Cross-polarized stimulated Brillouin scattering-empowered photonics

SJ_Zhang
Jun. 2, 2025

Abstract

This paper studies cross-polarized stimulated Brillouin scattering (XP-SBS) and its integration with quadratic nonlinearity in lithium niobate to enhance photonic device performance. Three novel applications are demonstrated: (1) a reconfigurable stimulated Brillouin laser with a 0.7-Hz narrow linewidth and 40-nm tunability, enabled by the thermo-optic phase matching of XP-SBS; (2) an efficient coherent mode converter achieving 55% conversion efficiency via intracavity Brillouin-enhanced four-wave mixing; (3) a Brillouin-quadratic laser and frequency comb operational in near-infrared and visible bands, benefiting from the interaction between XP-SBS and quadratic nonlinearity. These advancements promise substantial improvements in photonic technologies, including narrow-linewidth lasers, microcomb generation and optical signal processing, paving the way for more robust and versatile applications.

Main

Stimulated Brillouin scattering (SBS) is a nonlinear coherent photon–phonon interaction that has been a subject of extensive study since its discovery over a century ago^1,2,3. The SBS process is uniquely characterized by its ultranarrow megahertz linewidth, microwave-compatible gigahertz frequency shift and large frequency-selective gain, making it pivotal in enhancing our understanding of light–matter interactions and paving the way for innovative technologies^{4,5,6,7,8,9,10,11,12,13,14,15,16,17,18}. A highly coherent stimulated Brillouin laser (SBL)⁴ has been the cornerstone for optical atomic clock⁵, high-resolution spectroscopy^6,7 and high-precision optical gyroscopy^8,9. SBS has also been utilized to revolutionize the field of microwave photonics, where optical and electronic signals are processed and manipulated on the same platform^10,11,12,13. SBS microscopy, a newly invented functional imaging technique, has provided critical insights into the biomechanical properties of soft-matter and biological materials, making it a valuable tool in both medical research and materials science^14,15,16. SBS is also being investigated for its potential role in generating optoacoustic quantum entanglement¹⁷ and beginning to impact fields such as quantum sensing and optical neural network¹⁸.

In recent years, there has been growing interest in studying fundamental physics and enhancing the performance of SBS-based devices by adding more degrees of freedom and integrating other nonlinear optical phenomena. For example, optical angular momentum modes in ring-core optical fibres have demonstrated new control mechanisms over SBS interactions¹⁹. Additionally, Brillouin scattering in few-mode fibres can be used for simultaneous multiparameter sensing based on Brillouin optical time-domain reflectometry²⁰. More importantly, SBS has been introduced to address a long-standing thermal instability challenge in the generation of dissipative Kerr soliton (DKS) microcombs, a groundbreaking technology with a wide range of demonstrated applications^21,22. The interplay between SBS and Kerr nonlinearity makes Brillouin–DKS thermally self-stable, rendering the technology more user-friendly and suitable for field deployment^{23,24,25,26,27,28}.

Polarization is another degree of freedom that can be leveraged to expand the SBS domain for more innovative applications. Despite the weak birefringence in optical fibres, cross-polarized SBS (XP-SBS) has been observed and applied in Brillouin–DKS generation to fundamentally narrow the comb linewidth, reduce the soliton timing jitter and achieve the coveted turnkey microcomb²³. In principle, the use of anisotropic materials such as lithium niobate (LN) can greatly enhance the XP-SBS effect, provided that the complex, orientation-dependent optical, acoustic and photoelastic properties are carefully considered^29,30,31,32.

Only very recently has SBS in LN been studied theoretically and measured experimentally^33,34,35,36. Although XP-SBS in LN has also been observed spectroscopically^32,35, the question remains whether XP-SBS in LN can be made strong enough, which is a crucial prerequisite for interacting with other nonlinear phenomena and enhancing the performance of SBS-based devices.

