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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.
Highlights
Slow light can be achieved in a variety of physical systems [1,2,3,4,5,6] where the group velocity for the medium can be made much smaller than c over a certain spectral range
In this article we introduce a framework for describing the real-time dynamics of energy dissipation as a pulse interacts with an extended propagation medium
A complete understanding of real-time loss is important in applications such as slow and fast pulse propagation experiments where the timing of energy flows in and out of the pulse are crucial
Summary
Slow light can be achieved in a variety of physical systems [1,2,3,4,5,6] where the group velocity for the medium can be made much smaller than c over a certain spectral range. We previously detailed an approach for calculating real-time loss that was appropriate for point-wise analysis [13, 14] This previous analysis was analogous to other methods developed to describe dissipation in general viscoelastic and dielectric media [15,16,17,18,19,20]. Each of these methods of analysis calculates the energy density at single point within the medium (or, in the case of viscoelasticity, treats physically extended elements “en masse,” as pointlike) This point-wise analysis can lead to incorrect results when analyzing the propagation of an energy pulse through a distributed medium. We present methods for describing real-time dissipation for pulse propagation in an extended medium one-dimensional medium This method considers fixed past fields and potential future fields that are consistent (via Maxwell’s equations) throughout the medium. The approach in this paper is analogous to the first point-wise method which yields uirrec
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