Wave transformation -- Simulation and Application

TL;DR

This paper analyzes electromagnetic wave transformations, correcting a textbook error, and demonstrates simulations of wave interactions with objects like cylinders and spheres, aiding physics education.

Contribution

It provides a detailed mathematical analysis, correction of a classic textbook error, and simulation illustrations of wave transformations and scattering problems.

Findings

Corrected an error in a classic electromagnetic textbook.

Simulated wave interactions with cylinders and spheres.

Provided visualizations to aid understanding of wave transformations.

Abstract

This paper focus on the theoretical analysis and simulation of electromagnetic wave transforms, which is widely encountered in teaching physics. When the electromagnetic wave is not consistent with the shape of the object, it is often necessary to introduce electromagnetic wave transforms to analyze the interaction between the two. In this paper, we discuss three common waves, namely plane wave, cylindrical wave and spherical wave. We first analyze the mathematical transformation equations between them, and then use computer programs to draw a simulation image to intuitively show the derivation results. During the derivation, we corrected an error in a classic electromagnetic textbook. Finally, several specific electromagnetic examples are solved by electromagnetic wave transformation. These examples include the scattering of plane waves by ideal conductor cylinder, sphere and ideal dielectric cylinder. The simulation results are displayed intuitively in the form of images.