Intramodal stimulated Brillouin scattering in suspended AlN waveguides

2.1 Design of SBS in AlN waveguide

Figure 1(a) shows the schematic diagram of the designed suspended AlN waveguide. A 400-nm c-axis–oriented AlN thin film on silicon wafer is etched by 260 nm depth to define ridge waveguides. The waveguides are enclosed by rectangular slots, forming a suspended structure that isolates the waveguides from the silicon substrate. The incident optical waves including the modulated pump waves ω _p ± Ω/2 and probe wave ω _pr spatially overlap and induce a modulation of the material density via electrostriction and radiation pressure, thereby generating optically excited acoustic waves. The acoustic waves periodically modulate the permittivity of the medium, inducing a moving refractive index grating that scatters the incident probe wave into Stokes and anti-Stokes sidebands ω _pr ± Ω with a Brillouin frequency shift of Ω [35]. The interaction between the optical waves and the acoustic wave establishes a feedback loop that leads to exponential amplification of the scattered light. The dispersion curve of the optical mode TE₀₀ and the phase matching condition are shown in Figure 1(b). This work focuses on intramodal forward stimulated Brillouin scattering (FSBS), in which copropagating probe wave ω _pr and Stokes wave ω _pr − Ω are guided within the same spatial mode and interact via an optically induced acoustic wave at frequency Ω. The phase-matching condition requires that k(ω _pr) = k (ω _pr−Ω) + q(Ω), where k(ω _pr) is the optical wavevector at optical frequency ω _pr, and q(Ω) is the acoustic wavevector at frequency Ω [36]. In this scenario, the same acoustic mode is simultaneously phase-matched to both Stokes and anti-Stokes scattering processes, which reveals that Stokes and anti-Stokes processes are inherently coupled in the intramodal FSBS. Figure 1(c) shows the cross section of the ridge waveguide, along with the simulated x-components of the optical field, acoustic displacement, and strain field obtained in the finite-element method (FEM) simulations. The waveguide cross section is defined by the following dimensions: core width w ₁, defect width w ₂, etching depth h ₁, and plate height h ₂. The core width w ₁ and defect width w ₂ were carefully designed to optimize the Brillouin sideband optical power (see Supporting Information for details). The sideband optical power is proportional to the product G _b·L _SBS [37], where G _b is the Brillouin gain coefficient and L _SBS = (1 − e^−αL )/α is the active interaction length, α representing the optical propagation attenuation coefficient, and L being the total length. According to the simulated results, there exists a trade-off between reducing w ₁ to increase G _b and increasing w ₁ to increase L _SBS, and the product G _b·L _SBS reaches its maximum value when w ₁ is 2.2 μm (see Supporting Information for details). The Brillouin resonance frequency can be tuned by varying the defect width w ₂, with the resonance frequency decreasing as the defect width increases. Based on these results, we design a waveguide with core width of w ₁ = 2.2 μm, defect width of w ₂ = 6.6 μm, etching depth of h ₁ = 260 nm, and plate height of h ₂ = 140 nm. Additionally, the length of 50 μm taper waveguide is placed between the grating coupler and the straight waveguide to avoid the occurrence of multimode propagation within the waveguide. For comparison, we also design a single-mode waveguide with core width w ₁ of 0.9 μm and defect width w ₂ of 5.3 μm to demonstrate the tunability of the Brillouin scattering response.

Figure 1:

Design of suspended AlN waveguides on silicon platform. (a) 3D model of the suspended AlN device. (b) Phase-matching condition for intramodal forward stimulated Brillouin scattering. (c) Cross section of waveguide and simulation results showing the x-component of the fundamental TE₀₀ optical mode, mechanical displacement, and strain field.

