Effect of geometry, anisotropy and composition on the third-order optical nonlinearities of multilayer hyperbolic metamaterials - INVITED

. Quantum technologies require advanced optical metamaterials whose properties can be tailored and controlled as desired. Hyperbolic metamaterials have great potential for applications in nonlinear nanophotonics, such as all-optical switching, optical limiting, mode-locking and optical sensing. In this work, we show how to obtain strong third-order optical nonlinearities in hyperbolic multilayers exploiting the e ff ect of bulk plasmon polaritons. We demonstrate the tunability of these properties with angle and polarization, and we propose a model to predict them. We evidence the enhancement of the nonlinear response in low-loss metamaterials.


Introduction
Predicting, boosting and adjusting the nonlinear response of optical materials is fundamental for the design of efficient nonlinear optical devices with optimized and reconfigurable features to be employed in photonic integrated circuits [1].For this reason, strong scientific efforts are being made in developing metamaterials whose properties can be tailored by nanostructuring and actively controlled by external parameters.In such a way, light manipulation at the nanoscale can be achieved, which is an essential condition for the progress of quantum technologies.
Hyperbolic metamaterials are one of the most interesting class of cutting-edge plasmonic nanocomposites in advanced nanophotonics due to their anisotropic optical properties, their near-zero permittivity, and their capability to sustain high-k modes (bulk plasmon polaritons, BPP) generated by the spatial mode matching of surface plasmon polaritons (SPP) sustained at the metal-dielectric interfaces [2,3].These peculiar properties allow to obtain enhanced nonlinear optical properties in the visible spectrum, and can be engineered by changing the geometry and composition of the metamaterials [2,4].
In this work, we design hyperbolic multilayers (HM) with different geometry and composition to have their ENZ wavelength (λ ENZ ) in the VIS spectrum.We investigate their third-order nonlinear optical response, i.e. the nonlinear refractive index n 2 and nonlinear absorption coefficient β.We show the advantage of spectrally matching the ENZ regime with BPP modes to obtain strong optical nonlinearities.We demonstrate the angle and polarization tunability of these properties [4].We point out the enhancement of the optical Kerr effect (OKE) using a lowloss metal component.* e-mail: domenico.genchi@unipd.it

Methods
HM with different layers thickness are fabricated by magnetron sputtering depositions of alternated Au (or Ag) and Al 2 O 3 thin films arranged in four-bilayer stacks.The layered nanostructure is inspected by cross-sectional scanning electron microscopy (SEM), the surface roughness is measured by atomic force microscopy (AFM), and the layers thickness is obtained by angle-resolved spectroscopic ellipsometry (SE).The linear optical properties are investigated by UV-VIS spectroscopy and SE.The OKE is spectrally investigated in the visible range at different angles with TE and TM polarizations by the z-scan technique [5] using a Nd:YAG laser (λ=355 nm, 18 ps pulses, 10 Hz repetition rate) coupled to an optical parametric amplifier.The z-scan measurements are performed with a beam intensity of 350 MW/cm 2 .
The effective permittivity of the HM is calculated by effective medium theory (EMT).The electromagnetic response of the HM is simulated by EMUstack [6].The nonlinear optical properties are calculated by the effective filling fraction model we have proposed in [4].

Discussion
The effective permittivity of HM is tuned by changing the thickness of the dielectric layers (t d ) while keeping the same thickness of the metal layers (t m =15 nm).For example, the parallel component ε ∥ (real part) is plotted in Fig. 1(a) for Au/Al 2 O 3 HM having t d equal to 30 nm (AuAlu33) and 85 nm (AuAlu16).The metal filling fraction ( f m ) is decreased (from 33% to 16%) by increasing t d , and so λ ENZ is spectrally redshifted (from 543 nm to 666 nm).With t d =85 nm a plasmonic resonance (absorptance peak in Fig. 1(b)) generated by the SPP coupling is obtained near λ ENZ , falling near the minimum of Im[ε Au ], far from the interband absorption region of gold (300-500 nm).The fabricated AuAlu16 is displayed in the inset of Fig. 2 as an example.All the samples of the present work have a surface roughness ≈1 nm.
The ENZ resonance produces a high local intensity enhancement, so that a peak of positive n 2 and β (in Fig. 2) is obtained in proximity of λ ENZ far from the range of Au interband transitions, which give the main contribution to the nonlinear response at λ≤550 nm (yellow area).The obtained nonlinear optical properties can be continuously modulated in absolute value and spectrally by tilting the sample, that is changing the incidence angle and polarization [4].This is due to the concomitant effect of anisotropy and variation of SPP coupling within the metamaterials.The data obtained at 0 • and 60 • with TE polarization are shown in the insets of Fig. 2 as examples.
The effective permittivity can be also modified by changing the metal component in the HM, e.g. using Ag, as shown in Fig. 1(a) (gray curve).A larger number of BPP modes (absorptance peaks in Fig. 1(b)) are sustained by a 15/85 Ag/Al 2 O 3 HM (AgAlu16, f m =16%) owing to a lower optical damping (Im[ε Ag ]<Im[ε Au ]) and a blueshifted interband absorption (in the UV range).An ENZ resonance is obtained near λ ENZ (632 nm).Here, the nonlinear refractive index is increased by a factor 10 compared to AuAlu16 due to lower losses, and a large negative β is obtained, as shown in Fig. 2. The nonlinear response of AgAlu16 is also enhanced compared to a 15 nm Ag film, whose n 2 and β are null at the chosen intensity.
All the measured nonlinear parameters are in good agreement with those computed by our model [4].

Conclusions
A strong third-order nonlinear optical response in Aubased and Ag-based hyperbolic metamaterials is obtained choosing the optimal geometry to spectrally match the ENZ regime with BPP modes where the loss of the metal component is minimum.We demonstrate the angle and polarization tunability of the nonlinear properties as an effect of the intrinsic anisotropy of HM and the modification of SPP coupling at their inside.The optical nonlinearities are enhanced by using a low-loss metal.The good agreement between the experimental and simulated parameters in all the considered configurations validate our model as a predictive tool to design nonlinear multilayered metamaterials.The outcomes evidence the huge potential of HM as platforms for nonlinear optical devices, like alloptical modulators, optical limiters, mode-lockers and optical sensors.

Figure 1 .Figure 2 .
Figure 1.(a) Effective permittivity (parallel, real part) and (b) absorptance of the fabricated Au/Al 2 O 3 (orange and yellow) and Ag/Al 2 O 3 (gray) HM.The vertical dashed lines indicate the λ ENZ of each HM.Inset: SEM image of the sample AuAlu16.