Negative Refraction in Time-Varying Strongly Coupled Plasmonic-Antenna–Epsilon-Near-Zero Systems

Time-varying metasurfaces are emerging as a powerful instrument for the dynamical control of the electromagnetic properties of a propagating wave. Here we demonstrate an efficient time-varying metasurface based on plasmonic nano-antennas strongly coupled to an epsilon-near-zero (ENZ) deeply subwavelength film. The plasmonic resonance of the metal resonators strongly interacts with the optical ENZ modes, providing a Rabi level spitting of $\sim 30\%$. Optical pumping at frequency $\omega$ induces a nonlinear polarization oscillating at $2\omega$ responsible for an efficient generation of a phase conjugate and a negative refracted beam with a conversion efficiency that is more than 4 orders of magnitude greater compared to the bare ENZ film. The introduction of a strongly coupled plasmonic system therefore provides a simple and effective route towards the implementation of ENZ physics at the nanoscale.

Figure 1

Linear properties. (a) Dielectric permittivity ($ϵ$) for the ITO layer based on a Drude model with real part $\mathrm{Re}\{ϵ\}$ and imaginary part $\mathrm{Im}\{ϵ\}$. (b) SEM image of the square lattice antenna pattern on ITO film (gold antenna length $L=460\mathrm{nm}$, with period $p=800\mathrm{nm}$ on a $d=40\mathrm{nm}$ thick ITO film). (c) FDTD calculations of linear transmission through the metasurface using the ITO dielectric permittivity in (a). (d) Experimentally measured linear transmission of the metasurface (linear interpolation of measurements performed for antenna lengths of 400, 450, 500, 600, and 650 nm, $p=800\mathrm{nm}$).

Figure 2

FDTD simulation of the normalized energy density (calculated as the $|E{|}^2$-field distribution normalized to the input $|E{|}^2$) in (a) for the 2D nano-antenna pattern on top of a 40 nm layer of ITO. (b) Depth profile of the normalized energy density across the metasurface [dashed white line in (a)]. (c) The normalized energy density versus wavelength calculated at the two points indicated with “1” and “2” in (a).

Figure 3

Simulations and experiments. (a) Nonlinear FDTD simulation of input probe beam. The arrow indicates the probe direction (pump not shown), the red shaded area shows the metasurface area, and the dashed line indicates the location of the $E$-field source. (b) Phase conjugated and negative refracted beams are generated at the metasurface. (c) NR efficiency (NR energy normalized to input probe energy, expressed in percent) simulated with a nonlinear FDTD based on the same material and geometry as those used in the experiments (dashed red line) and antenna length $L=460\mathrm{nm}$ (indicated in the graph). Also shown (solid-black curve) is the measured curve for $1\mathrm{GW}/{\mathrm{cm}}^2$. The blue and black dashed lines show the simulated NR efficiency with plasmonic antennas with longer or shorter lengths (250 and 650 nm, indicated in the graph) so as to be detuned from the ENZ wavelength. The NR efficiency drops by nearly an order of magnitude thus highlighting the role played by strong coupling in the FWM enhancement. (d) The measured negative refraction (and an example of PC) signal efficiency for antennas on a film of 40 nm of ITO (antenna length $L=460\mathrm{nm}$, period $p=800\mathrm{nm}$) for various pump powers indicated in the graph legend in $\mathrm{GW}/{\mathrm{cm}}^2$. The NR efficiency of the bare ITO film for a pump power of $2\mathrm{GW}/{\mathrm{cm}}^2$, multiplied by 1000 is shown for reference (dashed black curve).

Figure 4

Theoretical model and measurements. (a) NR efficiency ${\eta }_{\text{norm}}$ as measured for the antenna-ITO coupled system for a pump intensity $0.5\mathrm{GW}/{\mathrm{cm}}^2$ and periodicity 600 nm and, (b) for periodicity 800 nm (antenna length is 460 nm in both cases).