2.2 Fabrications

The polycrystalline AlN film with a thickness of 400 nm is deposited on (001) silicon substrate via physical vapor deposition (PVD). A detailed schematic of the fabrication process is presented in Figure 2(a). Initially, a 300 nm-thick SiO₂ hard mask and a 60 nm-thick chromium (Cr) layer are sequentially deposited on AlN layer, serving as a dual-layer mask for AlN patterning [38], [39]. Next, a 460 nm-thick AR-P 6,200.13 electron-beam resist is spin-coated onto the hard mask, and electron-beam lithography (EBL) is employed to define the waveguide and grating coupler structures. The exposed pattern is then transferred to the Cr mask via inductively coupled plasma reactive ion etching (ICP-RIE) using a Cl₂/O₂ gas mixture, followed by transfer to the SiO₂ hard mask using CHF₃/Ar plasma. The SiO₂ layer acts as an effective etch mask for AlN patterning using a Cl₂/BCl₃/Ar-based ICP-RIE process. The etch selectivity between the Cr mask and the SiO₂ hard mask is approximately 1:13, while the selectivity between the SiO₂ hard mask and AlN is about 1:2.2. To define slot windows, a second lithography and etching cycle is performed in the previously AlN etched regions. Finally, the devices are released by removing the underlying silicon substrate through SF₆-based ICP-RIE dry etching. Figure 2(b)–(e) presents the optical microscope and scanning electron microscopy (SEM) images of the fabricated waveguide. As observed under the optical microscope in Figure 2(b) and (c), both the grating coupler and the Brillouin-active region are perfectly suspended without any structural damage. The released AlN waveguide exhibits a rose-red coloration, in contrast to the green hue of the unreleased regions. The distinct color difference serves as a visual marker for identifying the completion of the suspension process. Figure 2(d) shows SEM image of the Brillouin-active region, showing a core width of w ₁ = 2.2 μm, defect width of w ₂ = 6.6 μm, slot spacing of a = 5 μm, and slot width of b = 2 μm. A cross-sectional SEM image of the suspended waveguide is shown in Figure 2(e). The silicon substrate is undercut by isotropic dry etching to form air cladding on both upper and lower interfaces of waveguide, which significantly enhances the confinement of both optical and acoustic modes. The coupling loss of apodized focusing grating couplers is −7 dB per facet at the wavelength of 1,550 nm, and the waveguide propagation loss, measured by waveguide cutback experiments, is 2.7 dB/cm (see Supporting Information for details).

Figure 2:

Fabrication process and structural characterization of AlN waveguide. (a) Schematic illustration of the fabrication process of suspended AlN device. A dual-layer mask of SiO₂ and Cr layers is used to etch AlN waveguide and slot windows. (b) Optical microscope of suspended coupling grating. (c) Optical microscope of straight waveguide surrounded by the slot windows. (d) SEM image of the suspended straight waveguide. (e) SEM image showing a cross-sectional view of the suspended waveguide.

2.3 Experimental setup

The experimental setup, as depicted in Figure 3, explores the Brillouin nonlinearity in the device via a heterodyne four-wave mixing (FWM) experiment [40]. A monochromatic laser operating at 1,545 nm serves as the pump source, which is modulated by intensity modulator (IM) to generate two sidebands that excite a coherent phonon wave at frequency Ω. The modulated pump waves are subsequently amplified using an erbium-doped fiber amplifier (EDFA 1), and its polarization is controlled via polarization controller (PC). Meanwhile, a probe wave at 1,550 nm is split into two optical paths. In the upper path, after amplified by the second erbium-doped fiber amplifier (EDFA 2), the probe wave is combined with the modulated pump waves and coupled into the device under test (DUT). As shown in inset (a) of Figure 3, the incident waves coupled into the DUT consist of both the modulated pump waves ω _p, ω _p ± Ω/2 and the probe wave ω _pr. After passing through the DUT, the red-detuned (Stokes) and blue-detuned (anti-Stokes) sidebands of the probe wave are generated due to the phase modulation induced by Brillouin and Kerr nonlinearities, as illustrated in inset (b). A band-pass optical filter (OF) centered at 1,550 nm with a bandwidth of 2 nm is used to filter out the modulated pump waves, allowing the photo-detector (PD) to detect the sideband signals of the probe wave. In the lower path, the probe wave undergoes a frequency shift of Δ = 200 MHz using an acousto-optic modulator (AOM), serving as the optical local oscillator (LO) for heterodyne detection. The inset (c) shows that the anti-Stokes and Stokes sidebands with frequencies of ω _pr ± Ω can be resolved as distinct RF tones Ω ∓ Δ. By sweeping the output frequency of the radio-frequency generator (RFG), the peaks of the heterodyne Brillouin signal are detected using a radio-frequency spectrum analyzer (RFSA). The measured response results from the combined effects of FWM and SBS in the device, where the presence of FWM significantly enhances the sensitivity of SBS signal detection.

