Integral Equations Techniques for time varying inhomogeneous medium

Research Staff: Ahmed Al-Jarro, Phillip Sewell, Trevor M. Benson, Alexander Nerukh

Collaborators: Department of Computational Electromagnetics, Institute of Radio Physics & Electronics NASU, Kharkov, Ukraine

This work is funded by the University of Nottingham, School of Electrical and Electronic Engineering

Significant interest has been focused upon the interaction of electromagnetic signals and time varying media. The motivation for studying such phenomena include wavelength shifting and terahertz wave generation applications, as well as gaining insight into the behaviour of high speed switches, lasers, and resonators.

Computational methods that can account for time varying and inhomogeneous media include the finite difference time domain method (FDTD), the transmission line method (TLM), as well as time domain integral equation techniques (IET). A particular advantage of the IET approach is that it can often identify the general properties of a specific class of problems rather than just solving specific instances. It is also very efficient for structures of a small inhomogeneous medium placed in a large background.

This project has looked at 1D problems using an elegant and efficient algorithm to simulate 2D computational structures. Also dimensionality reduction was explored to maintain this high efficiency where the fundamental modal fields which indicate the presence of the waveguide confinement by possessing frequency dependent propagation constants and modal impedances.

A full 3D vectorial algorithm has been derived which promises to significantly extend the practical range of structures that can be simulated.

Publications:

[1] A. Al-Jarro, P. Sewell, T.M. Benson, A. Nerukh, Effective and Flexible Analysis for Propagation in Time Varying Waveguides, Special issue...
[2] A. Al-Jarro, P. Sewell, T.M. Benson, A. Nerukh, Effective and Flexible Analysis for Propagation in Time Varying Waveguides, 11th European conference on integrated optics, Prague, 2-4 April, 331-334, 2003.