A Fast FDTD Analysis of Guided Wave Structures Using a Continuously Variable Mesh with Second Order Accuracy

Abstract

This paper describes some important improvements to the FDTD method. First, a two-dimensional FDTD algorithm for hybrid mode analysis is described. By using a phase shift of β.Δz along the z-direction for the limiting case of Δz → 0, the propagation constant of hybrid modes can be calculated with only a two-dimensional mesh and a truly two-dimensional grid size. Second, a continuously variable grading scheme is introduced in which the first order error term is eliminated and a second order accuracy is achieved without using additional wave equations at the boundary of neighbouring lattices. This grading scheme can be applied to the 2D as well as to the 3D FDTD algorithm. Both developments represent important improvements in terms of computational efficiency of the FDTD method.

Indexing terms:

• Finite difference time domain method
• Graded mesh