Brillouin and Kerr nonlinearities of a low-index silicon oxynitride platform

Stimulated Brillouin scattering (SBS), which is an interaction between optical and acoustic waves, is currently revolutionizing photonic integrated circuit designs.^1–8 Featuring a narrow-band (tens of MHz) gain resonance shifted around tens of GHz away from the pump light, the on-chip SBS plays a significant role in microwave photonics,^9–11 narrow-linewidth integrated lasers,^7,12,13 and on-chip nonreciprocal light propagation.^3,14

An efficient on-chip SBS process requires simultaneous guiding of both the optical and gigahertz acoustic waves in a waveguide, making it challenging to realize on most integrated platforms. Several encouraging results have been demonstrated recently on various platforms, including chalcogenide,² silicon,⁵ doped silica,¹⁵ aluminum gallium arsenide,¹⁶ and aluminum nitride.¹⁷ In addition, SBS has also been observed in silicon nitride-based waveguides,^7,8,18 opening the pathway to intersect Brillouin scattering with Kerr nonlinearities in low-loss and mature platforms.

Silicon oxynitride (SiON) is another highly-developed integrated platform that has appealing properties, including low propagation loss, a wide transparency window, the absence of multi-photon absorption effects, and stress-free fabrication.^19,20

The optical and mechanical properties of SiON could be tuned continuously between those of SiO₂ and Si₃N₄ at different nitrogen/oxygen (N/O) ratios.^21,22 For example, a variety of SiON known as Hydex (n = 1.7 @ 1550 nm) has been widely used for Kerr-based nonlinear optic applications including optical frequency comb,²³ optical neural network,²⁴ and quantum photonics.²⁵ A slightly higher index of SiON (n = 1.83 @ 1550 nm) was also proposed in Refs. 20 and 26 for Kerr-based applications. In both cases, the SiON platforms have a refractive index close to that of silicon nitride (n = 1.98 @ 1550 nm) instead of silicon oxide (n = 1.45 @ 1550 nm). The relatively high refractive index induces a high nonlinear index, making it useful for Kerr-based nonlinear optic applications.

However, from the Brillouin perspective, a high refractive index SiON is less attractive due to the high content of nitrogen, which leads to a meager photoelastic coefficient p₁₂ because of the weak p₁₂ of the Si₃N₄.¹⁸ Moreover, high-index SiON also has similar mechanical properties to Si₃N₄, such as high acoustic velocity that prevents acoustic confinement when cladded with SiO₂.^7,8,18

In this paper, we investigate the Brillouin and Kerr properties of a SiON integrated platform with a relatively lower refractive index (n = 1.513 @ 1550 nm). Contrasting to the SiON platforms mentioned earlier, the SiON platform investigated here has a larger photoelastic coefficient p₁₂, a lower acoustic velocity, and a larger cross section, all of which lead to an enhanced SBS effect. We experimentally observed, for the first time to our knowledge, backward Brillouin scattering in SiON waveguides. We also characterized the Brillouin gain coefficient g_b of the SiON waveguides with different widths. We found out that the g_b of this SiON waveguide can potentially be increased to 0.9 m⁻¹ W⁻¹ by simply tailoring the waveguide cross section. This sufficiently large Brillouin gain coefficient, together with the low propagation loss, makes it possible to generate decent SBS gain for a plethora of Brillouin-based applications on this SiON platform.

Furthermore, we also measured the nonlinear parameter γ and nonlinear index n₂ of this SiON platform through four wave mixing (FWM) experiments in a ring resonator. While the measured γ is an order of magnitude lower when compared to that of high-index SiON, we expect that with lower losses and higher pump power, the unique interplay between the SBS and Kerr effect, such as a Brillouin-assisted Kerr frequency comb,^27,28 could be observed in this integrated platform.

We performed the backward Brillouin scattering and four-wave mixing experiments in 5 cm straight waveguides and microring resonators, respectively, as shown in Fig. 1(a). The cross section of this platform is shown in Fig. 1(b).^29,30 The 2.2 m-thick SiON layer has a refractive index n of 1.513 at 1550 nm [nitrogen content N/(N + O) is 0.14]. The refractive index contrast Δn between the core and the cladding is 4.4%, enabling a bending radius of 600 m with negligible radiation losses.

The SiON film is deposited by Plasma Enhanced Chemical Vapor Deposition (PECVD) on a 15-m-thick silicon dioxide film thermally grown on a silicon substrate. After the SiON PECVD process, an annealing treatment for 4 h at 1175 °C in the N₂ and O₂ atmospheres is conducted to reduce both material losses induced by residual N–H bonds and stresses. The waveguides are then patterned by contact photolithography, followed by a reactive ion etching step on the SiON film. A 7-m-thick layer of borophosphosilicate glass (BPSG) is employed as the upper-cladding material. This low viscosity glass permits covering the waveguides completely without any voids that would generate scattering and additional losses.

Figure 1(c) shows a photograph of the microring resonators in this platform with a free spectral range (FSR) of 50 GHz and coupling coefficients varying from 0.05 to 0.8. Figure 1(d) shows a photograph of several groups of 5 cm straight waveguides with different widths. The measured propagation loss of those straight waveguides is 0.25 dB/cm with a coupling loss to lensed-tip fibers of ∼3 dB/facet.

