Negative refraction in time-varying, strongly-coupled plasmonic antenna-ENZ systems

TL;DR

This paper demonstrates a novel time-varying metasurface combining plasmonic nano-antennas with ENZ materials, enabling efficient negative refraction and phase conjugation at the nanoscale through strong coupling and nonlinear effects.

Contribution

It introduces a strongly coupled plasmonic-ENZ system that enhances nonlinear optical processes and enables negative refraction with high efficiency at the nanoscale.

Findings

Achieved ~30% Rabi splitting of plasmonic and ENZ modes.

Generated phase conjugate and negative refracted beams with high efficiency.

Demonstrated a simple route to implement ENZ physics at the nanoscale.

Abstract

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 sub-wavelength film. The plasmonic resonance of the metal resonators strongly interacts with the optical ENZ modes, providing a Rabi level spitting of ~30%. Optical pumping at frequency {\omega} induces a nonlinear polarisation 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 four 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

Equations

$$E(\omega )\propto \int {\epsilon }_0{\chi }^{(3)}(\omega )⋮{\mathbf{E}}_{\text{p}}^2(\omega ){\mathbf{E}}_{\text{s}}^{\ast }(\omega )\cdot {\mathbf{E}}_{det}(\omega )dV$$

$${\eta }_{\text{norm}}(\omega )=\frac{|E_{\text{metasurface}}{|}^2}{|E_{\text{ITO}}{|}^2}$$

Full text

Introduction. Time-varying systems and metasurfaces are of interest in view of the fundamental physics questions that have arisen Mendonça (2000); Nation et al. (2012); Yablonovitch (1989); Westerberg et al. (2014); Prain et al. (2017); Bacot et al. (2016); Vezzoli et al. (2018) and also in view of the potential applications ranging from perfect lenses to spectral and temporal shaping of light fields Maslovski and Tretyakov (2003); Pendry (2008); Shaltout et al. (2015); Sounas and Alù (2017); Shaltout et al. (2019); Sartorello et al. (2016); Nicholls et al. (2017); Rahmani et al. (2018); Nicholls et al. (2019); Ciattoni et al. (2018). Recent results have shown that thin films of epsilon-near-zero (ENZ) materials with a dielectric permittivity close to zero Liberal and Engheta (2017); Alu et al. (2007) at optical wavelengths in the visible or near-infrared spectral regions are promising candidates to achieve rapid (on the optical wave oscillation timescale) temporal changes of the optical properties Vezzoli et al. (2018). The very large order-of-unity refractive index changes that can be induced optically Alam et al. (2016); Caspani et al. (2016); Clerici et al. (2017); Carnemolla et al. (2018) makes it possible to achieve efficient temporal modulation uniformly across the medium Shaltout et al. (2015); Marini and De Abajo (2016) even in deeply subwavelength thin films Capretti et al. (2015a); Luk et al. (2015); Capretti et al. (2015b), resulting in optically-induced negative refraction with unity efficiency Vezzoli et al. (2018). However, the results demonstrated so far rely on high-intensity optical pumping of the ENZ film in order to achieve such large changes in the refractive index. Recently, the combination of ENZ films with plasmonic structures has led to a significant reduction of the required optical powers for the Kerr nonlinear contribution to the refractive index Alam et al. (2018).

Coupling between light and matter can be enhanced when two resonant systems with the same optical resonant frequency are brought into close contact Törmä and Barnes (2014). Strong coupling occurs when the strength of the coupling mechanism (measured by the splitting of the two resonant frequencies De Liberato et al. (2007)) dominates the intrinsic losses in the system thus resulting in a double peaked structure in the absorption spectrum or equivalently, in two well-separated polariton branches in the spectral domain. In the temporal domain, this will give rise to Rabi oscillations between the populations on these two branches and the combination of light-matter states where the matter component can contain a large fraction of the total energy. Strong coupling has been observed in a variety of systems Benz et al. (2013); Törmä and Barnes (2014), ranging from single atoms in cavity Thompson et al. (1992), quantum dots in photonic crystal Yoshie et al. (2004) to Bose-Einstein condensates Plumhof et al. (2014) and superfluids Amo et al. (2009).