Figure 3:

Heterodyne four-wave mixing experiment. RFG, radio frequency generator; BC, bias voltage; IM, intensity modulator; EDFA, erbium-doped optical fiber amplifier; PC, polarization controller; OC, optical coupler; AOM, acousto-optic modulator; RFD, radio frequency driver; DUT, device under test; OF, optical filter; PD, photodetector; RFSA, RF spectrum analyzer. (a) The incident light includes the modulated pump lights and probe light. (b) Stokes and anti-Stokes sideband signals generated driven by Kerr and Brillouin nonlinearities, and the modulated pump lights is filtered out by an optical filter. (c) The filtered output light is blueshift by Δ = 200 MHz. The Stokes and anti-Stokes sidebands corresponds to the beat frequency signal Ω ± Δ.

The Brillouin nonlinearity is a resonant process that exhibits a Lorentzian line-shape around the acoustic resonant frequency, as described by the following:

where Ω_b is the resonant frequency of the acoustic mode, Q is the acoustic quality factor, and G _b = 2|γ _SBS(Ω_b)| is the peak Brillouin gain coefficient. In contract, the background Kerr nonlinearity can be approximated as constant over the narrow frequency sweep range and is given by γ _K = n ₂ ω/(c·A _eff), where n ₂ is nonlinear refractive index of AlN, and A _eff is the effective mode area. Consequently, the interference between the FSBS and the Kerr nonlinearity gives rise to a Fano-like line-shape, which can be described by the following normalized fitting function [36]:

here, φ represents the relative phase between the SBS and Kerr nonlinearities, L _SBS/L denotes the ratio of the Brillouin active region to the total waveguide length. The key parameters G _b, Ω_b, and Q can be extracted through nonlinear fitting of Eq. (2).

3.1 Tailorable Brillouin nonlinearity in straight waveguides

The Brillouin nonlinearity response of fabricated waveguides is measured using a heterodyne four-wave mixing experiment. The phase interference between the discrete-state SBS and the continuous-state FWM in the waveguide gives rise to a Fano-like asymmetric peak-dip spectral profile. Figure 4(a) and (b) shows the normalized Stokes and anti-Stokes sideband signals for the waveguide with w ₁ = 2.2 μm, w ₂ = 6.6 μm and the total length of 1.014 cm, under an on-chip pump power of 31.62 mW (15 dBm) and a probe power of 15.68 mW (12 dBm). By fitting the experimental Brillouin gain spectrum using Eq. (2), we extract the key parameters: the Brillouin gain coefficient of G _b = 91.8 m⁻¹ W⁻¹, resonant frequency of Ω_b/2π = 2.32 GHz, acoustic quality factor of Q = 230, and the Brillouin linewidth of Γ = Ω_b/Q = 10.1 MHz. These experimental results show good agreement with the theoretically predicted Brillouin gain of 104 m⁻¹ W⁻¹ and a Brillouin frequency of 2.25 GHz, as obtained using full-vector finite element simulations (see Supporting Information for details). The Kerr nonlinearity coefficient is calculated as γ _K = 13.57 m⁻¹ W⁻¹, based on the nonlinear refractive index n ₂ = 3.6 × 10⁻¹⁹ m²/W and the effective mode area A _eff = 1.07 × 10⁻¹³ m². The Brillouin nonlinearity coefficient is given by γ _SBS = G _b/2 = 45.9 m⁻¹ W⁻¹, which is 3.38 times greater than the Kerr nonlinear coefficient (|γ _SBS|/|γ _K| = 3.38), indicating a significantly enhanced Brillouin nonlinearity in the Brillouin-active waveguide. The extracted Brillouin gain coefficient is approximately one order of magnitude lower than that of silicon-based platforms [40], primarily due to the lower nonlinear refractive index in AlN waveguide. However, it is comparable to the highest reported values for lithium niobate with a fixed crystallographic orientation [11], [13], and the measured Brillouin linewidth is approximately 2.6 times narrower than that observed in lithium niobite [11], demonstrating the improved optical and acoustic confinement achieved in our AlN-based platform. Figure 4(c) and (d) illustrates the characteristic Brillouin resonance of the waveguide with dimensions w ₁ = 0.9 μm and w ₂ = 5.3 μm. Compared to the spectral line shown in Figure 4(a) and (b), the Brillouin response in Figure 4(c) and (d) also exhibits a Fano-like line-shape, but with the emergence of two Brillouin resonance peaks. This behavior is primarily attributed to inhomogeneous broadening and mode hybridization [35], both of which contribute to a reduction in the peak gain coefficient and spectral line broadening. The inhomogeneous broadening arises from waveguide width variations induced by EBL overlay errors or proximity effects, particularly in long waveguides, which result in the superposition of multiple, slightly shifted Brillouin resonances. Meanwhile, mode hybridization occurs when two closely spaced acoustic modes are simultaneously excited during the RF power sweep, making them difficult to distinguish. In this device, the multi-peak response is more likely dominated by inhomogeneous broadening, due to the higher susceptibility of the narrower 0.9 μm waveguide to physical and chemical damage during dry etching. Nonlinear fitting of Stokes sideband signal yields acoustic frequencies of Ω₁/2π = 4.925 GHz, Ω₂/2π = 4.93 GHz, as shown in Figure 4(c). The fitting curve at the frequency of Ω₂ shows a better agreement with the measured data. The Brillouin gain coefficient at Ω₂ is G _b = 31 m⁻¹ W⁻¹, with quality factor Q = 231.9, linewidth Γ = 21.3 MHz. For the anti-Stokes sideband signal in Figure 4(d), the acoustic frequencies are Ω₁/2π = 4.92 GHz, Ω₂/2π = 4.93 GHz, and the Brillouin gain coefficient at Ω₂ is G _b = 23.8 m⁻¹ W⁻¹, with quality factor Q = 221, linewidth Γ = 22.3 MHz. Compared to the waveguide with a width of 2.2 μm, a higher acoustic frequency around 4.93 GHz is observed as the defect width decreases from 6.6 µm to 5.3 µm, which is consistent with the simulation results (see Supporting Information for details). Meanwhile, the reduction in the Brillouin gain coefficient and resonance broadening are attributed to the inhomogeneous broadening effect. These observations confirm the relatively strong optically stimulated Brillouin scattering in suspended AlN waveguides and further demonstrate the tunability of Brillouin nonlinearity by adjusting the waveguide width.

