Controlling second-harmonic generation at the nanoscale with monolithic AlGaAs-on-AlOx antennas

We review recent achievements in the field of nanoscale nonlinear AlGaAs photonics based on all-dielectric optical antennas. After discussing the motivation and main technological challenges for the development of an AlGaAs monolithic platform for χ(2) nonlinear nanophotonics, we present numerical and experimental investigations of the second-order nonlinear response and physical reasons for high efficiency of second-order nonlinear interactions in the AlGaAs nano-antennas. In particular, we emphasize the role of the dipolar resonances at the fundamental frequency and the multipolar resonances at the second harmonic wavelength. We also discuss second-harmonic generation directionality and show possible strategies to engineer the radiation pattern of nonlinear antennas.


Introduction
In recent years, light manipulation by means of nanoscale structures has attracted enormous interest due to its impact on modern photonic technologies [1][2][3][4][5][6]. Not only might nanoscale objects facilitate integration of various linear and nonlinear functionalities in nanophotonic circuits, but they also tremendously improve miniaturization allowing one to replace bulky components, which typically rely on free-space optics. The opportunity of fabricating ultrathin devices compatible with planar manufacturing technology enhances this drive. Many devices and functionalities have been demonstrated through the exploitation of metallic and/or dielectric nanoparticles for different applications. Those based on metallic nanostructures exhibiting plasmonic resonances have already had a significant impact in diverse application areas such as sensing, nanomedicine, telecommunications, quantum optics, and photovoltaics [7][8][9][10][11][12][13]. However, plasmonic nanostructures have an inherent weakness related to the Ohmic losses at optical frequencies, which limit their usefulness in certain applications. For example, the losses generate Joule heating that could hamper the use of plasmonics in some applications such as sensing where a temperature increase, if not mitigated, could alter or even damage the properties of a monitored analyte [14][15][16]. In dielectric materials, this problem is less severe given their relatively smaller optical losses in the visible and near-infrared wavelength range.
At the same time, nanostructures made of dielectrics with a relatively high refractive index are capable of tight light confinement [17][18][19][20]. For these reasons, metal-less nanophotonics employing high-refractive index dielectrics and semiconductors, such as silicon, germanium, tellurium, gallium arsenide, aluminium gallium arsenide, gallium phosphide, are now emerging as a promising alternative to plasmonic nanostructures for nanophotonic applications [21].
In particular, significant progress has been achieved with high permittivity dielectric nanoparticles in a low refractive index background, which exhibit negligible dissipative losses and strong Mie resonances in the visible and near-infrared spectral ranges. These new systems may be employed in many applications such as directional scattering and emission, surface enhanced vibrational spectroscopy, and flat metasurfaces for phase-front engineering. Depending on a particular application, one of the two approaches-metal or metal-less nanophotonics-may have beneficial properties [22][23][24][25][26][27][28][29]. For example, in metallic nanoparticles the electric field is strongly confined close to the metal surface, enhancing light-matter interaction close to the surface, whereas in dielectric nanoparticles the electric field of the resonant modes penetrates deep inside their volume, enhancing light-matter interaction with the bulk of a nanoparticle [30][31][32][33][34][35][36][37][38][39][40]. This encourages the use of all-dielectric nanoantennas for strengthening the nonlinear optical response from the nanoparticles and some promising results have already been achieved in the framework of semiconductor nanoparticles.
Semiconductors exhibit quite strong second-and/or third-order nonlinear optical susceptibilities compared to other materials such as insulators (e.g., SiO 2 , TiO 2 ); however, typical values of the nonlinear susceptibility are small, requiring light fields comparable to the characteristic atomic field strength, and high pump intensities are often needed to obtain nonlinear signals that might be of practical use in applications. Since the power of the nonlinearly generated second (third) harmonic frequency scales with the fourth (sixth) power of the fundamental field strength, the possibility to confine the electromagnetic energy into tiny volumes in nanoparticles is very important to enable the downscaling of the required optical powers [23]. Using a silicon platform, third-harmonic generation (THG) in silicon-on-insulator (SOI) nanoantennas has been recently investigated. In the pioneering works [41,42], it was experimentally confirmed that a strong enhancement of THG (up to 100 over the case of a silicon slab) can be achieved in isolated silicon nanodisks by optically exciting at frequencies near the magnetic dipolar resonance. Another experimental demonstration showed an increase of two-photon absorption (TPA) by almost two orders of magnitude in hydrogenated amorphous silicon nanodisks with respect to an unstructured silicon film [31], allowing one to achieve strong self-modulation of femtosecond pulses, resulting in an important step towards active photonic devices [43]. Although these outcomes clearly illustrate the potential of all-dielectric nanoparticles for nonlinear nanophotonic applications, they are limited by the inherent constraints of the SOI platform in which they have been obtained.
