Broadband giant nonlinear response from electrically tunable polaritonic metasurfaces

Optically-thin nonlinearities in semiconductor heterostructures with optical modes in nanoresonators have recently demonstrated efficient three-wave-mixing at very low pumping intensities of the order of few tens of kW cm -2 . In these subwavelength structures, the efficiency and the spectral bandwidth of the wave mixing depends solely on nonlinearity of the constituent meta-atoms. Here we exploit this property to demonstrate an electrically-tunable nonlinear metasurface that combines a plasmonic nanocavity and a quantum-engineered semiconductor heterostructure, in which the magnitude and the spectral characteristics of the nonlinear response are controlled by bias voltage through the quantum-confined Stark effect. We demonstrate tuning the peak second-harmonic-generation (SHG) efficiency in the range of 8.7 – 10.75 μm and modulation of SHG intensity at a fixed pump wavelength by applying bias voltage. An SHG power conversion efficiency of 0.082 % was achieved using a peak pump intensity of only 80 kW cm -2 .


Abstract
Optically-thin nonlinear polaritonic metasurfaces created by coupling of intersubband nonlinearities in semiconductor heterostructures with optical modes in nanoresonators have recently demonstrated efficient three-wave-mixing at very low pumping intensities of the order of few tens of kW cm -2 . In these subwavelength structures, the efficiency and the spectral bandwidth of the wave mixing depends solely on nonlinearity of the constituent meta-atoms. Here we exploit this property to demonstrate an electrically-tunable nonlinear metasurface that combines a plasmonic nanocavity and a quantum-engineered semiconductor heterostructure, in which the magnitude and the spectral characteristics of the nonlinear response are controlled by bias voltage through the quantum-confined Stark effect. We demonstrate tuning the peak second-harmonicgeneration (SHG) efficiency in the range of 8.7 -10.75 μm and modulation of SHG intensity at a fixed pump wavelength by applying bias voltage. An SHG power conversion efficiency of 0.082 % was achieved using a peak pump intensity of only 80 kW cm -2 .
Metasurfaces constructed through a two-dimensional array of engineered subwavelength structures, capable of controlling local scattering amplitude, phase, and polarization states, have opened an entirely new way of manipulating light 1 . In the past decade, researches on electrically reconfigurable metasurfaces that can overcome the static limit of passive flat optics have been of particular interest, since they can provide a platform enabling dynamic manipulation of light and on-chip integration with other electronics 2 . Based on electrically reconfigurable linear metasurfaces, interesting applications, such as intensity and phase modulation [3][4][5] , dynamic beamshaping [6][7][8] , varifocal lenses 8 , and programmable holography 9 , have been demonstrated.
As a linear counterpart, nonlinear metasurfaces that generate nonlinear optical responses in engineered subwavelength-thin films open new avenues for flat nonlinear optics that can have significant advantages over bulk nonlinear crystals such as relaxed phase-matching constraint and the ability to engineer local nonlinear responses at a deep subwavelength scale [10][11][12][13] . Nonlinear metasurfaces provide new possibilities for innovative applications, including nonlinear holography [14][15][16][17][18] , optical encryptions [19][20][21] , nonlinear optical switching and modulation 22,23 , and applications for generating new frequencies based on nonlinear frequency mixing 13 . To realize such applications, various nonlinear platforms using plasmonic [24][25][26] or dielectric structures 18,[27][28][29][30] for efficient second or third harmonic generation (SHG or THG) in subwavelength films have been proposed. However, these structures are mostly composed of passive resonators using materials with intrinsically low nonlinear response, thus requiring a high-power ultrafast laser and limiting the electrical tuning of nonlinear response. Only a few studies employing plasmonic or dielectric metasurfaces demonstrated electrical modulation of nonlinear response based on electric-fieldinduced SHG or optical rectification [31][32][33][34] .
Recently, a nonlinear intersubband polaritonic metasurfaces comprised of plasmonic nanocavities filled with a multiple quantum well (MQW) layer with giant nonlinear optical responses were studied [35][36][37][38][39][40] . Owing to the resonant nonlinearities associated with intersubband transitions (ISTs) between electron subbands in an n-doped conduction band of a semiconductor heterostructure, the MQW structures can produce giant 2 nd and 3 rd order nonlinear responses for the optical field polarized along vertical (z) direction with respect to semiconductor layers ( (2) zzz χ and (3) zzzz χ , respectively) 41 . The values of these nonlinearities can be up to 4 -5 orders of magnitude higher than that in natural nonlinear materials. Giant intersubband nonlinear response of MQW systems enables efficient frequency conversion in the nonlinear intersubband polaritonic metasurfaces using only moderate pump intensities of approximately few tens of kW cm -2 and SHG conversion efficiency of as high as 0.08 % was reported using a peak pump intensity of only 11 kW cm -2 in the mid-infrared (MIR) range 38 . An ability to electrically tune the nonlinear response of the meta-atoms in the intersubband polaritonic metasurfaces allows one to extend their optical bandwidth and to control and modulate nonlinear response at the individual nanoresonators level.