In addition to its anisotropic properties relevant to XP-SBS, LN is also non-centrosymmetric, meaning it exhibits second-order (quadratic) nonlinearity, which is orders of magnitude stronger than third-order (Kerr) nonlinearity. Consequently, microcomb generation utilizing quadratic nonlinearity (quadratic microcombs) tends to have a lower pump threshold and higher pump–comb conversion efficiency compared with DKS microcombs³⁷. More importantly, quadratic nonlinearity offers a feasible solution for extending the microcomb wavelength into hard-to-reach ultraviolet and mid-infrared spectral ranges and enables exciting applications including random number generation³⁸ and optical Ising machines³⁹. Beyond these demonstrations, an intriguing question is whether XP-SBS can be combined with quadratic nonlinearity to explore new opportunities and expand the already rich potential of quadratic microcombs⁴⁰.

This Article presents an attempt to address the two aforementioned questions. We show three distinct photonic applications enabled by strong XP-SBS and its interaction with quadratic nonlinearities in a free-space cavity consisting of a bulk LN. These applications are highlighted in the conceptual schematic of potential XP-SBS uses (Fig. 1). (1) We demonstrate a reconfigurable SBLs with a 0.7-Hz narrow fundamental linewidth over 40-nm broadband tunability and arbitrary transverse-mode selection. The reconfigurability and mode selection are made possible by the high thermo-optic phase-matching tunability of XP-SBS. (2) We achieve an efficient coherent mode convertor (polarization, transverse and longitudinal modes) that utilizes intracavity Brillouin-enhanced four-wave mixing (BE-FWM)^41,42. Mode conversion efficiency as high as 55% can be obtained owing to the interplay between XP-SBS and co-polarized SBS (CP-SBS) in the quadruply resonant cavity. (3) We realize a Brillouin-quadratic laser and a frequency comb at both near-infrared and visible bands by combining XP-SBS and quadratic nonlinearity in periodically poled LN (PPLN). A strong and efficient interaction between the XP-SBS and quadratic nonlinearity is attainable due to the prohibition of the competing cascaded SBS process. Finally, switching between the Brillouin-quadratic laser and the frequency comb is achieved by changing the pump polarization.

Fig. 1: Conceptual schematic showing potential XP-SBS applications.

Three highlighted demonstrations of XP-SBS-empowered photonics are shown using a free-space LN cavity. On-chip device implementation is foreseeable with the rapidly growing LNOI PIC technology. OC, optical coupler; M1–M3, mirrors.

Although the three XP-SBS applications demonstrated here use a free-space LN cavity, the rapidly growing LN on insulator (LNOI) photonic integrated circuit (PIC) technology⁴³ makes more on-chip device implementations foreseeable in the near future (see the ‘Discussion’ section for details).

Results

Reconfigurable SBL generator

Achieving the efficient excitation of SBL in a cavity requires good overlap between the Brillouin mode resonance and the Brillouin gain spectrum. Traditionally, this Brillouin phase-matching condition is achieved by the precise control of the cavity length within only a few micrometres⁴⁴, which is particularly challenging for monolithic cavity fabrication. Moreover, once the fabrication is finished, the SBL is not reconfigurable for broadband tunable operation due to the fixed cavity length and the resulting fixed phase-matching condition, which is not preferred for field-deployable applications.

Our reconfigurable SBL generator consists of a birefringent free-space ring cavity within a z-cut x-propagation PPLN crystal (Fig. 2a; Methods and Supplementary Fig. 1 provide more details). The quality (Q) factors are measured to be 2.136 × 10⁸ and 2.147 × 10⁸ for p and s polarizations at the fundamental modes, respectively. The free spectral range (FSR) for the two polarizations is ~397 MHz and their FSR difference is measured to be 1.15 MHz.