Figure 4:

Normalized Stokes and anti-Stokes spectral lines obtained from the heterodyne FWM experiment for different waveguides dimension, and the vertical axis is in linear scale. (a–b) w ₁ = 2.2 μm and w ₂ = 6.6 μm. (c–d) w ₁ = 0.9 μm and w ₂ = 5.3 μm.

3.2 Brillouin nonlinearity in serpentine waveguides

To further investigate the relationship between Brillouin sideband signal response and active length, serpentine waveguides with different lengths are fabricated. The schematic diagram and corresponding SEM image are presented in Figure 5(a) and (b). The layout consists of three straight sections of length L ₁ and two curved sections of radius R, allowing for a more compact device footprint. The intensity of the Brillouin beat sideband signals as a function of pump power is investigated, as illustrated in Figure 5(c), the intensities of the Stokes and anti-Stokes beat signals exhibit linear relationship on the on-chip pump power with the probe power fixed at 15.85 mW (12 dBm), which agrees with the trend of sideband signal observed at low input power [41]. Figure 5(d) shows the variation in the relative Stokes signal intensity with scanning frequency for different Brillouin active interaction lengths. The relative signal intensity here refers to the ratio between the beat signal intensity of the sideband and that of the probe wave, that is P _as/s = P (Ω ± Δ)/P (Δ). Notably, the Fano dip observed in the spectrum arises from destructive interference between the FWM and SBS components when their relative phase satisfies φ = (2m + 1) π (m = 0, 1, 2…), whereas the Fano peak corresponds to constructive interference at φ = 2mπ. Substituting φ = (2m + 1)π into Eq. (2) yields the value approaching zero, where the logarithmic variation becomes more significant, resulting in more pronounced Fano dip in Figure 5(d) as L _SBS increases. Significantly, the active interaction lengths of 9.997 mm waveguide (total length of 15.628 mm with L ₁ = 5 mm and R = 0.1 mm) exhibited 7-dB improvement in extinction ratio of the Fano dip compared to the shorter 0.685 mm straight waveguide (total length of 0.7 mm), while the baseline of relative signal intensity remains nearly unchanged and the resonance frequency consistently maintained at 2.32 GHz. The more pronounced Fano-like line-shape is attributed to the continuous accumulation of Brillouin interaction with the increasing active lengths L _SBS according to Eq. (2).

