Electromagnetic simulation

This teaching unit deals with solving electromagnetic problems on the computer. Based on Maxwell's equations, it shows how to simulate the behavior of electromagnetic waves in different media. It includes a detailed implementation of simulations based on the Finite Difference Time Domain (FDTD) method.

An introduction to diffraction problems in the harmonic regime by a bounded obstacle will be given for the case of 2D and 3D scalar waves.

On completion of this course, students will be able to :

• Apply a finite-difference time-domain (FDTD) numerical scheme to discretize Maxwell's equations in 1D, 2D and 3D
• Implement the FDTD method in Python using the Numpy and Matplotlib libraries
• Simulate the propagation of electromagnetic waves in different media
• Choose the right parameters to ensure the stability of the digital schema and limit errors resulting from digital processing.
• Model a diffraction problem in the harmonic regime and learn about certain modal methods.

M1 Physics

Recommended prerequisites :

Python programming

CCI

• Python basics, using the NumPy and Matplotlib libraries
• Treatment of the wave equation with the finite-difference time-domain (FDTD) method
• Simulation of electromagnetic wave propagation in different 1D media and analysis of the effect of different parameters introduced in the numerical simulation.
• Yee mesh
• Perfect Matching Layer (PML)
• Introduction to MATLAB programming
• Theory of diffraction by a bounded obstacle in the harmonic regime (2d-3d) for scalar waves
• Implementation of a modal method for a circular or spherical obstacle
• Introduction to the resonant structure of the diffraction matrix.