Strong coupling at room temperature has also been reported between plasmonic resonators and deeply sub-wavelength ENZ films Jun et al. (2013); Schulz et al. (2016); Campione et al. (2016a); Hendrickson et al. (2018); Passler et al. (2018). In this strongly coupled system, the fundamental plasmonic resonance of a metal antenna resonator is coupled to optical modes supported by the deeply sub-wavelength ENZ thin film at the frequency where the real part of the dielectric permittivity crosses zero, called ENZ modes. The ENZ modes can be seen as a long-range surface waves which arise from the interaction of two Surface Plasmon Polaritons (SPPs) at the two interfaces of the thin film Vassant et al. (2012a); Campione et al. (2015, 2016b); Runnerstrom et al. (2017); Luk et al. (2015); Vassant et al. (2012b). These ENZ modes exhibit a large density of states and can homogeneously confine the EM radiation within the ENZ Campione et al. (2015); Ciattoni et al. (2013). Due to the impedance mismatch at the interface between air and the ENZ medium, excitation of the ENZ optical modes is inefficient, while adding strongly coupled antennas enables high electromagnetic fields inside the ENZ film, resulting in enhanced nonlinear responses.

Here, we study optically-induced negative refraction from a time-varying, strongly-coupled ENZ metasurface based on gold nano-antennas on top of a deeply sub-wavelength ENZ film. Experiments were performed by optically pumping at normal incidence a metasurface composed of rectangular metallic nano-antennas on a 40-nm-thick ENZ film and probing the resulting temporal variation of the metasurface with a probe beam incident at a small angle. The generation efficiency of the negative refracted (NR) and phase conjugated (PC) waves can provide a quantitative estimate of the strong coupling between the ENZ and the antenna modes, resulting in efficient optically-induced temporal variations of the material properties across a broad bandwidth (1200 - 1700 nm). The optically-induced temporal modulation Maslovski and Tretyakov (2003); Pendry (2008) and resulting negative refraction and phase conjugation of the input probe beam generated in the strong-coupling regime are four orders of magnitude larger and cover a bandwidth that is three times broader in the ENZ wavelength region when compared to the bare ENZ film.

Metasurface properties. Figure 1(a) shows the real and imaginary parts of the dielectric permittivity via ellipsometry measurements of the 40 nm ITO film on a 1-mm-thick SiO2 substrate. The ITO film exhibits a zero-crossing of the real part at 1400 nm (ENZ wavelength). Figure 1(b) is an example SEM image of the metasurface (top view) showing the geometry of the gold antennas deposited on the ITO surface with length L and periodicity p (see Supplementary information). The length of the antennas is such that their plasmonic resonance crosses the ENZ wavelength of the ITO film and the periodicity p $\sim 600-800$ nm of the square lattice was chosen so as to maximise the density of the antennas whilst avoiding antenna-to-antenna coupling.

Figures 1(c) and (d) show the numerically simulated (FDTD) and measured transmission spectra around the ENZ wavelength. For an incident optical beam normal to the metasurface and polarized along the long axis of the antenna, the spectra show two resonances corresponding to the two polariton branches of the strongly coupled metasurface. The experimental spectral splitting of the two polariton branches is $\sim 420$ nm corresponding to a strong coupling efficiency of $\sim 32$% (see Supplementary information) Campione et al. (2015).