Despite the spectacular achievements of silicon technology, only χ (3) effects have been observed since, because of its centrosymmetric crystal structure, silicon does not exhibit bulk quadratic optical nonlinearity. In order to overcome this limitation, non-centrosymmetric materials have recently been studied such as AlGaAs alloys. Al x Ga 1-x As is a popular III-V material for integrated nonlinear optics [44,45] because it combines some properties that it shares with Si (a similar refractive index in the near infrared, a comparatively high χ (3) nonlinear index, and a good thermal conductivity) with additional key advantages including (1) a direct band gap for Al molar fraction below 0.45 that increases with the Al content enabling TPA-free operation at 1.55 μm [46], (2) a high non-resonant second-order susceptibility (d 14 ≈100 pm V −1 for GaAs in the near infrared), and (3) a broad spectral window of transparency in the mid-infrared (up to 17 μm). In this context, the hybridization of AlGaAs with SOI and AlGaAs-based monolithic platforms have a significant potential for χ (2) nonlinear nanophotonics.
Here we overview the recent results obtained in the field of second-order nonlinear effects in AlGaAs nanoantennas. The paper is organized as follows. Section 2 presents the fabrication of AlGaAs nanoparticle-based monolithic platform for χ (2) nonlinear nanophotonics. In section 3, the linear optical properties of these nanoparticles are described which can be considered as nanoscale resonators. Obviously, efficiencies of nonlinear processes are significantly increased through the enhancement of local fields at the resonances, allowing for nonlinear optical components to be scaled down in size and offering exclusive prospects for all-optical light control at the nanoscale. In section 4, we compare the theoretical predictions with recently obtained experimental results, particularly emphasizing the role played by the dipolar resonances at the fundamental frequency and the multipolar resonances at the second harmonic frequency. In section 5, we then discuss directionality issues and show some possible strategies to engineer the radiation pattern of nonlinear nano-antennas, using the properties of the fundamental frequency field (i.e. polarization state and propagation direction) as tuning parameters. In section 6, we discuss a more general framework which includes sum and difference frequency generation and optical parametric amplification. Finally, an outlook for this young and active research field of second-order nonlinear photonics in dielectric nanoantennas is given.

Fabrication and technological challenges
The basic requirement for fabricating AlGaAs monolithic nanoantennas is that they are surrounded by a low refractiveindex medium compatible with nanophotonic technology. Two options are available: air (refractive index n=1) or aluminum oxide (n≈1.6). In the former case, the nanoantenna can be more efficiently decoupled from the underlying GaAs wafer, but it has to be suspended with photonic-crystallike fabrication techniques. In the latter case, one can use the wet oxidation of an underlying AlAs layer [33], resulting in a better thermal dissipation, at the price of a slightly smaller optical confinement due to the lower index contrast between the nanostructure (n≈3.2 for Al 0.18 Ga 0.82 As in the near IR) and its environment. A few hybrid schemes are also possible, based on the transfer of epitaxial AlGaAs on silica [47] or benzocyclobutane (BCB) [48], or on the CMOS-compatible wafer bonding of an AlGaAs heterostructure on silicon oxide [49]. However, they fall out of the scope of this review, which focuses on monolithic devices that lend themselves to the perspective of full optoelectronic integration with optical sources and detectors. Finally, because of its relative simplicity, the AlGaAs-on-oxide is the only monolithic nanoantenna with second-order nolinearity demonstrated to date [33,34].
