J. Eur. Opt. Society-Rapid Publ. 21, 23( 2025) 229
estimate the spectral dependence of the frequency doubling process. Thiscanbedoneifwecalculatethechromatic dependence of the total accumulated phase between the interacting modes TE 00 and TM 00, all along the propagation trajectory. The resulting expression for the SHG efficiency of equation( 1) now takes the form j = j(/( Dm, k)). Notably, the dependence of the accumulated phase /( Dm, k) on Dm and k differs between the straight and the curved sections, given that Dm has a strict waveguide width dependence( namely, Dm = Dm( w)). In what follows we compute the spectral dependence of the U-shaped design, phasematched in both the straight and curved section.
The results of these calculations, reported in Figures 4e and 4f, are again performed under the undepleted-pump approximation. In Figure 4e, we report the 3D color map of the total intensity I SHG converted around the SH vs the propagation length x and the wavelength k, normalized to the driving field intensity I 0. The spectrum of I SHG( x, k) is clearly peaked at the SH wavelength k 0 / 2, for which the constructive power build-up is guaranteed by the design, all along the U-shaped waveguide. On the contrary, we have not expressly optimized the conversion for the adjacent wavelengths, since it could possibly attenuate the conversion at k 0 / 2. The resulting SH narrow-band power buildup exhibits an unclear behavior which is not necessarily constructive in the whole spectral domain and along the whole waveguide length. Moreover, a spectral asymmetry is evident with respect to the typical sinc 2 shape [ 61 ]. This is even more evident in the plot of the final I SHG in Figure 4f. Here the sinc 2 symmetry breaking is due to the fact that, to preserve a constructive power build-up at k 0 / 2, we change the waveguide width w 0? w 1 while switching from the straight to the curved section. This responds to the quest of fulfilling both the MPM and 4-QPM conditions, respectively. While doing that, we span Dm over the narrow-band SHG spectrum, spanning also over different partially constructive interference conditions. As a result, the symmetry of the sinc 2 SH generated intensity, resulting from a straight propagation through a v( 2) phase-matched waveguide, is broken in a U-shaped geometry where PM is granted all along the waveguide at k 0 / 2.
In perspective, it is interesting to note how a wrapped snaking waveguide, composed by different U-shaped sections optimized for different SHG wavelengths, could be designed to optimize a broad-band or comb-like SHG spectrum.
5 Fabrication process
The technology we have developed to fabricate AlGaAs-OI waveguides [ 62 ] is based on adhesive bonding [ 17, 63 ] between a GaAs substrate, with the desired epitaxy of AlGaAs on top, and a thermally oxidized Si carrier wafer( see Figs. 5a – 5d, for the entire process).
In Figure 5a, we schematize the bonding process. The AlGaAs epitaxy is grown by molecular beam epitaxy( MBE) on a( 100) GaAs substrate and it consists of two layers: an active Al 0. 18 Ga 0. 82 As membrane( 400 or 110 nm, depending on the design) and a sacrificial
Al 0. 8 Ga 0. 2 As etch-stop layer. A SiO 2 layer is then deposited on the AlGaAs wafer to improve adhesion in the following bonding process. A thin benzocyclobutene( BCB) layer is spin coated on the thermal SiO 2( 2 lm) of the Si carrier, and then the AlGaAs wafer is back-flipped on it. The bonding is carried out by applying pressure and heat.
The 350 lm-thick GaAs substrate is removed in two steps using a citric acid / hydrogen peroxide solution( volume ratio 5:1): the first one at 60 ° C to rapidly remove most of the substrate, the second one at 20 ° C to remove the last 50 lm at a slower etch rate to minimize the tolerances due to the etching process. The sample is then rinsed in deionized water and quickly cleaned with HCl [ 22 ]. The etch-stop layer is removed using a buffered oxide solution( BOE 7:1). The result of this process is sketched on Figure 5b.
After the substrate removal, a thin SiO 2 protective layer is deposited on the Al 0. 18 Ga 0. 18 As membrane. The e-beam lithography( EBL) is carried out using hydrogen silsesquioxane( HSQ) resist( Fig. 5c). Finally, the patterns are transferred to the semiconductor membrane by ICP-RIE using aSiCl 4 / Ar gas mixture( Fig. 5d).
With this process we fabricated optical waveguides and ring resonators( Figs. 5e and 5f). In Figure 5e, we show a set of micro-rings with a radius R = 50lm with bus waveguides wrapping around to optimize the evanescent coupling. In Figure 5f, we show four scanning electron microscope( SEM) pictures: two narrow coupled waveguides( top left), PhC waveguides for dispersion management [ 40 ]( top right), a waveguide facet( bottom left) and sub-wavelength( SW) grating couplers [ 64 ]( bottom right).
5.1 Experimental characterization
The nonlinear characterization of the structures described in this paper is currently in progress and it will be the object of future work. In Figures 5g and 5h we report a preliminary linear characterization of a ring resonator. The particular bell shape of the transmission spectrum( Fig. 5g) is due to SW grating couplers used to inject and to extract light into / from the chip. We notice a good extinction ratio, which indicates the vicinity to the critical coupling condition. We estimated quality factors of around 10 5. We measured a group index( Fig. 5h) consistent with the designed dispersion profile. The associated group velocity dispersion b 2 �2.5 ps 2 / m around the pump wavelength confirms the prescribed anomalous dispersion regime, suitable for solitons generation.
6 Conclusion and perspectives
While OFCs are deeply studied in either purely quadratic [ 1 – 3, 32 ] orKerr [ 4, 5, 7, 17, 18, 50, 53 ] systems, only recently mixed v( 2) + v( 3) nonlinear passive resonators have been conceptualized and demonstrated [ 10 – 12, 30, 37, 38 ], thanks to key technological advances leading to the possibility of efficient nonlinear micro-photonics integration [ 55, 65 ]. In this work, we have proposed and discussed the perspective impact of AlGaAs for v( 2) + v( 3) nonlinear