Fig. 2: Reconfigurable SBL generator.

a, Experimental setup for the reconfigurable SBL demonstration. The setup is also used for the Brillouin-quadratic laser and frequency comb generation. ECDL, external cavity diode laser; AMP, optical amplifier; CIR, circulator; PBS, polarization beamsplitter; HWP, half-wave plate; TS, translation stage. b, Working principle of the birefringence-based tuning method. By tuning the PPLN crystal temperature from T1 to T2, perfect Brillouin phase matching can be achieved. c, Crystal orientation and laser polarizations in the XP-SBS process. The large phase mismatch (>20π) leads to negligible quadratic nonlinearity in the reconfigurable SBL generator. d, Temperature-dependent offset frequency between two orthogonally polarized fundamental modes. The inset shows two resonances corresponding to two orthogonally polarized modes within one cavity FSR when the pump frequency is scanned. The offset frequency between them is measured simultaneously using a frequency-calibrated MZI (Methods). e, Intracavity power dynamics of pump and SBL with slowly scanned crystal temperature when the pump frequency is locked to the cavity by the PDH technique. The rate of temperature change is ~0.002 °C s^–1. f, Measured optical spectra of the reconfigurable SBLs. g, SBL spectrum with 48-dB SR. h, High-order spatial mode profiles of the generated XP-SBL. These far-field images are captured using a near-infrared camera with a field of view of 2 mm × 2 mm. i, Measured fundamental laser linewidths under different conditions.

Since the refractive indices and their thermo-optic coefficients of the bulk PPLN crystal differ for orthogonal polarizations, the offset frequency between two orthogonally polarized mode families can be adjusted via the PPLN crystal temperature in the high-Q-factor cavity. Figure 2b illustrates such birefringence-based tuning method to achieve a tunable XP-SBS phase-matching condition, enabling reconfigurable SBL generation. The strong XP-SBS gain is provided by the large non-diagonal photoelastic coefficient p₄₁ in the PPLN crystal (Fig. 2c; see the ‘Discussion’ and Methods sections for details). In particular, this birefringence-based tuning method can also be applied to different spatial mode families with orthogonal polarizations in our multimode free-space cavity.

In Fig. 2d, the thermal tuning coefficient of the offset frequency between the two orthogonally polarized fundamental modes is measured to be 188.8 MHz °C^–1, indicating that the perfect phase-matching condition can always be achieved within 2.1 °C. Figure 2e depicts the intracavity power dynamics of pump and SBL with slowly scanned PPLN crystal temperature, showing the temperature range within which efficient pump–SBL conversion is achieved. Here the pump and SBL are p and s polarized, respectively, and reversing the polarizations results in the same dynamics.

Tuning the PPLN crystal temperature is so convenient and efficient that perfect XP-SBS phase matching is consistently achieved in our setup, spanning wavelengths from 1,540 nm to 1,580 nm (Fig. 2f), which is limited by the amplifier’s operating wavelength and mirror coatings. In principle, the demonstrated birefringence-based tuning method is universal for reconfigurable SBL at any wavelength. Furthermore, the suppression ratio (SR) between the SBL and the pump is as high as 48 dB (Fig. 2g), due to counterpropagation and polarization-dependent suppression, which benefits non-reciprocal devices based on SBS, such as optical isolators⁴⁵. In addition to the demonstrated fundamental–fundamental mode conversion (Fig. 2d–g), we can also select the spatial mode of the XP-SBL by further fine-tuning the PPLN crystal temperature. This enables fundamental–high-order mode conversion (Fig. 2h) and introduces another degree of freedom for exciting applications, such as mode multiplexing. However, the decreased optical mode overlap in high-order-mode XP-SBL generation results in a higher threshold and lower output power (Supplementary Figs. 9 and 10).

