Time-varying materials in the presence of dispersion: Plane-wave propagation in a Lorentzian medium with temporal discontinuity

Diego M. Solís, Raphael Kastner, Nader Engheta*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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-traveling in a (generally lossy) Lorentzian-like medium scatters from the temporal interface that results from an instantaneous and homogeneous 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 suffices 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.

Original languageEnglish
Pages (from-to)1842-1853
Number of pages12
JournalPhotonics Research
Volume9
Issue number9
DOIs
StatePublished - 1 Sep 2021

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