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

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-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.

13 pages (including four appendices), 9 figures (including 2 figures in the appendix section)

References in corpus (4)

• Circuit elements at optical frequencies: nano-inductors, nano-capacitors and nano-resistors
• Dynamic release of trapped light from an ultrahigh-Q nanocavity via adiabatic frequency tuning
• Parametric amplification and bidirectional invisibility in PT-symmetric time-Floquet systems
• A Generalization of the Kramers-Kronig Relations for Linear Time-Varying Media

Cited by in corpus (12)

• Photonics of Time-Varying Media
• Temporal Brewster angle
• Asymmetric frequency conversion with acoustic non-Hermitian space-time varying metamaterial
• Tapered Photonic Switching
• Parametric Mie resonances and directional amplification in time-modulated scatterers
• Spectral Causality and the Scattering of Waves
• Temporal boundaries in electromagnetic materials
• Static-to-dynamic field conversion with time-varying media
• Wave Analysis and Homogenization of Spatiotemporally Modulated Wire Medium
• Temporal metamaterials with gain and loss
• Edge Waves and Transmissions for Temporal Laminates and Imperfect Chiral Interfaces
• Spatiotemporal Isotropic-to-Anisotropic Meta-Atoms