In Fig. 2(a) we report the normalised energy density, calculated from finite difference time domain (FDTD) simulations as the $|E|^{2}$-field distribution normalised to the input $|E|^{2}$ distribution at 1400 nm wavelength for the metasurface (L = 460 nm and p = 800 nm) upon normal incidence of the pump beam. Figure 2(b) shows the normalised energy density along the vertical line [white dashed line in (a)]. For a 1400 nm laser pulse polarized parallel to the long axis of the antenna and at normal incidence, the field intensity is enhanced by a factor greater than 50 with respect to the bare ITO. In Fig. 2(c) we plot the wavelength dependence of the energy density across the full bandwidth covering the two polariton branches calculated at two different points indicated as “1” and “2” in Fig. 2(a), showing an enhancement that is 40 times greater with respect to the bare ITO layer over a $\sim 300$ nm bandwidth.

Experiments.

By using a pump and probe set-up, we perform a degenerate four wave mixing (FWM) experiment (i.e. a single pump beam and a single probe beam, both at the same wavelength) in the 1180 nm to 1710 nm spectral range. The optical pump beam has normal incidence on the sample, while the probe is incident at a small ($6^{\circ}$) angle. The two incident laser pulses are co-polarized (parallel to the long axis of the antenna) and have a temporal duration of 240 fs, the same central wavelength, and 100 kHz repetition rate. The generated NR and PC are measured with a photodiode and compared to the transmission of the bare ITO in order to evaluate the efficiency of the nonlinear process. In Fig. 3 we show a comparison of the experimental results to a nonlinear FDTD simulation reproducing the experiment conditions (antenna length L = 460 nm, period p = 800 nm). The linear properties of the ITO film are based on the experimental measurements shown in Fig. 1(a), while the nonlinear response is described via the third order nonlinear susceptibility $\chi^{(3)}=9\cdot 10^{-18}$ m2/V2 Humphrey and Kuciauskas (2006). In these simulations, we blue-shift the central wavelength of the probe by 100 nm from the pump in order to discriminate the output NR and PC fields. Figures 3(a) and (b) show the simulated near field distribution for the incident probe and the generated NR and PC fields. The simulated NR efficiency (i.e. the NR efficiency normalised to the input probe energy, expressed in $\%$) is shown for a pump intensity of 1 GW/cm2 in Fig. 3(c) (red dashed curve) and matches well to the raw experimental data (black curve). Figure 3(c) also shows the same FDTD simulations with detuned plasmonic antennas (i.e. antenna lengths of 250 and 650 nm) so as to be out of the strong coupling regime. The FWM efficiency drops in both cases by an order of magnitude, providing strong evidence that strong coupling is enhancing the nonlinear process.

In Fig. 3(d) we show the measured NR signal efficiency for various pump powers indicated in the graph in GW/cm2. The dotted black curve shows for comparison the NR efficiency at 2 GW/cm2 pump power for the bare ITO film, multiplied by 1000. We see that the measured FWM efficiency of the metasurface is enhanced by more than four orders of magnitude when compared to the bare ITO. The absolute efficiency of both the NR and PC (one example shown, red-dotted line) nonlinear processes is of order $\sim 1$% over a very large bandwidth of $\sim 300$ nm. Both the NR and PC exhibit the same trend, as expected for a deeply sub-wavelength film that is uniformly modulated at twice the probe beam frequency Pendry (2008). To verify the FWM process is primarily due to the strong coupling between the gold antennas and ITO film, and is not due solely to the gold nonlinearity, we repeated all experiments for the gold antennas deposited on a glass substrate. We find the gold antennas alone do not produce a detectable signal at the same pump powers.

