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Optics Express

Optimal electromagnetic energy transmission and real-time dissipation in extended media

Scott Alan Glasgow, Michael J. Ware

Published Feb 19, 2014• 1 citation
Publisher

Abstract

Pulse reshaping effects that give rise to fast and slow light phenomena are inextricably linked to the dynamics of energy exchange between the pulse and the propagation medium. Energy that is dissipated from the pulse can no longer participate in this exchange process, but previous methods of calculating real-time dissipation are not valid for extended propagation media. We present a method for calculating real-time dissipation that is valid for electromagnetic pulse propagation in extended media. This method allows one to divide the energy stored in an extended medium into the portion that can be later transmitted out of the medium, and that portion which must be lost to either dissipation or reflection.

DOI
10.1364/oe.22.004453

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Pulse reshaping effects that give rise to fast and slow light phenomena are inextricably linked to the dynamics of energy exchange between the pulse and the propagation medium. Energy that is dissipated from the pulse can no longer participate in this exchange process, but previous methods of calculating real-time dissipation are not valid for extended propagation media. We present a method for calculating real-time dissipation that is valid for electromagnetic pulse propagation in extended media. This method allows one to divide the energy stored in an extended medium into the portion that can be later transmitted out of the medium, and that portion which must be lost to either dissipation or reflection.
We discuss the inevitable dissipation of energy that must accompany the creation of a pulse-medium excitation state in a passive dielectric. We show that there is a minimum amount of energy that an optical pulse must deposit in the medium to create a given pulse-medium state and that energy deposited beyond this minimum value must be dissipated in the medium. We compare this notion of dissipation to a related concept found by determining the fraction of energy stored in a medium that is irrecoverable by future fields. These two notions of dissipation are model-independent and form upper and lower bounds for real-time loss. Any model-dependent notion of loss that falls outside these bounds has serious conceptual difficulties. We show that a traditional notion of real-time loss based on a multiple-Lorentz oscillator model fails to give reasonable results in classes of passive linear media near EIT, while the notions of loss we introduce give sensible results for all passive media.
We examine the energy exchanged between an electromagnetic pulse and a linear dielectric medium in which it propagates. While group velocity indicates the presence of field energy (the locus of which can move with arbitrary speed), the velocity of energy transport maintains strict luminality. This indicates that the medium treats the leading and trailing portions of the pulse differently. The principle of causality requires the medium to respond to the instantaneous spectrum, the spectrum of the pulse truncated at each new instant as a given locale in the medium experiences the pulse.
We describe the temporal and spatial dynamics of propagating electromagnetically induced transparency pulses in an optically thick medium. Results include pulse velocities as slow as c/165c/165c/165 with 55% transmission, strong-probe-field effects, and the observation of near diffraction-limited transmitted beam quality.
Spectral reshaping and nonuniform phase delay associated with an electromagnetic pulse propagating in a temporally dispersive medium may lead to interesting observations in which the group velocity becomes superluminal or even negative. In such cases, the finite bandwidth of the superluminal region implies the inevitable existence of a cutoff distance beyond which a superluminal pulse becomes subluminal. In this paper, we derive a closed-form analytic expression to estimate this cutoff distance in abnormal dispersive media with gain. Moreover, the method of steepest descent is used to track the time-frequency dynamics associated with the evolution of the center of mass of a superluminal pulse to the subluminal regime. This evolution takes place at longer propagation depths as a result of the subluminal components affecting the behavior of the pulse. Finally, the analysis presents the fundamental limitations of superluminal propagation in light of factors such as the medium depth, pulse width, and the medium dispersion strength.