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We introduce a mechanism that can both hold and amplify electromagnetic waves by rapidly changing the permittivity of the medium during the wave travel from a positive to a dispersionless (i.e. non-Foster) negative value and then back again. The underlying physics behind this phenomenon is theoretically explored by considering a plane wave in an unbounded medium. Interestingly, we show that a rapid positive-to-negative temporal change of {\epsilon}(t) causes the propagation of the wave to stop (observed by a frozen phase in time) while the amplitude of the frozen field exponentially grows. Stepping the permittivity back to the original (or a new) positive value will cause the wave to thaw and resume propagation with the original (or the new) frequency, respectively. We numerically study the case of dipole radiation in such time-varying non-Foster structures. As a possible implementation, we propose a parallel plate waveguide platform loaded with time-dependent media emulating parallel lumped non-Foster negative capacitors. Such non-Foster time-varying structures may open new venues in controlling and manipulating wave-matter interaction., Comment: 51 pages (20 pages of main text and 31 pages of supplementary materials), 21 figures (6 figures in the main text and 15 figures in the supplementary materials)

We envision the use of an indium tin oxide (ITO) thin film as part of a bi-layered silicon-photonics subwavelength device to boost nonlinearity-assisted all-passive nonreciprocal behavior. The asymmetric p-polarized oblique excitation of a mode near the epsilon-near-zero (ENZ) frequency, with highly-confined and enhanced normal electric field component and large absorption, allows to harness ITO's strong ultrafast nonlinear response for the generation of a notable nonreciprocal performance in the two-port element. Though limited by loss, we find the device's optimal operational point and the maximum nonreciprocal transmittance ratio attainable vs. light intensity -- including an apparent upper bound slightly over 2 --, and we perform exhaustive numerical simulations considering nonlinear processes of both anharmonic and thermal nature that validate our predictions, including steady-state and pulsed-laser excitations., Comment: 12 pages (including 5 appendices), 9 figures (4 in the main text and 5 in the appendices)

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

We investigate, theoretically and numerically, the dependence of a material's nonlinear-optical response on the linear relative electric permittivity $\epsilon$ and magnetic permeability $\mu$. The conversion efficiency of low-order harmonic-generation processes, as well as the increase rate of Kerr-effect nonlinear phase shift and nonlinear losses from two-photon absorption (TPA), are seen to increase with decreasing $\epsilon$ and/or increasing $\mu$. We also discuss the rationale and physical insights behind this nonlinear response, particularly its enhancement in $\epsilon$-near-zero (ENZ) media. This behavior is consistent with the experimental observation of intriguingly high effective nonlinear refractive index in degenerate semiconductors such as indium tin oxide [\textit{Alam et al., Science 352 (795), 2016}] (where the nonlinearity is attributed to a modification of the energy distribution of conduction-band electrons due to laser-induced electron heating) and aluminum zinc oxide [\textit{Caspani et al., Phys. Rev. Lett. 116 (233901), 2016}] at frequencies with vanishing real part of the linear permittivity. Such strong nonlinear response can pave the way for a new paradigm in nonlinear optics with much higher conversion efficiencies and therefore better miniaturization capabilities and power requirements for next-generation integrated nanophotonics., Comment: 10 pages, 8 figures

We explore the mathematical theory to rigorously describe the response of media with linear time-varying, generally dispersive, electromagnetic constitutive parameters. We show that even when the temporal inhomogeneity takes place on a time scale comparable or shorter than the driving fields' time period, one can still define a physically meaningful time-varying dispersion. Accordingly, a generalized set of Kramers-Kronig relations is investigated to link the real and imaginary parts of the time-varying frequency-dispersive spectra characterizing the medium's constitutive response. Among others, we study the case of a Lorentzian dielectric response with time-varying volumetric density of polarizable atoms and present the varying circuital equivalents of the governing differential equation, which in turn allow us to use the notion of generalized time-varying impedances/admittances of a time-dependent resistor, inductor and capacitor., Comment: 16 pages, 5 figures, 3 appendices