Plasmonic metamaterial time crystal

Abstract

Periodically driven optical materials and metamaterials have recently emerged as a promising platform for realizing photonic time crystals (PTCs) -- systems whose optical properties are strongly and periodically modulated on time scales comparable to the optical cycle of light. These time-varying structures are the temporal counterparts of spatial photonic crystals (SPCs), for which a large and periodic dielectric contrast is achieved spatially on wavelength scales. Just as SPCs have revolutionized control over light-matter interactions by engineering the photonic density of states in space, PTCs promise comparable breakthroughs from a fundamentally new perspective: a temporal one. However, harnessing such phenomena at optical frequencies poses severe experimental challenges, as it requires order-unity modulation depths of the optical properties at optical cycle rates, a regime that has remained elusive to date. Here, we report the first optical realization of a photonic time crystal, achieved with a surface plasmon cavity metamaterial operating at Terahertz frequencies. We demonstrate strong (near-unity) and coherent (sub-optical cycle) periodic driving of the plasmonic metamaterial enabled by field-induced dynamical modulation of the carriers' kinetic energy and effective mass -- reaching up to 80% of their rest mass, an exceptionally high value that forms the basis for time-crystalline phenomena with plasmons. Our experimentally informed theory reveals rich physics within the experimentally accessible parameter regime of this system, including parametric amplification and entangled plasmon generation, and establishes a robust new platform for time-domain photonics.

Figures (3)

• Figure 1: a) Conceptual representation of a combined SPC and PTC in real space (top panel) and reciprocal space (bottom panel). Periodicity in space (resp. time) generates replicas (purple and green lines) of the bare photonic band structure (dark grey lines) translated along the momentum (resp. frequency) axis. Crossings between the bare dispersion and the spatial (resp. temporal) replicas, as indicated by the dashed lines, open frequency (resp. momentum) gaps in the resulting band structure (solid lines). Insets show allowed and/or forbidden wave solutions inside the two types of gaps. b) Plasmonic metamaterial under consideration: a spatially periodic lattice of metal/insulator/plasmonic (m/i/p) cavities (m=Au, i=$\mathrm{Si_3N_4}$, p=InSb). The time and frequency resolved response of the metamaterial to a multi-cycle periodic drive (green pulse) is obtained by employing a broadband probe pulse (purple) that is electro-optically sampled (red pulse). c) Equilibrium power reflectivity of the metamaterial at 290K (solid black curve) and normalized amplitude of the Fourier transform of the multi-cycle driving field (green) d) Electric field (white vectors) and magnetic field (color bar) profiles of the cavity mode at the resonance frequency of 0.77 THz
• Figure 2: Temporal response of the metamaterial under a multicycle drive with a peak field of 40kV/cm: frequency-resolved power reflectivity (central panels) and phase (right panels) spectra as a function of time $\tau$ during the drive (left panels) a) Coarse grained dynamics measured over the complete duration of the drive b) Close up on the dynamics in the vicinity of the peak driving field with sub-cycle temporal resolution. c) Comparison of the sub-cycle dynamics shown in b) obtained from a parametrically driven cavity model (see text for details).
• Figure 3: Plasmonic time crystal phenomena computed for the experimentally accessible regime of parameters of this platform a) Stability diagram: growth rate of the cavity mode as a function of drive frequency $\omega_\mathrm{d}$ and modulation strength $\eta_0$ relative to the equilibrium cavity frequency $\omega_\mathrm{c}^0$. The solid contour line defined by $\mathrm{Im}(\mu)/\omega_\mathrm{c}^0=\Gamma/\omega_\mathrm{c}^0=0.12$ marks the threshold for parametric amplification given the observed losses. Dashed contour line indicate regions exhibiting average reflectivity above one. Operating points of the present cavity design (star) and an electrostatic cavity (dot) are indicated (see text) b) Wigner function of the cavity state accounting for the losses. Top panel: no drive. Middle panel: this experiment's parameters ($\eta_0/\omega_\mathrm{c}^0=0.18$, $\omega_{\rm d}/\omega_\mathrm{c}^0 = 0.92$) Bottom panel: an electrostatic cavity ($\eta_0/\omega_\mathrm{c}^0=0.4$, $\omega_{\rm d}/\omega_\mathrm{c}^0 = 0.8$) c Plasmonic time crystal $k-$gap openings. Real and imaginary parts of the eigenmodes' frequency $\omega$ as a function of momentum (or Bloch-momentum) $k$, normalized to the plasma frequency $\omega_\mathrm{p}$ and including the losses, for the equilibrium (dashed lines) and the temporally-modulated systems (solid lines). Top panel: a dispersive insulator/plasmonic interface. Bottom panel: our dispersion-free plasmonic metamaterial design for cavities tuned in the electrostatic regime (shown in the first Brillouin zone of the metamaterial of period $d$. The drive frequency corresponds to $\omega_\mathrm{d}/\omega_\mathrm{p}=0.68$ in both cases.