Here, we employ Stark tuning of intersubband nonlinearities 42 to demonstrate for the first time the electrically tunable nonlinear response in the intersubband polaritonic metasurfaces. The MQW structure used in this work comprises a coupled three-quantum-well system in which three electron subbands are predominantly confined and controlled in each quantum well with different well widths, and broadband giant (2) zzz χ can be induced through the quantum confined Stark effect (QCSE). By combining plasmonic nanocavity structures capable of generating SHG in free-space and applying bias voltages to the MQW layer, broadly tunable efficient SHG was achieved in the MIR region for the input pump wavelength range of 8-11 μm.

Results
Active nonlinear metasurface based on Stark tuning of intersubband nonlinearities. The concept underlying the operation of our electrically tunable nonlinear metasurface is illustrated in Fig. 1. The metasurface was constructed using an array of plasmonic nanocavity meta-atoms, with a 400-nm-thick MQW layer sandwiched between a top Au plasmonic nanoantenna and a bottom Au ground plane. The two metallic layers within the plasmonic nanocavity were used as contact layers for applying bias voltages to the MQW layer. In this configuration, SHG is produced in reflection and the maximum second harmonic (SH) wavelength is tuned by the bias voltage applied to the metasurface. In addition, it is possible to strongly modulate the SH signal generated from the metasurface at a fixed pump wavelength by using an applied voltage pulse. Electrical tuning of the SHG is achieved through Stark tuning of the intersubband nonlinearity of the MQW structure. Fig. 2a shows the unbiased (0V) conduction band diagram for a single period of the MQW structure, with four quantized electron subbands designed for the electrical tuning of the giant 2 nd order nonlinear response. The MQW layer was designed by repeating the coupled threequantum-well structure twenty times using In0.53Ga0.47As/Al0.48In0.52As heterostructures, where first and fourth, second, and third electron subband are confined predominantly to the left, middle, and right well, respectively. In this structure, the IST energy, Eij, between electron subbands i and j can be tuned according to the bias voltage applied to the MQW layer through the QCSE.
Supplementary Figs. 1a and 1b present the conduction band diagrams corresponding to applied bias voltages of +4V and -4V, respectively, over the 400 nm-thick MQW layer. The associated IST energies are shown in Supplementary Fig. 1c. The giant 2 nd order nonlinear response of the MQW structure is produced principally by the resonant transitions occurring within the first three electron subbands; therefore, the intersubband nonlinear susceptibility tensor element of the MQW as a function of the bias voltage is expressed using the equation 43 where ω is the pump frequency, e is the electron charge, Ne,1 and Ne,2 are the averaged electron densities located at the first and second electron subbands, respectively.
and ij γ h denote the IST energy, the transition dipole moment as a function of the bias voltage V, and the linewidth, respectively, for the transition between electron subbands i and j (cf. Supplementary Table 1). Fig. 2b shows the calculated (2) ,1 3 zzz χ − values as a function of both the bias voltage (ranging from -4V to +4V) and the pump wavelength. At 0 V, the (2) ,1 3 zzz χ − peak value of 210 nm V -1 occurs at a wavelength of 9.7 μm. As the positive bias is applied to the MQW layer, the peak wavelength position of (2) ,1 3 zzz χ − shifts to a shorter wavelength owing to the increased E21 and E31 (see Supplementary Fig. 1c), with the opposite trend observed for the negative bias. The calculation results indicate that a broadband giant 2 nd order nonlinear response exceeding 120 nm V -1 can be induced in the 8 -11 μm wavelength range by applying bias voltages. Although the 2 nd order nonlinear response modulation of MQW structures by the QCSE has been reported previously 42 , this study represents the first instance of broadband (2) zzz χ peak tuning based on three quantum wells through the QCSE and its application to electrically tunable nonlinear metasurfaces.