Table 1 summarizes the Brillouin gain properties of the bulk PPLN crystal for both XP-SBS and CP-SBS cases (Supplementary Figs. 6–8). XP-SBS with the birefringence-based tuning method has three overwhelming advantages: (1) flexible tunability for broadband SBL generation; (2) inhibition of cascaded SBS process for SBL power scaling; (3) large SR between the SBL and the pump. Additionally, the XP-SBS gain coefficient is over three times higher than that of a single-mode fibre. This Article presents a comprehensive study of the SBS gain in bulk PPLN crystals. The ~10-MHz Brillouin gain bandwidth is almost ten times larger than the ~0.9-MHz Brillouin mode cavity linewidth, resulting in substantial noise suppression in the SBL. The noise suppression factor is determined by (1 + Γ_B/γ)² (ref. ²⁵), where Γ_B is the Brillouin gain bandwidth and γ is the Brillouin mode cavity linewidth. In Fig. 2i, we measure the fundamental linewidths for the pump and generated SBLs (Methods and Supplementary Fig. 11). The noise suppression from the pump is approximately 20 dB in all cases, leading to SBL fundamental linewidths of ~0.7 Hz, which agrees well with the calculated result⁴⁶.

Table 1 Comparison of the measured SBS gain properties and SBL generation at ~1,550 nm

Efficient mode converter

The large XP-SBS gain and birefringence-based tuning method can be applied for efficient mode conversion utilizing BE-FWM^41,42 in the cavity. During the BE-FWM interaction, four optical fields—two lasers involved in the Brillouin dynamic grating (BDG) writing process and two lasers associated with the BDG read-out process—interact through the BDG^41,42. First, we write the BDG in the LN crystal by loading an s-polarized writing laser into the cavity and exciting an s-polarized SBL (Fig. 3a,b and Supplementary Fig. 12). The cavity length is carefully adjusted for perfect phase matching of the CP-SBS process (s–s) with Brillouin frequency shift Ω_B. Second, we load a p-polarized reading laser into the cavity with power below the threshold for XP-SBL generation. The BDG information is read out by generating a reflected s-polarized signal due to the extracted XP-SBS gain (p–s) from the written BDG. Since the reading laser co-propagates with the writing laser, the reflected s-polarized signal is the Stokes light of the reading laser with a frequency shift equal to the acoustic frequency Ω_B of the written BDG. Owing to cavity birefringence, adjusting the crystal temperature tunes the resonant frequency of the s polarization in the cavity to match the frequency of the reflected s-polarized signal (Fig. 2b). This results in cavity enhancement and increased output power for the reflected signal, enabling efficient mode conversion of the reading laser.

Fig. 3: Efficient mode conversion with intracavity BE-FWM.

a, Experimental setup of a mode converter utilizing the BE-FWM process. The large phase mismatch (>20π) leads to negligible quadratic nonlinearity in the efficient mode converter. b, Schematic of the BE-FWM process. c, Phase-matching diagram for an efficient BE-FWM process. d, Optical spectra showing the BE-FWM process. e, Output power of the resonant reflected signal by changing the input power of the reading laser. The input power of the writing laser is 520 mW. f, Output power of the resonant reflected signal by changing the input power of the writing laser. The input power of the reading laser is 120 mW. g, Spatial mode profiles of the resonant reflected signal. These far-field images are captured by a near-infrared camera with a field of view of 2 mm × 2 mm.

Figure 3c shows the phase-matching diagram for efficient BE-FWM and the frequency separation ΔΩ between the writing and reading lasers is determined by the birefringence^41,42:

where ω_write is the optical frequency of the writing laser, n_write is the refractive index for the writing polarization and Δn is the refractive index difference at the writing laser frequency. In our case, n_write = n_e in the CP-SBS process with s–s polarization conversion and n_read = (n_o + n_e)/2 in the XP-SBS process with p–s polarization conversion, where n_e and n_o are the refractive indices of the extraordinary and ordinary light in the LN crystal, respectively.