Until recently, a development of an AlGaAs photonic platform was hindered by the difficulty of fabricating monolithic shallow waveguides and cavities as in the silicon-oninsulator (SOI) system, and in particular by the shortcomings of the wet selective oxidation of AlGaAs epitaxial layers. The latter was discovered in 1990 and results in a non-stoichiometric alumina (AlO x , also called AlOx) with optical and electrical properties similar to SiO 2 [45]. The use of AlOx layers thinner than 100 nm is standard in VCSEL technology [50] and has also results in the demonstration of an optical parametric oscillator in an AlGaAs waveguide [51]. However, the fabrication of high-quality μm-thick AlOx optical substrates is critical because the selective oxidation of AlGaAs optical substrates induces a strong contraction of the oxide. This typically results in important optical losses in integrated photonic devices, due to defects at the interface between AlOx and the adjacent crystal [52].
Nanoantennas are typically grown by molecular-beam-epitaxy on [100] non-intentionally doped GaAs wafer, with a 400 nm layer of Al 0.18 Ga 0.82 As on top of an aluminum-rich substrate, to be oxidized at a later stage. In order to improve the eventual optical quality of the interface between AlOx and the adjacent crystalline layers, such substrate consists of 1 μm-thick Al 0.98 Ga 0.02 As layer sandwiched between two transition regions with varying aluminum molar fraction. In order to obtain an array of nanocylinders shown in figure 1(a), circles were patterned using scanning electron microscope lithography, with radii between 175 nm and 225 nm equally spaced by 3 μm. Then the samples were dry-etched with non-selective ICP-RIE with SiCl 4 :Ar chemical treatment. The etching depth of 400 nm, controlled by laser interferometer, defined the nanocylinders and revealed the AlAs layer. The etched sample was then oxidized at 390°C for 30 min in an oven equipped with in situ optical monitoring, under a precisely controlled water vapor flow with a N 2 :H 2 gas carrier. After oxidation, each Al 0.18 Ga 0.82 As nanocylinder lies upon a uniform AlOx substrate (figure 1(b)), whose low refractive index enables sub-wavelength optical confinement in the nanocavity by total internal reflection. As expected from the strong selectivity of oxidation kinetics relative to aluminum molar fraction, no post-oxidation cross-section reduction has been observed by transmission electron microscopy on a thin slice of Al 0.18 Ga 0.82 As nanopillars. Note also that Al 0.18 Ga 0.82 As oxidation is negligible under these experimental conditions. While initially the fabrication conditions with temperature cases below 400°C and Al content 0.45 have never been considered, our approach shows an extremely shallow surface oxidation which may provide an upper limit to the optical quality of very-high-Q (10 5 ) microcavities; however, its impact here is negligible because the Q-factor of our subwavelength nanoantennas is considerably smaller.
From figure 2, which summarizes the above fabrication steps, it is apparent that deep etching into the Al 0.98 Ga 0.02 As layer (step c) is possible to increase the lateral confinement of the nanoantenna optical modes. While this is indeed the  approach reported in [34], for nonlinear optical applications we find it more appropriate to let the crystalline nanocylinders to sit on a uniform AlOx layer, which is a better heat sink than a nanoscopic AlOx pedestal.

Linear properties of the nanoantennas for SHG enhancement
The design of antennas for enhancing the second-order nonlinear optical response requires information on their basic properties such as resonant frequencies, bandwidth, field distribution and radiation diagrams at fundamental and second harmonic (SH) frequencies. Different strategies can be employed to model such nanoantennas. Once the optical response of a nanoparticle is calculated numerically, a very powerful approach to interpret the linear and nonlinear scattering resorts to multipole decomposition [53]. Adjusting phase and amplitude of the different multipole contributions provides a robust tool to engineer the radiation patterns at the desired operating frequencies.
The scattering spectra of Al 0.18 Ga 0.82 As cylinders at near-IR wavelengths were simulated using finite element method simulations in COMSOL [32]. The pump can be chosen as a plane wave or a light field with a more complex structure ( figure 3). Let us first recall what has been reported using either plane waves or focused Gaussian beams, with propagation along the cylinder axis (z) and the electric field, E, along the x axis.