We developed a finite element model⁸ in COMSOL to estimate the SBS response of the SiON waveguides. We take the bottom and upper cladding as the same material in our model since the BPSG glass and the SiO₂ have similar optical and mechanical properties.^31,32 The simulated optical field and the corresponding acoustic response of the 2.2 m-wide SiON waveguide are shown in Figs. 2(a) and 2(b), respectively. The optical field is well confined around the SiON core area because of the total internal reflection (TIR). However, the TIR condition does not hold for the acoustic response because the acoustic velocity of the SiON (∼6.2 km/s) is higher than that of the SiO₂ (∼5.9 km/s). As a result, part of the acoustic field would leak into the cladding, as shown in Fig. 2(b). Nevertheless, most of the acoustic field still remains inside the SiON core because of the relatively large cross section area.³³ This results in a large overlap between the optical and acoustic fields, which leads to an improved Brillouin gain coefficient. Material properties applied in our model and extensive simulation results are included in the supplementary material.

To verify the simulation results, we characterized the backward Brillouin scattering responses of the SiON waveguides with a pump-probe experimental apparatus.^8,18 The pump and probe light are intensity-modulated and coupled into the opposite facets of the waveguide. We keep the pump frequency fixed at 1561 nm while sweeping the probe at frequencies down-shifted from the pump. When the frequency difference between the pump and the probe is close to the Brillouin frequency shift of the SiON waveguide, the probe will experience the SBS gain, and a peak will be detected at the lock-in amplifier (see the supplementary material for more details about the Brillouin characterizations).

Several 5 cm-long SiON straight waveguides are characterized to investigate the influence of waveguide width on the Brillouin gain spectra. The measured Brillouin gain spectra of the 2.0, 2.2, 2.3, 2.4, 2.6, and 3.5 m-wide waveguides are shown in Figs. 2(c)–2(h), respectively. All waveguides show a clear Brillouin gain peak well above the noise floor with the Brillouin frequency shift increasing from 14.22 GHz for the 2.0 m-wide waveguide to 14.48 GHz for the 3.5 m-wide waveguide. The discrepancy between the experiment and simulation in Brillouin frequency shift is mainly caused by a lack of knowledge about the exact mechanical properties of the SiON. Figure 2(i) plots the measured Brillouin gain coefficient g_b and the linewidth of the SiON waveguides with different widths (see the supplementary material for more details about the Brillouin gain coefficient calculation). The Brillouin gain coefficient g_b increases from 0.1 to 0.32 m⁻¹ W⁻¹ when the waveguide width increases from 2.0 to 3.5 m. In the meantime, the linewidth of the peak decreases from 358 to 105 MHz. The increasing Brillouin gain coefficient and the narrowing of the linewidth indicate improved acoustic confinement when the SiON waveguides become wider.

The Brillouin gain coefficient can be further increased by optimizing the cross-section of the waveguide (maintaining the core as a rectangular shape) through a genetic algorithm.^8, Figures 3(a) and 3(b) show the simulated optical mode and the acoustic response of the optimized SiON waveguide for SBS. The dimension of such a waveguide is 3.6 × 3.0 m² with a top cladding of 6 m and a bottom cladding of 12 m. The optimized cross-section is a trade-off between the optical mode area and the overlap between the optical and displacement fields. Compared to waveguides measured in this work, less acoustic field is scattered into the cladding, while the optical field is still well confined and relatively small in the optimized waveguide structure. The Brillouin gain spectrum of the optimized waveguide structure is shown in Fig. 3(c). The simulated peak Brillouin gain coefficient of this waveguide is 0.9 m⁻¹ W⁻¹, which is 3× higher than the waveguide structure measured in this work. Furthermore, the propagation loss on this SiON platform can also be significantly lowered by reducing sidewall roughness and improving the thermal annealing process,³⁰ allowing for a longer effective waveguide length for the SBS process. Figure 3(d) estimates the SBS gain of both the measured and the optimized SiON waveguides with different propagation losses. The optimized Brillouin gain coefficient, along with the improved propagation loss, can enhance the SBS gain from less than 0.5 dB to nearly 1.5 dB for a 60 cm waveguide. The actual SBS gain from the optimized waveguide might be lower than our estimations, as indicated by the discrepancy between the measurement and simulation results; nevertheless, it would still be sufficient for applications like SBS-based narrow-bandwidth microwave photonic notch filters.^8,10

We further investigate the Kerr nonlinearities of this SiON platform. Hig-index SiON platforms are widely used for Kerr-based nonlinear optics applications because of the relatively large nonlinear parameter γ.¹⁹ However, the nonlinear parameter γ is highly dependent on the refractive index and the geometry of the waveguide. The SiON waveguide in this work has a relatively lower refractive index and a larger cross section compared with other SiON platforms,^19,20 and the nonlinear index n₂ and nonlinear parameter γ of the SiON waveguide in this platform have never been characterized before.

