9; radius = 0.1;` and creating a spatial grid using `meshgrid`. Wavenumber Decomposition: Calculate the free-space wavenumber from the incident wavelength and derive the scattered wavenumber outside the cylinder. Code implementation involves `k0 = 2*pi*freq/3e8;` for wavenumber calculation and handling complex propagation constants. Series Expansion: Construct field expressions using Bessel functions (describing incident fields) and Hankel functions (describing scattered fields), truncating the infinite series to balance accuracy and computational efficiency. The MATLAB code typically employs `besselj(n,k0*r)` for Bessel functions and `besselh(n,2,k0*r)` for Hankel functions, with series summation up to a calculated truncation order `N_max = ceil(k0*radius + 10)`. Visualization: Compute field distributions at spatial grid points and display total field and scattered field amplitude/phase characteristics using color mapping or contour plots. Implementation uses `pcolor` or `contourf` functions with `abs(E_total)` for field magnitude and `angle(E_total)` for phase visualization. ### Key Extensions Multi-physics Coupling: Extendable to non-ideal conductors (with finite conductivity) or dielectric cylinder analysis by modifying boundary conditions and material parameters in the code. Time-Domain Simulation: Combine with Finite-Difference Time-Domain (FDTD) methods to simulate transient scattering processes, requiring temporal discretization and field updating algorithms. This method serves as a fundamental computational electromagnetics application suitable for preliminary analysis in antenna design, stealth technology, and related fields. The MATLAB implementation provides a framework for understanding wave-object interactions through numerical simulation.