To account for wavelength dependence of the refractive index of Al 0.18 Ga 0.82 As, the analytical model proposed in [54] can be used, which was derived from comparison with experimental measurements. We define the extinction as Q e =Q s +Q a , where Q s =C/πr 2 and Q a =A/πr 2 are the scattering and absorption, respectively, with C being the scattering cross-section, A being the absorption crosssection, and r being the cylinder radius. A plot of Q e in the near-infrared spectral region calculated for a cylinder with radius r=187 nm and height h=400 nm on a substrate with a refractive index of 1.6 is presented in figure 4(a). We can observe two resonant peaks for wavelengths shorter than 1500 nm while, for longer wavelengths, the scattering efficiency monotonically decreases. In particular, the sharpest and strongest resonance observed at λ=1475 nm is mainly due to a MD resonance, as already discussed in the literature [55][56][57]. The broader resonance at λ=1200 nm has electric dipole character. To understand the SHG properties of such nanopillars for a fundamental frequency (FF) in the spectral range indicated in figure 4(a), we calculated the scattering efficiency at the corresponding SH wavelengths shown in figure 4(b). Since, in this spectral region the antenna has a multipolar response, it has been calculated using exciting dipoles at different random positions that allow exciting all dark and bright modes [29]. By comparing figures 4(a) and (b), we can see that, as expected, in the longer wavelength range, where the FF frequency sits, the scattering is dominated by lower-order multipoles, while in the SH frequency range a multitude of scattering contributions due to higher-order multipoles are responsible for the observed features. It is also important to stress the presence of the long absorption tail below approximately 725 nm, which determines the minimum possible wavelength at which SHG can be highly enhanced via the bulk χ (2) of Al 0.18 Ga 0.82 As.

SHG from AlGaAs nanoantennas: efficiency considerations
SHG from AlGaAs nanoantennas has been recently investigated in [32-34, 48, 58]. In striking contrast with typical plasmonic materials, since AlGaAs is a non-centrosymmetric material, there is a strong volume contribution to the overall efficiency of the SHG process. Moreover, the only non-zero element of the second-order nonlinear susceptibility ( ) c 2 ijk of Al 0.18 Ga 0.82 As has i ≠ j ≠ k, with d 14 =χ (2) / 2≈100 pm V −1 [59].
In order to quantify the potential of AlGaAs nanocylinders for nonlinear nanophotonics, one can model the SHG phenomenon with COMSOL by using the nonlinear polarization induced by χ (2) as a source in the simulations, and then define the SHG efficiency as: where  S SH is the Poynting vector of the SH field,n is the unit vector normal to a surface A enclosing the antenna, and I 0 is the incident field intensity (I 0 =1 GW cm −2 in the simulations). The calculated SHG efficiency for a cylinder with r=187 nm and h=400 nm on a substrate of n=1.6 is shown in figure 5(a). As can be seen in the figure, there are three different SHG peaks. The corresponding fundamental frequencies fall inside the broad MD resonance peak and, thus, the associated field enhancement improves the efficiency of the nonlinear process. Inside this broadband resonance, the frequency selection rules for the maximum SH signal are determined by the resonances of the nanoantennas at shorter wavelengths; in figure 5(a) one can recognize that the three maxima in the SHG process correspond to three peaks of the scattering efficiency in figure 4(b). This behavior, neglecting possible absorption at the SH or the FF, can be intuitively explained by evaluating parameter υ=(Q FF ) 2 ×Q SH ×ζ, where Q FF and Q SH are the absorption and scattering efficiencies of the fundamental and second-harmonic modes, respectively, and ζ is the spatial overlap between the pump and the harmonic modes [32,40]. Thus, the conversion efficiency is expected to increase as Q FF 2 because the intensity of the SH signal scales as the square of the intensity. From these observations, it is straightforward to understand that in order  to maximize η SHG , the cylinder geometry should, from one side, guarantee a fair tradeoff between the need of a high Q FF and a high Q SH to maximize the product (Q FF ) 2 ×Q SH and, from the other side, support a mode at the SH wavelength with a good spatial overlap ζ with the pump mode [36,40].
