Light scattering at a temporal boundary in a Lorentz medium

Abstract

Temporal discontinuity in the permittivity of a nondispersive dielectric (temporal boundary) is a conventional model for considering electromagnetic phenomena in dynamic materials and metamaterials. Here we apply a more general model of a Lorentz medium with the rapidly changing density of its structural elements (oscillators) or their resonant frequency to determine the realms of applicability of the conventional temporal boundary model. We demonstrate the dependence of the continuity conditions and the energy relations at a temporal boundary on the nonstationarity mechanism and the ratio between the rate of nonstationarity and the characteristic frequencies in the system.

Photonics of time-varying media

“…As we consider more realistic and complicated electrodynamic models of materials, such as anisotropy, dispersion, and broken translational symmetry in space, the temporal scattering is expectedly modified. [27][28][29][30][31][32][33] To date, research on these topics is very active, as discussed in the following sections.…”

Floquet metamaterials

“…In order to highlight the role of the microscopic picture in the temporal scattering process, we can consider a Drude-Lorentz material, in which the time-domain polarization vector follows the dynamic equation [85] If we assume that the time interface is formed by switching ω p from ω p1 to ω p2 at t = 0 , there are different options in which such an event can be realized: for instance, we can create or annihilate carriers in the material, such that the volume carrier density N suddenly jumps from N 1 to N 2 [85,87], as shown in Fig. 4e, or we may consider alter the effective mass of the electrons from m * 1 to m * 2 , as shown in Fig.…”

Efficient Phase Conjugation in a Space-Time Leaky Waveguide

“…For simplicity, we assume that the involved material is lossless and nondispersive, such that it can respond to the time switching instantaneously, but extensions to dispersive and non-Hermitian media can be considered quite straightforwardly. 21,[33][34][35]53 Intuitively, we may model the structure with a terminated transmission line, as in Figure 2b. The PRS can be modeled by a shunt inductance L, 54−56 and the free-space impedance Z 0 and the one of the dielectric slab Z are both dependent on the input polarization and transverse momentum.…”

“…The theoretical investigation of these temporal discontinuities dates back to more than half a century ago − and has been recently revived in the metamaterials community, with the discovery that time switching can offer a new dimension for wave engineering. − In unbounded media, an abrupt switching event of the material properties in time corresponds to the dual of a spatial interface between two media, since at such a time interface momentum is conserved, but frequency can change. Wave scattering at a single temporal discontinuity has been extensively studied in various forms, also involving anisotropy, , material dispersion, − and broken spatial symmetries. − …”

“…The combination of spatial and temporal interfaces and the presence of a strong resonance realize the space-time slab cavity shown in Figure c. For simplicity, we assume that the involved material is lossless and nondispersive, such that it can respond to the time switching instantaneously, but extensions to dispersive and non-Hermitian media can be considered quite straightforwardly. ,− , …”