In Fig. 3d–f, the writing laser (s), the generated writing SBL (s), the reading laser (p) and the reflected signal (s) are all in their fundamental modes. As shown in Fig. 3d, the reflected signal, or the Stokes light of the reading laser, can only be observed when the BDG is formed by the writing laser and the generated writing SBL. In addition, cavity enhancement of the reflected signal can be achieved by tuning the LN crystal temperature. The frequency separation between the writing and reading lasers was measured to be as large as 27.7 nm, which agrees well with the calculated value of 27 nm. Figure 3e,f shows the output power of the resonant reflected signal as a function of the reading and writing laser powers, respectively. A maximum output power of 120 mW and a conversion efficiency of 55% from the reading laser to the reflected signal are achieved due to the large XP-SBS gain and the birefringence-tuned cavity enhancement, which agree very well with the simulated results (Figs. 3e,f (dashed lines) and Supplementary Section VII). Similar to reconfigurable SBL generation (Fig. 2h), we can also select the spatial mode of the resonant reflected signal by further fine-tuning the PPLN crystal temperature (Fig. 3g and Supplementary Fig. 12).

By leveraging XP-SBS to implement BE-FWM, the birefringence-based tuning method can be used to ensure that all four interacting waves are resonant within the same high-Q-factor cavity, leading to a high conversion efficiency. This further highlights the flexibility and tunability of XP-SBS with the birefringence-based tuning method, which enables this fundamental investigation of intracavity BE-FWM. A distinct advantage of the XP-SBS mode converter lies in its ability to achieve efficient, high-degree-of-freedom mode conversion—including polarization, optical frequency and spatial mode—within a single experimental setup. In particular, polarization conversion and frequency upconversion with the anti-Stokes generation of the reading laser⁴⁷ are also possible⁴⁸ (Supplementary Fig. 14). Beyond efficient mode conversion, BE-FWM can also benefit applications including optical sensing⁴⁹, all-optical signal processing¹¹, all-optical delay⁵⁰, microwave photonic filter⁵¹ and ultrahigh-resolution optical spectrometry⁵².

Efficient Brillouin-quadratic laser and frequency comb

Efficient Brillouin-quadratic laser and frequency comb generation can be achieved by combining XP-SBS with polarization-dependent quadratic nonlinearity (Fig. 2a shows the experimental setup). In Fig. 4a, the p-polarized SBL generated from the s-polarized pump can efficiently generate the second-harmonic (SH) signal at 775 nm through type-I phase matching (ordinary wave (o) + o→extraordinary wave (e)) with a nonlinear coefficient of d_eff = 2.8 pm V^–1. The output SH power reaches as high as 217 mW when the pump power is 1,800 mW (Fig. 4b), corresponding to a conversion efficiency of 12%. A higher output SH power is expected by optimizing the cavity parameters such as the output coupling⁵³. The fundamental linewidth of the generated SH light (Fig. 4c) is measured to be 2.8 Hz (Fig. 2i), which is 6 dB larger than the p-polarized SBL, in good agreement with the theoretical prediction.

Fig. 4: Efficient Brillouin-quadratic laser and frequency comb.

a–c, XP-SBS process: s–p; second-harmonic generation (SHG) process: type-I phase matching, o + o→e. a, Schematic of the whole processes. f, frequency. b, Output power of the first-order SBL and its SH as a function of the input pump power. Total powers of SBL and its SH are plotted as the black dotted points. The total power conversion efficiencies are plotted as the blue dotted points. c, Optical spectrum of the SBL SH. d–f, XP-SBS process. p–s; quadratic processes: type-0 phase matching, e + e→e or e→e + e. d, Schematic of the whole processes. SFG, sum-frequency generation; DFG, difference-frequency generation; OPG, optical parametric generation. e, Optical spectrum of the Turing comb centred at 1,540.8 nm. The inset shows the large SR between the pump and XP-SBL. f, Optical spectrum of the Turing comb centred at 770.4 nm. All the lasers and frequency combs are in their fundamental modes.

In Fig. 4d, we first generate an s-polarized SBL from a p-polarized pump and then utilize the type-0 phase matching (e + e→e), with an even larger d_eff = 15.2 pm V^–1, for quadratic frequency comb generation resulting from four cascaded quadratic nonlinearities: SH generation, optical parametric generation, sum-frequency generation and difference-frequency generation⁵⁴. In Fig. 4e,f, we plot the Turing comb spectra at both fundamental and SH bands. We also observe chaotic comb generation (Supplementary Fig. 15). This Article presents a demonstration of Brillouin-quadratic laser and frequency comb generation.