The MQW structure includes a fourth electron subband, and the ISTs among the second to fourth level electrons, with a non-zero electron population at the second level (Ne,2) due to the high doping level and thermal population, can also produce a strong 2 nd order nonlinear response, (2) ,2 4 zzz χ − , as shown in Fig. 2c. The (2) ,2 4 zzz χ − exhibits a relatively weak nonlinear response for the positive bias voltage, but it increases to 22 nm V -1 for wavelengths reaching to 9 μm as the negative bias voltage increases as a result of the increased IST energies, E23 and E42, and their corresponding dipole elements (see Methods for calculation details). The designed MQW structure was grown by molecular-beam-epitaxy on a semi-insulating InP substrate; its intersubband absorption measurement result is illustrated in Supplementary Fig. 2 with accompanying discussion. The measured E12 value was about 10 meV smaller than the calculated value shown in Fig. 2a, forming the intersubband absorption at a longer wavelength of 10.6 μm.
To achieve efficient SHG based on the broadly tunable giant nonlinear response of the MQW, a meta-atom structure was designed, as shown in Fig. 3a. We designed the complementary Vshaped nanoantenna with a gap in the x-direction between the neighboring unit cells in which plasmonic resonances at the fundamental frequency (FF) and SH frequency are tuned easily by adjusting the antenna length (L) and the bending angle (θ). The MQW region without the top Au nanoantenna was etched, which induces the enhanced Ez field mode following the top nanoantenna shape for an input pump beam 44 and, simultaneously, uniform vertical current injection from the external bias voltage. The meta-atom structure was designed to induce the enhanced local Ez field in the MQW layer at the FF ω ( Fig. 3b) and the SH frequency 2ω (Fig. 3c) for x-and y-polarized input beams, respectively. The electrically tunable effective nonlinear susceptibility out of the metasurface can be expressed as 35 : For nonlinear optical characterization, a wavelength tunable quantum cascade laser and a calibrated InSb photodetector were used. The optical setup used for the SHG signal measurement is shown in Fig. 5a. By applying bias voltages from -4 V to +4 V with 2 V step, SHG output spectra for the three metasurfaces were measured, with the results shown in Fig. 5b. Each SHG spectrum was normalized to its maximum SHG output signal. Experimentally, broadband SHG spectral peak tuning for the 10.75 -8.7 μm input pump wavelength range (930 to 1150 cm -1 in wavenumber) was achieved. As the bias voltage was changed from -4 V to +4 V, the SHG spectral peak for the M1 and M2 metasurfaces was blue-shifted, which is consistent with the tendency of the according to the bias voltage (cf. Fig. 2b). For the M3 metasurface by changing the bias voltage from +4V to -4V, relatively broad SHG output spectrum was observed owing to the simultaneous effects of the 1-3 and 2-4 level ISTs, with the peak narrowing gradually and blue-shifted because of the growing dominance of the coupling with 2-4 level ISTs, resulting ultimately in the formation of the SHG spectral peak at a pump wavelength of 8.7 μm at -4 V. The electrically tunable SHG output spectra were simulated for the -2V shifted bias voltage ranging from -6 V to +2 V, as shown in Supplementary Fig. 10, and exhibited close agreement with the experimental spectra. The simulation result for M1 meta-atom array shows broader SHG spectral tuning than the measurement because the simulation assumed a uniform conduction band bending over the depth of the 400-nm-thick MQW layer. However, due to the formation of the Schottky contacts in the fabricated metasurface, major band bending occurs near the top MQW surface for a negative bias and near the bottom MQW surface for a positive bias. In this configuration, the modal overlap factor for the SHG is induced strongly near the top MQW surface, resulting in dominant SHG spectral tuning for negative biases (see Supplementary Fig. 11). We note that when ohmic contacts are formed at both sides of the MQW layer, even broader SHG spectral tuning can be achieved with a single meta-atom array. The measured SH peak power as a function of squared input peak power and squared input peak intensity for the three metasurfaces at their optimal operating pump  Supplementary Fig. 9 with accompanying discussion).

Discussion
In summary, we proposed and experimentally demonstrated electrically tunable nonlinear metasurfaces for broadband efficient SHG and a strong SH signal modulation based on the Stark tuning of intersubband nonlinearity. The energy levels of the electron subbands in the coupled three quantum well structure are modulated by the QCSE according to the bias voltage, leading to a broadband and giant 2 nd order nonlinear response in the 8-11 μm wavelength range. Our approach can be extended to other nonlinear optical processes, such as sum-and difference-frequency generation and THG, and can also be applied to near-IR 47 13 13 241meV 14 14 340 meV   Finally, the sample was mounted on a Cu plate using an Ag paste. The device fabrication process is illustrated in Supplementary Fig. 3.  For positive and negative DC bias voltages applied to the device, the maximum SHG occurs at higher and lower pump frequencies (ω1 > ω2 > ω3), respectively. When a voltage pulse is applied to the device, strong SHG signal modulation is induced at a fix pump frequency.