Time dependence of internal intensity of a dielectric sphere on and near resonance

Abstract

Transient intensities inside a large dielectric sphere (circumference/incident wavelength > 50) are computed for excitation with plane-wave pulses having a Gaussian time dependence. The center frequency of the pulse is either on or near a morphology-dependent resonance (MDR). For each internal point considered, the time dependence of the electric field is determined from the frequency spectrum of the field at that point. The frequency spectrum is the product of the incident field spectrum and the transfer function at that point. In a sphere both the internal spectrum and the associated time dependence vary with spatial location, particularly when the incident frequency is near a MDR. The time dependence of the intensity at an internal location near the surface shows an exponential tail with a time constant of 1/Δωr, where Δωr is the resonant linewidth of the MDR, so long as the incident spectrum overlaps the MDR significantly, i.e., when Δω ≤ Δω0 and Δω0 ≥ Δωr, where Δω0 is the width of the incident pulse spectrum and Δω is the detuning, the difference between the MDR frequency and the center frequency of the incident Gaussian pulse.