Model and data analysis. In order to further understand the nonlinear enhancement, we model the pump-probe interaction in the metasurface as a FWM process in which the four-orders of magnitude enhancement of the negative refraction and phase conjugation processes emerge as a result of the increased optical energy density in the ENZ layer. Indeed, in the strongly coupled system the E-field of both pump and probe is strongly enhanced inside the ITO layer as the plasmonic antennas convert the incident propagating waves into waves localised in their near-field. We model the nonlinear generation of beams in a FWM process starting from the numerically simulated distribution of linear fields, as described for instance in Ref. O’Brien et al. (2015). FWM is driven by a nonlinear polarization in the ITO layer, $P\propto E_{\textrm{p}}^{2}E_{\textrm{s}}^{*}$, where $E_{\textrm{p}}$ is the pump field, $E_{\textrm{s}}$ the probe field and $P$ is the microscopic source of the measured fields of the NR and PC beams. By making use of the reciprocity theorem, one can calculate the expected FWM E-field generated by $P$ as:

[TABLE]

where the integral is calculated over the ITO volume and $E_{det}$ is the field inside the ENZ film generated by a point-source representing the detector in the far-field (see Supplementary information). The FWM efficiency, measured in the experiment as the ratio between the energy radiated into NR (or PC) and the incident probe energy and is thus proportional to $|E|^{2}$. This is true both for the bare ITO and the metasurface. Taking the ratio between the efficiency, $\eta_{\textrm{metasurface}}$, of NR for the metasurface and the efficiency, $\eta_{\textrm{ITO}}$, of NR for bare ITO removes of the spectral dependence of the nonlinear permittivity $\chi^{(3)}$, of the linear permittivity, the sample thickness and all other constants:

[TABLE]

This relation directly estimates the trend of the normalised efficiency of the NR and PC processes from the energy density calculation shown in Fig. 2(c). Figure 4 shows the result, together with the corresponding measured $\eta_{\textrm{norm}}$ based on the experimental data shown in Fig. 3(d) for p = 800 nm and an additional periodicity p = 600 nm. As can be seen, our model based on the energy density enhancement in the metasurface explains the experimental results for the two different antenna configurations studied in this work, although the longer wavelength peak in the spectrum appears to have higher visibility in the experiments with respect to the theoretical model. Our primary conclusion is that the strong coupling between the plasmonic antennas and ENZ film enhances light-matter interaction and, therefore, increases the conversion efficiency of our time-varying metasurface by a factor greater than 15000. Such efficient time-varying surfaces can be obtained by optically pumping the metasurface with relatively low and readily accessible optical pumping powers of 0.5 mW, corresponding to peak intensities on the surface of 0.5 GW/cm2.

Conclusions. Our experiments show that strongly-coupled plasmonic antenna-ENZ systems can be temporally modulated with an optical pump beam through a $\chi^{(3)}$-mediated process. Optical pumping at frequency $\omega$ induces a nonlinearity-mediated oscillation at frequency $2\omega$, which following the original predictions Maslovski and Tretyakov (2003); Pendry (2008), leads to the generation of a phase conjugate and a negative refracted beam. We observe a 15000-fold enhancement in the negative refraction and phase conjugation signals compared to the bare ENZ films. We have developed a nonlinear model which elucidates the relation between FWM enhancement and the increased energy density inside the ENZ film which arises from strong coupling. Efficient time-varying surfaces with optically pumping at relatively low and readily accessible powers provide a route towards applications in which light is controlled by light in compact, subwavelength devices alongside a means to investigate fundamental physics, potentially including photon pair generation from deeply subwavelength systems.

Acknowledgements. Data for this work is available for download data . DF acknowledges financial support from EPSRC (UK Grants EP/M009122/1 and EP/P006078/2). M.C. acknowledges the support from the United Kingdom Research and Innovation (UKRI, Innovation Fellowship EP/S001573/1). Purdue team acknowledges support by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0017717 (sample characterization), and Air Force Office of Scientific Research (AFOSR) award FA9550-18-1-0002 (numerical modeling). S.V., S.M., A.J., S.A.M. and R.S. acknowledge funding by EPSRC (EP/P033431 and EP/M013812). S.A.M. acknowledges the Lee-Lucas Chair in Physics and the DFG Cluster of Excellence Nanoscience Initiative Munich (NIM). T.H. acknowledges the Schrödinger Scholarship.