Of note, the pump experiences no quadratic nonlinearity but only efficiently transfers the energy to the XP-SBL. In contrast to direct visible SBL generation in microresonators whose noise suppression is limited by a large cavity loss⁵⁵, the demonstrated visible Brillouin-quadratic laser and frequency comb take full advantage of the narrow SBL linewidth at the near-infrared band. Similar to our previously reported Brillouin–DKS comb generation^23,24,25, we anticipate feasible Brillouin-quadratic soliton comb generation⁵⁶ with an ultralow fundamental linewidth and timing jitter through dispersion engineering, for example, in LNOI microresonators, fulfilling the long-sought need for high-coherence laser sources across a range of applications.

Discussion

XP-SBS gain in different platforms

The strong XP-SBS gain is primarily determined by the large non-diagonal photoelastic coefficient³², which depends on both crystal type and orientation. It has been found that XP-SBS gain is common in birefringent ferroelectrics³², such as LN, BiFeO₃ (ref. ³²) and LiTaO₃ (ref. ⁴³). In our z-cut x-propagation LN (3m point group), the XP-SBS gain is determined by the large non-diagonal photoelastic coefficient p₄₁. However, if the LN crystal orientation is changed to z-cut y propagation, the non-diagonal photoelastic coefficient p₅₁ becomes zero due to the crystal symmetry, resulting in no XP-SBS gain³².

Among the birefringent ferroelectrics with large XP-SBS gain, LN crystals are particularly promising due to their potential for integrating various important optical effects and extending to the LNOI platform (see the ‘Outlook: expanding to the LNOI platform’ section). For example, in addition to the already-utilized thermo-optic effect, other effects such as the electro-optic effect, acousto-optic effect and photorefractive effect³¹, among others, can be leveraged for faster birefringence tuning.

Although we have previously observed the SBS process between orthogonal polarizations in low-birefringence-fibre Fabry–Pérot cavities^23,25, it is distinctly different from the XP-SBS gain in LN crystals, as fibres do not have any non-zero non-diagonal photoelastic coefficients. In low-birefringence fibres, the effective XP-SBS gain results from the polarization rotation of both pump and SBL⁵⁷. On the other hand, no XP-SBS gain is observed in polarization-maintaining fibres⁵⁸.

Outlook: expanding to the LNOI platform

This Article presents a comprehensive study of the SBS properties in bulk PPLN crystals and the initial conceptual demonstrations of SBS-based devices in a free-space LN cavity. With the rapid progress in LNOI PIC technology, the on-chip implementations of SBS-enabled devices are becoming increasingly feasible^{35,43,59,60,61,62,63,64,65,66,67,68}. In particular, CP-SBL has been recently demonstrated in an LNOI racetrack resonator⁵⁹, and an XP-SBS gain of ~0.37 cm GW^–1 has also been observed in an LNOI waveguide³⁵. Although the Q factor is 100 times lower and the observed on-chip SBS gain coefficient is currently 50 times lower than that of the free-space cavity, the experimental SBL threshold is at the same level of ~100 mW (refs. ^59,69) owing to the 500,000-fold smaller mode volume. Moreover, LNOI PIC fabrication has been optimized to reach a propagation loss as low as 0.2 dB m^–1, supporting a Q factor greater than 100 million⁶². Besides, the photonic design has been numerically shown to enable the tailoring of both Brillouin gain coefficients and bandwidths³³. These advances point towards the imminent realization of more power-efficient SBS on the LNOI PIC platform. Parallel progress in nonlinear LNOI PIC has enabled on-chip soliton microcombs through Kerr nonlinearity^61,62, as well as quadratic microcombs⁶³, broadband frequency conversion^64,65 and all-optical switching⁶⁶ via quadratic nonlinear processes. Recent demonstrations of multiplexing devices on the LNOI PIC platform further enable on-chip mode sorting following the mode converter^67,68. Overall, the core components enabling XP-SBS-empowered photonics have already been demonstrated independently on the LNOI PIC platform. As such, the results presented in this study are directly transferable to integrated photonic implementations. The prospect of monolithic integration with other LNOI-based functionalities further positions this material system as a leading candidate for next-generation, highly functional PICs⁴³.

