Numerical Calculation of Precursor Fields in One Dimensional Photonic Crystal

R. Safian, C.D. Sarris, and M. Mojahedi (Canada)


Superluminal, Precursors, One Dimensional Photonic Crystal, Joint Time-Frequency Analysis.


The presence of superluminal (in excess of the speed of light in vacuum) or negative group velocities in passive or active Lorentzian medium, one-dimensional photonic crys tal (1DPC), undersized waveguide, and other structures has been theoretically predicted and experimentally observed. While due to the temporal or structural dispersions the group velocity in these media is abnormal, it has been ar gued that such behavior is not contradictory to the require ments of relativistic causality (Einstein causality), since the earliest field oscillations known as the precursors or fore runner must and will obey Einstein causality. In this paper, for the first time, by using finite difference time domain (FDTD) technique in conjunction with the joint time fre quency analysis (JTFA) we present the dynamical evolution of these earliest field oscillations; clearly indicating that de spite the observed abnormal group velocities the precursor fields are indeed subluminal, and as such, must be associ ated with the arrival of “genuine information”. Moreover, this work presents the combined FDTD and JTFA as a vi able tool in studying the dynamical evolution of the tran sient and steady-state pulse propagation in dispersive me dia.

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