**1. Introduction**

Recent technological advances have allowed reducing the size of semiconductor photonic devices to the sub-micrometer scale, with a remarkable impact in several research domains like integrated optofluidics [1] and nonlinear photonics [2]. Because of the high-refractive-index contrast and subwavelength size, the normal field component can be very strong at the semiconductor–air interface. This makes nanophotonic devices very sensitive to the complex refractive index of the surrounding medium and thus promising candidates for chemical or biological sensing in liquid or gaseous environments with lab-on-chip integrated photonic sensors [3]. This is all the more true for resonators and waveguides operating in the mid-infrared, where many absorption resonances of important analytes occur [4]. For these reasons, suspended silicon structures operating in the linear regime have been recently proposed as an alternative to their silicon-on-insulator counterparts [5,6], where the SiO2 substrate exhibits nonnegligible losses around 2.8 μm and beyond 4 μm, while the transparency of silicon itself ends beyond 8.5 μm [7]. A further asset of nanoscale high-contrast photonics in respect to μm-sized devices is the combination of strong nonlinear light–matter interaction with higher flexibility in dispersion and mode coupling engineering [8].

In this context, AlxGa1-xAs is an attractive material for its high second-and third-order nonlinear coefficients (d14 <sup>≈</sup> 100 pm·V−<sup>1</sup> [9], n2 <sup>≈</sup> 10−<sup>17</sup> m2·W−<sup>1</sup> [10]), well-established processing technology, direct bandgap (for x < 0.45) that increases with Al molar fraction x and its broad transparency spectral region ranging from near- to mid-IR. The exploitation of AlGaAs nonlinearity for frequency mixing was once challenging because of its optical isotropy, which hinders birefringent phase-matching (PM), and its optical losses associated with the implementation of quasi-PM in the near-IR. In the last two decades, however, efficient guided-wave frequency mixing has been reported, based on form birefringence [11,12], modal PM [13] and counterpropagating PM [14]. In each of those cases, the nonlinear waveguides relied on total internal reflection between an aluminum-poor AlGaAs core and aluminum-rich claddings with a relatively low refractive-index step (Δn ≈ 0.2), which was also the case for the demonstration of χ(3) guided-wave devices [15].

In the last years, high-contrast AlGaAs nonlinear photonic structures have been reported at the nanoscale level, based on either selective oxidation of an AlAs substrate [16,17] or epitaxial liftoff followed by bonding on glass [18], for both second-harmonic generation (SHG) [16–18] and spontaneous parametric down-conversion (SPDC) [19]. Their higher refractive-index step (Δn ≈ 1.5) made them suitable for shallow etching fabrication, with a huge impact on integration up until the demonstration of the first χ(2) metasurfaces [20,21]. Similar AlGaAs-on-oxide structures have also been demonstrated for waveguides and microresonators fabricated by wafer bonding, both in χ(3) [22] and χ(2) devices [23,24]. However, the potential of AlGaAs-on-oxide guided-wave devices is still affected by either the intrinsic limits of wafer bonding technology in terms of homogeneity and throughput or by the intrinsic scattering loss of devices based on native AlAs oxide [25,26].

Within this context, an alternative approach to high-contrast AlGaAs photonics was pioneered more than a decade ago with substrate-removed electrooptic modulators [27,28]; then, suspended microdisk resonators were used both in optomechanics [29] and nonlinear optics [30–32]. Finally, suspended nonlinear nanowires [33] and nanorib waveguides [34] have been reported, and a suspended nonlinear photonic integrated circuit has been demonstrated for both SHG and SPDC in a microdisk coupled with two distinct waveguides at ω and 2ω [35].

Both nanowire and nanorib waveguides naturally lend themselves to mode birefringence phase-matching with a few advantages over multilayered form birefringent waveguides: (a) the attainable modal birefringence is sufficient to compensate dispersion in the whole AlGaAs transparency range, even close to the gap; (b) the modal areas of the fields are extremely small and tightly confined within the GaAs core, resulting in high conversion efficiency; and (c) the absence of aluminum oxide layers and the smoothness of top and bottom surfaces, which is defined by epitaxial growth, result in low scattering losses.

Here we compare the experimental performances and drawbacks of two different designs for AlGaAs suspended nonlinear waveguides (Figure 1): (a) a nanowire that recently allowed the demonstration of phase-matched SHG in both straight and snake-shaped configurations [33] and (b) a nanorib waveguide developed for frequency down-conversion towards the mid-IR range [34].

**Figure 1.** Suspended waveguide schemes: (**a**) nanowire anchored by tethers; (**b**) nanorib bounded by etch windows. Tethers and windows have no impact on optical propagation.
