Parametric oscillation of electromagnetic waves in momentum band gaps of a spatiotemporal crystal

Abstract

Photonic crystals have revolutionized the field of optics with their unique dispersion and energy band gap engineering capabilities, such as the demonstration of extreme group and phase velocities, topologically protected photonic edge states, and control of spontaneous emission of photons. Time-variant media have also shown distinct functionalities, including nonreciprocal propagation, frequency conversion, and amplification of light. However, spatiotemporal modulation has mostly been studied as a simple harmonic wave function. Here, we analyze time-variant and spatially discrete photonic crystal structures, referred to as spatiotemporal crystals. The design of spatiotemporal crystals allows engineering of the momentum band gap within which parametric amplification can occur. As a potential platform for the construction of a parametric oscillator, a finite-sized spatiotemporal crystal is proposed and analyzed. Parametric oscillation is initiated by the energy and momentum conversion of an incident wave and the subsequent amplification by parametric gain within the momentum band gap. The oscillation process dominates over frequency mixing interactions above a transition threshold determined by the balance between gain and loss. Furthermore, the asymmetric formation of momentum band gaps can be realized by spatial phase control of the temporal modulation, which leads to directional radiation of oscillations at distinct frequencies. The proposed structure would enable simultaneous engineering of energy and momentum band gaps and provide a guideline for implementation of advanced dispersion-engineered parametric oscillators.

Revealing non-Hermitian band structure of photonic Floquet media

“…S4). Then, the precise frequency of the primary gap and the approximate frequencies of secondary gaps at which the net gain is maximized can be identified by the spectral positions of the parametrically oscillating peaks (see (28,31). By tracking the oscillation frequencies with the variation in the driving frequency (Fig.…”

“…More specifically, for space-time periodic media, the Bloch-Floquet theorem justifies the existence of Floquet sidebands generated by the driving. Therefore, the emergence of such sidebands and their interactions in the effective band description are the key to understanding wave propagation in space-time periodic media (26)(27)(28)(29)(30)(31)(32)(33). In view of this, a new perspective on photonic Floquet media is now being provided by advances in non-Hermitian physics.…”

Using Time-Varying Systems to Challenge Fundamental Limitations in Electromagnetics

“…Indeed, as recognized by Chu, a more accurate definition of the fractional bandwidth of the antenna is in terms of the tolerable reflection coefficient over the band (and not simply the inverse of the Q factor), and therefore the antenna bandwidth is limited by the Bode-Fano limit applied to Chu's equivalent circuit for spherical waves. As discussed in [78] , this limitation can be surpassed by periodically modulating the matching network components at twice the frequency of the antenna resonance frequency to impart parametric gain [32] into the system. A realistic simulation of the proposed concept was also demonstrated based on a small loop antenna (see Figs.…”

“…Although in the subsequent decades several other works have further explored the implications of wave propagation in dynamic media [11], [12], [13], [14], it was not until recently when the field gained considerable momentum [15] partly owing to the improved fabrication and characterization techniques at various frequency regimes [16], [17], [18]. Consequently, it was soon discovered that time-dependent materials can enable many interesting and novel phenomena, such as interband photonic transitions [19], [20], nonreciprocal systems [21], [22], efficient wavelength conversion [23], [24], [25], [26], temporal aiming [27], Fresnel drag [28], negative extinction [29], entangled photon generation [30], [31], parametric oscillations [32], synthetic dimensions [33], topological phase transition [34], nonreciprocal gain [35], among others [36]. Several recent publications also further investigated the fundamental aspects of wave propagation in time-varying media, such as Refs.…”

ℏω versus ℏk: dispersion and energy constraints on time-varying photonic materials and time crystals [Invited]

“…This is true, for instance, for optical modulators and optical isolators based on traveling-wave modulations, where the frequency of the temporal perturbation can be significantly smaller than the operational frequency and the refractive index change can be low [13,[26][27][28] (with the caveat that, for spacetime-modulated optical isolators, the length of the device trade-offs with the coupling strength between modes [13] and the modulation frequency [29]). Conversely, for other time-varying systems that have recently been the subject of intense theoretical interest, such as photonic time crystals [30][31][32][33][34] and broadband optical parametric amplifiers based on momentum bandgaps [35], the modulation frequency is comparable or larger than the operational frequency, and the modulation strength needs to be sufficiently large to observe the relevant phenomena. For instance, the relative width of the momentum gaps in a time crystal is proportional to the relative modulation strength [36,37] and, therefore, the typical relative permittivity change for these systems is around 10% [38] and can be as high as 200% [32].…”