Moving Coordinate Frame FDTD Analysis of Long Range Tracking of Pulsed Fields in Graded Index Waveguides- Abstract

Abstract

Modeling of long range propagation of pulsed fields along guiding structures poses some major difficulties with the conventional FDTD scheme, arising from the vast computer resources needed to discretize the entire domain and the accumulation of numerical dispersion error. The moving frame FDTD approach, presented in this work, overcomes these difficulties by limiting the computational grid to a window centered about the propagating pulse and moving along with it at the local wavespeed of the medium. In this work, we first present an FDTD solution of the field equations as formulated in the moving coordinate frame, and then explore such issues as the numerical dispersion, which is shown to be reduced substantially compared with the stationary formulation, the numerical stability, and the absorbing boundary conditions at the leading, trailing and side boundaries of the moving window. Numerical results of pulsed field propagation along graded index waveguides are shown, and the capability of the method is demonstrated with propagation distances exceeding the order of 104 pulse lengths. We choose initial field distributions that give rise to pulsed beam fields. The propagation characteristics of these fields along nonuniform guides are explored analytically in the Appendix. The numerical results are also checked against frequency domain adiabatic mode solutions developed in the Appendix.