We devised a four-wave mixing (FWM) experiment for nonlinear parameter characterization. Because of the limited effective length of the available samples, the FWM conversion efficiency of the straight waveguide is comparable with that of the fiber pigtails, making it difficult to accurately measure the n₂ and the γ. We use the all-pass ring resonators to enhance the FWM in the SiON waveguide so that the contribution from fibers in the setup can be neglected.³⁴ The ring resonator applied in our experiment is made of a 2.2 m-wide SiON waveguide, and it has a free spectral range (FSR) of 50 GHz and a power coupling coefficient of 0.05. The pump laser is locked close to the resonance of the ring resonator to mitigate the thermal influence on the ring resonator. The probe laser is set close to 2× FSR away from the pump signal and is combined with the pump light with a 99:1 coupler. The combined pump and probe are coupled into the all-pass ring resonator with a lensed fiber with a spot size of 2 m. The signal is then coupled out of the chip and sent to the optical spectrum analyzer to measure the conversion efficiency from the probe to the signal (see the supplementary material for details of the FWM experiment).

To determine the field enhancement factor of the FWM process in the ring resonator, we first characterized the resonance response of the ring resonator with a vector network analyzer, as shown in Fig. 4(a) (see the supplementary material for details of the characterization). The measured full-width at half-maximum (FWHM) is 612 MHz with an extinction ratio of 8.9 dB, corresponding to a loaded Q-factor of 330 000 and a propagation loss of 0.27 dB/cm. Figure 4(b) shows the measured FWM response of the 50 GHz SiON ring resonator. A clear peak is shown at 2× FSR down-shifted from the pump frequency, which is the signal generated from the FWM process between the pump and idler in the ring resonator.

The nonlinear index n₂ and nonlinear parameter γ of the SiON waveguide in this platform can be estimated from the conversion efficiency between the idler and the signal (see the supplementary material for details of the calculation). Figure 4(c) shows the measured conversion efficiency of the FWM process at different pump powers. Based on this measurement, the calculated γ and n₂ of the 2.2 m-wide SiON waveguide are 0.024 m⁻¹ W⁻¹ and 4.16 × 10⁻²⁰ m²/W, respectively. We also estimated the nonlinear parameter γ of the SiON waveguides with different widths based on the measured value of n₂, as shown in Fig. 4(d). The γ decreases from around 0.025 to 0.020 m⁻¹ W⁻¹ when the waveguide width increases from 2.0 to 3.5 m.

For Brillouin-Kerr interactions, the balance between the nonlinearities needs to be considered. In this work, we have listed the Brillouin and Kerr properties of SiO₂, different types of Si₃N₄ waveguides, the Hydex waveguide, and the SiON waveguide in Table I. The thick Si₃N₄ waveguide¹⁸ has a large Kerr nonlinear parameter γ but negligible g_b, making it promising for Kerr-only applications. However, in Brillouin-Kerr microcavities, it is generally preferred to have a larger Brillouin gain, as it is easier to inhibit cascading or other unwanted interactions via mode manipulation. The SiON waveguides reported here have an order of magnitude larger Brillouin gain compared to Kerr nonlinearity. This g_b/γ ratio is similar to the previous demonstration of Brillouin-assisted Kerr frequency combs in Refs. 27 and 28, showing the potential to realize it on an integrated platform.

In conclusion, we have investigated the Brillouin and Kerr properties of a SiON integrated platform with a relatively low refractive index. We observed, for the first time, the backward Brillouin scattering response of the SiON waveguides. We also measured its nonlinear index n₂ and nonlinear parameter γ. These SiON waveguides can be fabricated on a versatile and low-loss integrated platform and can potentially lead to a plethora of Brillouin and Kerr-based applications, including narrow-bandwidth microwave photonic filters, narrow-linewidth lasers, and optical frequency combs.

See the supplementary material for details of the Brillouin and Kerr characterizations.

The authors acknowledge funding from the European Research Council Consolidator Grant (No. 101043229 TRIFFIC) and the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) Vidi (Grant No. 15702) and Start Up (Grant No. 740.018.021).

The authors have no conflicts to disclose.

D.M. and K.Y. developed the concept and proposed the physical system. K.Y. and Y.K. developed and performed numerical simulations. K.Y. performed the Brillouin characterization with input from R.B., K.Y., and O.D. Y.K. and K.Y. performed the FWM experiments. O.A.J.G., F.M., and A.M. developed and fabricated the samples. K.Y., D.M., and Y.K. wrote the article. D.M. led and supervised the entire project.

Kaixuan Ye: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Software (equal); Visualization (equal); Writing – original draft (equal). Yvan Klaver: Data curation (equal); Investigation (equal); Writing – original draft (equal). Oscar A. Jimenez Gordillo: Methodology (equal); Resources (equal). Roel Botter: Investigation (equal); Methodology (equal). Okky Daulay: Investigation (equal); Methodology (equal). Francesco Morichetti: Investigation (equal); Methodology (equal); Resources (equal). Andrea Melloni: Investigation (equal); Methodology (equal); Resources (equal). David Marpaung: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Project administration (equal); Supervision (equal); Writing – original draft (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.