Time-Varying Materials in Presence of Dispersion: Plane-Wave Propagation in a Lorentzian Medium with Temporal Discontinuity

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Main Authors: Solís, Diego M., Kastner, Raphael, Engheta, Nader
Format: Preprint
Published: 2021
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author Solís, Diego M.
Kastner, Raphael
Engheta, Nader
author_facet Solís, Diego M.
Kastner, Raphael
Engheta, Nader
contents We study the problem of a temporal discontinuity in the permittivity of an unbounded medium with Lorentzian dispersion. More specifically, we tackle the situation in which a monochromatic plane wave forward-travelling in a (generally lossy) Lorentzian-like medium scatters from the temporal "half-space interface" that results from an abrupt temporal change in its plasma frequency (while keeping its resonance frequency constant). In order to achieve momentum preservation across the temporal discontinuity, we show how, unlike in the well-known problem of a nondispersive discontinuity, the second-order nature of the dielectric function now gives rise to two shifted frequencies. As a consequence, whereas in the nondispersive scenario the continuity of the electric displacement D and the magnetic induction B suffice to find the amplitude of the new forward and backward wave, we now need two extra temporal boundary conditions. That is, two forward and two backward plane waves are now instantaneously generated in response to a forward-only plane wave. We also include a transmission-line equivalent with lumped circuit elements that describes the dispersive time-discontinuous scenario under consideration.
format Preprint
id arxiv_https___arxiv_org_abs_2103_06142
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle Time-Varying Materials in Presence of Dispersion: Plane-Wave Propagation in a Lorentzian Medium with Temporal Discontinuity
Solís, Diego M.
Kastner, Raphael
Engheta, Nader
Optics
Applied Physics
We study the problem of a temporal discontinuity in the permittivity of an unbounded medium with Lorentzian dispersion. More specifically, we tackle the situation in which a monochromatic plane wave forward-travelling in a (generally lossy) Lorentzian-like medium scatters from the temporal "half-space interface" that results from an abrupt temporal change in its plasma frequency (while keeping its resonance frequency constant). In order to achieve momentum preservation across the temporal discontinuity, we show how, unlike in the well-known problem of a nondispersive discontinuity, the second-order nature of the dielectric function now gives rise to two shifted frequencies. As a consequence, whereas in the nondispersive scenario the continuity of the electric displacement D and the magnetic induction B suffice to find the amplitude of the new forward and backward wave, we now need two extra temporal boundary conditions. That is, two forward and two backward plane waves are now instantaneously generated in response to a forward-only plane wave. We also include a transmission-line equivalent with lumped circuit elements that describes the dispersive time-discontinuous scenario under consideration.
title Time-Varying Materials in Presence of Dispersion: Plane-Wave Propagation in a Lorentzian Medium with Temporal Discontinuity
topic Optics
Applied Physics
url https://arxiv.org/abs/2103.06142