Figure 5:

Characteristic nonlinear Brillouin spectra of meander-shaped waveguides. (a) Schematic diagram of the meander-shaped suspended AlN waveguide. (b) SEM image of dashed part in (a). (c) Beat sideband signals intensity as a function of pump power. (d) Relative signal intensity as a function of scanning frequency with different Brillouin interaction lengths.

3.3 Brillouin interaction enhanced by FP resonator

The two Bragg gratings are patterned at both ends of the straight waveguide to form FP Fabry–Perot (FP) resonator, as illustrated in the lower waveguide of Figure 6(a). The design goal is to further improve the gain coefficient at smaller dimensions and lower input power. A zoomed-in SEM image of the Bragg grating is shown in Figure 6(b). Integrating the Bragg grating–based FP resonator into the Brillouin active region enables multiple coherent reflections within the structure, reducing the group velocity of light and thereby realizing a slow-light effect [42], which effectively increases the Brillouin interaction length between the light and the structure. The period and perturbation width of the Bragg gratings are carefully designed to align the resonant wavelengths of both the Bragg and coupled gratings (see Supporting Information for details). Specifically, the grating period Λ_b is 465 nm, the perturbation width Δw _b is 800 nm, the core width w _b of Bragg grating is 1.4 μm, and the resonant wavelength is approximately 1,551 nm. Figure 6(c) presents the transmission spectrum of the fabricated Bragg gratings and FP resonator. Within the stopband of a single Bragg grating, multiple resonance peaks emerge due to the coherent reflections of the FP cavity. We further compared the Brillouin spectrum of the straight waveguide and FP resonator, as shown in Figure 6(d). Under identical experimental conditions (13 dBm pump power, 12 dBm probe power, and 1,550 nm pump wavelength), the Fano peak of Brillouin relative sideband intensity for the straight waveguide is −62.5 dB at 1,545 nm probe wavelength. When the FP resonator is in a nonresonant state (1,545 nm probe wavelength, marked by the blue star in Figure 6(c)), the peak increases slightly to −60 dB. In contrast, when the FP cavity is resonant (1,553.64 nm probe wavelength, marked by the yellow star in Figure 6(c)), the peak reaches −56 dB – with a 6.5-dB enhancement compared to the straight waveguide with same length, owing to the simultaneous resonance enhancement of both Kerr and SBS sidebands by FP resonator. The Brillouin spectrum under the FP resonator in Figure 6(d) not only exhibits a significant enhancement in relative sideband intensity but also shows more pronounced Fano-like line-shape, which combines the advantages of simultaneously increasing both the injected pump power and the Brillouin interaction length, as previously mentioned and shown in Figure 5(c) and (d). Besides, Figure 6(e) and (f) shows the normalized Stokes and anti-Stokes sideband signals measured in FP resonator. The Brillouin gain coefficient of G = 150.37 m⁻¹ W⁻¹, acoustic frequency of Ω_b/2π = 2.32 GHz, quality factor of Q = 235, and linewidth of Γ = 9.87 MHz are obtained by nonlinear fitting. The Brillouin gain coefficient of the FP resonator is given by G = S ² G _b, where S denotes the slow-light factor and G _b = 91.8 m⁻¹ W⁻¹ is the gain coefficient of the straight waveguide. In this case, the gain coefficient G is 1.64 times greater than G _b, corresponding to a slow-light factor of S = 1.28. These results demonstrate that the FP resonator significantly enhances SBS interaction through slow-effect with shorter physical lengths and lower input pump power, opening a new path for Brillouin-enhanced devices in integrated waveguides.

Figure 6:

Bragg grating–based FP cavity for enhanced Brillouin interaction. (a) Schematic diagram of the straight waveguide and FP resonator, (b) SEM image of dashed part in (a). (c) Transmission spectra of the fabricated Bragg gratings and FP resonator. (d) Relative signal intensity as a function of scanning frequency for straight waveguide and FP resonator at resonance or nonresonance. (e) Normalized Stokes spectral line in FP resonator. (f) Normalized anti-Stokes spectral line in FP resonator.