The SHG efficiency measured from the AlGaAs-on-AlOx nanoantennas for the fundamental wavelength of 1550 nm [33] is shown in figure 5(b). The background SHG from the AlO x substrate is about three orders of magnitude below the SHG signal from the nanoantenna and was subtracted in the plot. Three well-defined features can be clearly identified in the emission behavior at approximately 195 nm, 205 nm and 220 nm. The calculated and measured radiusdependent behavior of the conversion efficiency reported in figure 5(b) singles out three resonances of the SHG nanocavity modes excited at three specific radii with a maximum for r=187 nm. The agreement between numerical and experimental values confirms that a model resorting only to bulk nonlinear coefficients captures the main physics of the SHG process. The experimental data display an overall SHG collected signal proportional to the square of the pump intensity [33], which confirms the second-order origin of this process; the fact that the SHG spectral bandwidth is √2 times narrower than the excitation laser line (about 15 nm) confirms that this signal stems solely from a coherent two-photon process.
The SHG spectra measured from the AlGaAs-on-AlOx nanoantennas of a radius of 225 nm is shown in figures 5(c), (d). (For these measurements, the experimental setup shown in figure 6(a) was used). Two resonances can be observed in the SHG spectral range at the fundamental wavelengths of approximately 1530 nm and 1670 nm for both co-polarized and cross-polarized configurations. Considering that in the experiment the pump wavelength was tuned with a step of 20 nm, a very good agreement with the modelling predictions can be inferred with slightly larger discrepancies for the crosspolarised geometry. In particular, figure 5(d) shows that both simulations and experiments exhibit two SHG peaks; however, the relative amplitude of these peaks is not well reproduced by numerical data. This may be due to fabrication imperfections, which may affect the SHG efficiency. As a matter of fact, from the high-resolution transmission electron microscopy images, we can identify the presence of a random tilt (up to 10 degrees) in some nanopillars with respect to the axis normal to the surface, causing a local re-orientation of the susceptibility tensor at the individual nanoantenna level. This can be attributed to an asymmetric sinking of the nanopillars due to the substrate softening during the annealing step rather than to nanofabrication inaccuracies. The detailed investigation of this phenomenon, however, goes beyond the scope of this paper.
Both experimental data and simulations in figures 5(b)-(d) show that the first two peaks, corresponding to smaller disk radii or longer wavelengths, have far-field SHG mainly co-polarized with the pump beam, while the peak excited at lower wavelengths (or for bigger disk radii if working at a fixed wavelength) has a far-field SHG mainly cross-polarized with respect to the pump beam. The polarization properties of the generated SH signal is however very rich and deserve further investigations [48].

SHG from AlGaAs nanoantennas: radiation pattern
A typical radiation pattern at the second harmonic frequency (inset in figure 5(a)) illustrates the multipolar character of the SH source as well as the absence of SHG radiation along the axis of the cylinder. This is due to the symmetry of the structure and the symmetry of the χ (2) tensor in zinc-blende crystals [60]. This is confirmed by investigating SHG from the individual AlGaAs antennas using a confocal microscope in reflection geometry as shown in figure 6(a). The light from an optical parametric amplifier (OPA) pumped with an amplified ytterbium-doped potassium gadolinium tungstate (Yb:KGW) laser was used as a fundamental light in the SHG measurements. The fundamental light was tuned to 1064 nm and had a pulse duration of about 150 fs and a repetition rate of 40 kHz, resulting in a constant average power of approximately 250 μW at the sample. The set of polarisers was used to control polarization of the fundamental light. Figure 6(b) shows a microscope image of the SHG radiated from a nanoantenna of radius 180 nm and height 400 nm excited with polarization along the x-axis and at a fundamental wavelength of 1064 nm. The antenna generates a bright green SHG signal. The substrate, instead, contributes with a photoluminescence (PL) signal centred at around 733 nm from the area illuminated by the excitation spot due to two-photon absorption in AlAs located beneath the AlO x layer [61]. The radiation diagram clearly shows two lobes in the 60°light-cone accessible with the objective of 0.85 NA in a x-z plane above the antenna, as predicted by simulations [58]. An online supplementary movie from which a z-scan in figure 6 was plotted is also included, showing only PL or both SHG and PL radiation, depending on collection objective focus.
