Assessment of Dispersive Materials using Recursive Implicit Time Domain Techniques

Numerical dispersion of the time domain beam propagation method (TD-BPM) using recursive convolution is assessed through the solution of wave equation in a Debye medium. The implicit and recursive technique is compared with other existing similar techniques, such as recursive finite difference time domain (FDTD) and TD-BPM using auxiliary differential equation (ADE). An empirical relation is established so that the inherently generated dispersion can be superseded. The outstanding feature of the technique includes avoidance of a large matrix inversion with high stability for multi-pole Debye medium even at large time steps and relaxed mesh-grid.