Refractive Index In Time Research Articles

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

Photonic time-varying systems have attracted significant attention owing to their rich physics and potential opportunities for new and enhanced functionalities. In this context, the duality of space and time in wave physics has been particularly fruitful to uncover interesting physical effects in the temporal domain, such as reflection/refraction at temporal interfaces and momentum-bandgaps in time crystals. However, the characteristics of the temporal/frequency dimension, particularly its relation to causality and energy conservation ( ℏ ω is energy, whereas ℏ k is momentum), create challenges and constraints that are unique to time-varying systems and are not present in their spatially varying counterparts. Here, we overview two key physical aspects of time-varying photonics that have only received marginal attention so far, namely temporal dispersion and external power requirements, and explore their implications. We discuss how temporal dispersion, an inherent property of any physical causal material, makes the fields evolve continuously at sharp temporal interfaces and may limit the strength of fast temporal modulations and of various resulting effects. Furthermore, we show that changing the refractive index in time always involves large amounts of energy. We derive power requirements to observe a time-crystal response in one of the most popular material platforms in time-varying photonics, i.e., transparent conducting oxides, and we argue that these effects are almost always obscured by less exotic nonlinear phenomena. These observations and findings shed light on the physics and constraints of time-varying photonics, and may guide the design and implementation of future time-modulated photonic systems.

Frequency Conversion of Lasers in a Dynamic Plasma Grating

When a dynamic medium in which the laser propagates changes its refractive index in time, the laser changes its frequency while keeping its wavevector unchanged to fullfil the dispersion relation. This is usually applied to upshift the laser frequency with ionizing plasma. We propose an alternative technique to modify light frequency. A transient plasma grating can be generated by two identical counterpropagating laser pulses via strongly coupled stimulated Brillouin scattering (SC SBS). The rapid evolution of the plasma grating affects the wave-dispersion relation and a band gap develops around the laser frequency, dependent on the grating amplitude. As a result, the lasers convert their frequency downward to the low edge of the band gap, while a free-traveling laser converts its frequency to both the upper and lower edge of the band gap. Depending on the considered setup, practical applications of this technique include either laser-frequency downshift or spectral splitting can be exploited. The former can be used for Raman amplification in plasma and the latter for dual-color x-ray generation by Thomson and/or Compton scattering.

Photonic quantum memory in two-level ensembles based on modulating the refractive index in time: Equivalence to gradient echo memory

We present a quantum memory protocol that allows us to store light in ensembles of two-level atoms, e.g., rare-earth-metal ions doped into a crystal, by modulating the refractive index of the host medium of the atoms linearly in time. We show that under certain conditions the resulting dynamics is equivalent to that underlying the gradient echo memory protocol, which relies on a spatial gradient of the atomic resonance frequencies. We discuss the prospects for an experimental implementation.

Refractive index control for optical quantum storage

Manipulating refractive index in time allows one to implement quantum storage in an extended resonant atomic system without recourse to inhomogeneous broadening of optical transitions or amplitude modulation of control fields, which when combined with other storage techniques provides the possibility to improve mode or channel capacity of optical storage devices. We discuss different methods of refractive index manipulation in the context of quantum storage applications, giving special attention to a simple frequency shift of an absorption structure relative to the resonant energy levels. We show that a linear modulation of refractive index in time without significant losses can be realized in doped solid-state materials such as Er3+ :Y2SiO5 crystal, to provide optical quantum storage.