In many cases, the absence of the SH radiation in the direction of the nanoantenna axis is a drawback caused by the symmetry of the system. An effective strategy to overcome this is to break the symmetry using excitation at oblique incidence. Figure 7(a) shows the radiation pattern of the SH signal generated with an s-polarized pump at λ=1445 nm from a cylinder with r=187 nm and h=400 nm for different angles of incidence of the fundamental beam. To understand the observed behavior, in figure 7(b) we show the scattering cross-section of this nanoantenna as well as the main multipolar contributions to the scattering process as a function of the pump wavelength. We can see that the antenna exhibits a strong SHG resonance of dominant magnetic and electric dipolar nature. The SHG efficiency and multipolar components of the total radiated SH field as a function of the incidence angle of the pump is shown in figure 7(c). With increasing incidence angle, the electric and magnetic dipolar contributions in the intensity of the SH scattering increase monotonically, leading to a radiation pattern that has a maximum along the cylinder axis. As the angle of incidence increases, the intensity of the SH light emitted in the normal direction increases, reaching a maximum at θ=45°, while the lobes in the other directions are progressively suppressed.
A similar behaviour is observed for the cross-polarized second harmonic generation process with the maximum efficiency for r=225 nm at a fundamental wavelength of around 1500 nm ( figure 5(b)). In figure 8, the fundamental wavelength is set to λ=1570 nm and the incidence angle is varied from 0 to 45°. The intensity of the SH light emitted in the normal direction increases with the incidence angle, reaching a maximum at θ=45°, while the lobes in the other directions are suppressed. The reason for this behavior is that, by changing the incidence angle, the dipolar contribution in the SH scattering increases monotonically (lower panel in figure 8) in the same way as it was observed in figure 7(b) for the co-polarized SH peaks.
Figures 7 and 8 demonstrate that it is indeed possible to achieve directional SH emission using AlGaAs nanoantennas which might be very helpful for the design of nonlinear emitters [58].

Outlook and perspectives
The results that we reported here show the huge potential of the AlGaAs monolithic platform for nonlinear nanophotonics. To date, it is demonstrations focused on SHG enhancement in nanocylinders. However, they pave the way for other interesting second-order optical phenomena in nanostructures, such as sum-and difference-frequency generation. The former process (SFG) might also be used for classical-quantum correspondence experiments [62], while the latter (DFG) might prove useful for nanoscale optical parametric amplification [63]. This new monolitic platform provides innovative means for the design of on-chip tunable light sources, which are essential in many fields of modern photonics. Moving beyond the realm of nonlinear applications, AlGaAs might be a very promising material system for new metal-less metasurfaces. Indeed, absorption in plasmonic metasurfaces limits their performances in the near IR, and there is currently important research activity for finding new materials that might replace popular metals such as Au and Ag [64,65]. Moreover, as discussed in section 2, AlGaAs can bring several advantages over Si for the future nanophotonic platforms. This, in conjunction with tailored fabrication processes, will allow for the realization of three-dimensional structures using only planar lithography and etching procedures. This possibility increases the degrees of freedom in engineering AlGaAs-based metasurfaces beyond what is currently possible with the SOI platform.

Conclusions
We have overviewed recent results in the field of secondorder nonlinear optics at the nanoscale facilitated with alldielectric optical antennas. We have first presented the technological challenges and the proposed solutions for an AlGaAs-based monolithic platform for χ (2) nonlinear nanophotonics. Then we have discussed the linear properties of all-dielectric nanoscale resonators, since efficiencies of nonlinear processes are significantly increased through the enhancement of the local fields due to the nanoparticle resonances. Having assessed the material platform, we have then reviewed the main reasons why these dielectric nano-objects offer such a high efficiency of χ (2) effects, supporting the theoretical predictions with experimental results. In particular, we emphasized the role played by dipolar resonances at the fundamental frequency and multipolar resonances at the second harmonic wavelength. We have also discussed SHG directionality and shown some possible strategies to engineer the radiation pattern of nonlinear antennas, using as a tuning parameter the properties of the fundamental field, such as polarization state and/or propagation direction. Finally, we have shown theoretically that symmetry breaking with oblique excitation can steer the SH radiation main lobe in different directions, including along the nanoantenna axis. We thank Professor Dragomir Neshev for the useful discussions.