Dynamic beam steering with all-dielectric electro-optic III–V multiple-quantum-well metasurfaces

Tunable metasurfaces enable dynamical control of the key constitutive properties of light at a subwavelength scale. To date, electrically tunable metasurfaces at near-infrared wavelengths have been realized using free carrier modulation, and switching of thermo-optical, liquid crystal and phase change media. However, the highest performance and lowest loss discrete optoelectronic modulators exploit the electro-optic effect in multiple-quantum-well heterostructures. Here, we report an all-dielectric active metasurface based on electro-optically tunable III–V multiple-quantum-wells patterned into subwavelength elements that each supports a hybrid Mie-guided mode resonance. The quantum-confined Stark effect actively modulates this volumetric hybrid resonance, and we observe a relative reflectance modulation of 270% and a phase shift from 0° to ~70°. Additionally, we demonstrate beam steering by applying an electrical bias to each element to actively change the metasurface period, an approach that can also realize tunable metalenses, active polarizers, and flat spatial light modulators.


Analysis of reflectance and phase modulations by resonant MQW heterostructures
To experimentally identify the optimal operation wavelength for observation of tunable amplitude and phase modulations, we fabricate a number of planar DBR/MQW/PMMA/Au heterostructures, which support high-Q Fabry-Pérot resonances (see Supplementary Fig. 1b) To gain a deeper insight, we use the data displayed in Supplementary Fig. 2 to extract the measured bias-induced wavelength shift of the first Fabry-Pérot resonance supported by the planar DBR/MQW/PMMA/Au heterostructure (see Supplementary Fig. 3). In Supplementary Fig. 3, the wavelength shift ∆λ is defined as an amount of the spectral shift in the resonance position when the bias is changed from 0 V to -10 V, that is, ∆λ = λ-10V -λ0V. Supplementary Fig. 3 also displays a bias-induced variation of the FWHM of the considered Fabry-Pérot resonance as a function of wavelength. In Supplementary Fig. 3, the FWHM difference is defined as a change in FWHM when the applied bias changes from 0 V and -10 V. We observe that both the wavelength shift ∆λ and the change in FWHM adopt larger values at shorter wavelengths. Our results are consistent with the analysis described in the prior work 1 , which reports the III-V compound MQW design used in our work. Based on the trend shown in Supplementary   Fig. 3, we believe that the strongest refractive index modulation occurs at wavelengths very close to the absorption band edge of our quantum wells, which we expect to correspond to the wavelength of ~915 nm.

Origin of the resonant modes in MQW resonators
To investigate the origin of each resonant mode in the MQW resonators, here we perform the simulations for the MQW structures, which are comprised of the partially etched double-slits (see Supplementary Fig. 6a). Note that in Supplementary Fig. 6a, the air gap between the resonant elements, which is otherwise present in the fabricated structures, is absent. Supplementary Fig. 6b shows the simulated reflectance spectrum, in which two resonant features are observed. The spatial distribution of the x-component of the electric field intenstity Ex shows that the MQW layer supports a Fabry-Pérot resonance within the MQW layer at the shorter-wavelength resonant dip (see Supplementary Fig. 6c).
Since Ex is primarily enhanced in the spatial region between the groups of double-slits, this Fabry-Pérot cavity resonance will be strongly suppressed when the fully etched air gap is present (see Supplementary Fig. 7a). However, we still observe strong filed enhancement within the fully etched air gap, which is mainly from the near-field interaction between MQW slabs (see Supplementary Fig. 7a). More interestingly, the double-slit structure can assist in exciting a guided-mode resonance (GMR), resulting in the large Ez intensity at the topmost interface of the MQW structure (see Supplementary Fig. 6d). Concurrently, we observe a quite signifcant Ez intensity inside the MQW layer (see Supplementary Fig. 6d).
On the other hand, for the longer-wavelength resonant dip, we observe that the double-slit 8 structure acts as a coupler, which effectively guides the incident light into the MQW layer, yielding a strong field confinement in the slits, as shown in Supplementary Fig. 6c. As a result, a Fabry-Pérot-like resonance can still survive when the MQW layer is truncated (see Supplementary Fig. 7b). This light coupler can also weakly convert the incident electric field from x-to z-component, as shown in Supplementary Fig. 6d.

Influence of oblique illumination on the optical diffraction
Because of the slight difference in structural period (910 nm) and laser wavelength (917 nm), optical diffraction can influence the far-field radiation pattern when the incident angle is non-zero. To clarify this point, we performed numerical simulations of the far-field radiation patterns for the MQW metasurface at 0 V with different angles of incidence. As shown in Supplementary Fig. 11a, we found that strong optical diffraction appears even when the incident angle is 5°. However, those diffracted beams' intensities are high compared as to the intensity of the zero-order beam, which is not observed in our measurements. This can be attributed to two different reasons; first, their diffraction angles are too large to be collected (based on the numerical aperture of the objective we used, the largest angle collected is about 16°) and second, the incident angle is almost zero in the real case. To experimentally eliminate this effect, we intentionally slightly defocused the laser beam onto the MQW metasurface when performing the far-field radiation measurements to minimize the incident angle.
To further verify the influence of non-zero incident angle on the far-field radiation pattern, we performed other simulations which numerically demonstrate the active switching of the first-order diffracted beam at different angles of incidence. As shown in Supplementary Fig. 11b, the intensity of the first-order diffracted beams are much higher as compared with the specularly reflected beam when the incident angle is greater than 5°, which is in conflict with our measurement results shown in Figs. 4d and 4e. As a result, we conclude that the MQW metasurface is under almost normal illumination (0° ≦ θin ≦ 5°), and the non-zero incident angle caused optical effect is fairly small in the real case. It is worth noting that the first-order diffracted beams can only be observed when electrical bias is applied, indicating that the demonstration of active switching of first-order diffracted beam is still valid even when the MQW metasurface is under oblique illumination.
where L = 100 μm and wMQW is the length and width of the hybrid Mie-GM resonant structure respectively, d1 is the thickness of p-GaAs, d is the thickness of MQW, ε0 is the permittivity in vacuum, and εr = 13.5 is the dielectric constant 6, 7 of the MQW. Therefore, the estimated highest modulation frequency f is: To experimentally evaluate the modulation speed of our MQW metasurface, an AC electrical bias with frequencies of 0.1 MHz and 1 MHz is applied to the sample and a highspeed InGaAs detector is used to detect the temporal amplitude response (see Supplementary Fig. 12a). As shown in Supplementary Fig. 12b

Supplementary Note 11
Measured J-V curves of MQW resonators Supplementary Fig. 17 shows the measured leakage current density of two MQW resonators. To avoid the dielectric breakdown, we applied a moderate bias ranging from 0 V to -10 V. For both of our samples, the measured current density is on the order of mA/cm 2 , which is much lower than the current density values (on the order of of ~kA/cm 2 ) necessary for observation for carrier-induced refractive index change in GaAs-based III-V semiconductor compounds [8][9][10] .
result, the larger the figure of merit, Δn/Δk of a quantum well, the better optical performance can be achieved in the tunable metasurface. As a proof of concept, we designed a tunable metasurface with an asymmetric coupled quantum well (ACQW) which can possess a larger Δn/Δk (about 10-18) 11 . As a comparison, the Δn/Δk of utilized MQW in this work is 1-5 (see Ref. 1). The unit element is also based on the double-slit structure, as shown in Supplementary Fig. 19a. After structural optimization, we found that about 200° phase shift with a Δn of 0.02 can be obtained at a wavelength of 808.8 nm (see Supplementary Fig. 19b). We also numerically study the beam steering functionality using such ACQW-based metasurface, which is realized by varying the periodicity of the metasurface (see Supplementary Fig. 19c). The simulated far-field radiation patterns even show that the intensity of the steered beams are much higher than the intensity of the specularly reflected beam when the utilized QW possesses larger Δn/Δk. These results indeed verify that the optical performance (in particular, directivity, which is defined as the peak intensity ratio between diffracted and mirror reflected beams) of tunable quantum well-based metasurfaces can be significantly improved when the quantum well system exhibits larger Δn/Δk. Since this is a proof-of-concept demonstration, the working wavelength here (λ = 808.8 nm) is slightly different from the one used in the main manuscript. By appropriately choosing a quantum well, we can shift the operation wavelength to the range of interest 12,13 . Due to the spatial symmetry, only half of the radiation pattern is presented. The total number of unit elements is set at 120.