Note added in proof: During the preparation of this manuscript, we became aware of the work by Rodrigues et al.³⁵ and Ye et al.⁵⁹ reporting SBS in LNOI PIC.

Methods

Experimental details

The free-space cavity is a four-mirror bow-tie cavity with an FSR of 397 MHz. Three reflective mirrors (M1–M3) are coated with high reflectivity of >99.95% from 1,530 nm to 1,580 nm. The output coupler is coated with high reflectivity of 1.03% from 1,530 nm to 1,580 nm. The four mirrors are coated with high transmission of >95% from 760 nm to 790 nm. Both end facets of the 25-mm-long 5% MgO-doped PPLN crystal are coated with high transmission at 1,550 nm and 775 nm (reflectivity of 0.13% at 1,550 nm and 0.09% at 780 nm). The cavity linewidth and Q factors are measured using a frequency-calibrated Mach–Zehnder interferometer (MZI) with an FSR of 0.998 MHz. The offset frequency between the two orthogonally polarized modes (within one cavity FSR; Fig. 2d) is measured using the same MZI with the scanned pump frequency, and the pump is linearly polarized at 30° with respect to p polarization. The input power and output power are measured from the output coupler.

The cross-section of the PPLN crystal is 12.3 mm × 1 mm, which is much larger than the beam diameter of ~100 μm inside the crystal. There are ten poling periods in the PPLN crystal, including a poling period of 20.6 μm for type-I phase matching at ~1,550 nm and a poling period of 19.1 μm for type-0 phase matching at ~1,541 nm. The PPLN crystal is temperature controlled with a resolution of 10 mK and the whole cavity is enclosed in a plastic box to prevent heat exchange with the ambient environment. When the PPLN crystal temperature deviates from the phase-matching condition for cascaded quadratic processes, an efficient XP-SBS process is still possible since there are multiple temperature points for perfect SBS phase matching. XP-SBS phase matching is more sensitive to temperature compared with quadratic nonlinearity phase matching. In the experiments of reconfigurable XP-SBL and efficient mode converter, another poling period is chosen such that the large phase mismatch (>20π) leads to negligible quadratic nonlinearity.

The pump laser (Toptica CTL1550) is loaded into the cavity via free-space components with efficient mode matching. The pump is locked to the free-space cavity for efficient SBL generation via the powerful Pound–Drever–Hall (PDH) technique. The phase modulation frequency is 1 MHz and the PDH error signal is obtained from the processed pump output from M2. The low-pass filter used in the demodulation of the PDH signal is 80 kHz. The modulation voltage of the phase modulator is chosen to be low without perturbing the SBL generation.

The optical spectra are measured by separately coupling the near-infrared and visible lights into the corresponding single-mode fibres. The optical power of SBL from the output coupler is calculated by the output power from the mirror M3 and the transmission ratio between the output coupler and mirror M3. The Brillouin frequency shifts are measured from beating the residual pump and the generated SBL.

The cascaded quadratic nonlinearities result in effective Kerr nonlinearity, which depends on the mismatches in both phase and group velocities. In Fig. 4a–c, the near-zero group-velocity mismatch and the perfect phase matching lead to zero effective Kerr nonlinearity⁴⁰, no modulation instability and no comb generation. However, in Fig. 4d–f, the large group-velocity mismatch (~300 fs mm^–1) and the perfect phase-matching result in a large effective Kerr nonlinearity, strong modulation instability and strong comb generation⁵⁴.

LN material properties

The photoelastic tensor of LN is given by the 6 × 6 matrix³¹

where p₁₂ = 0.09, p₃₁ = 0.179 and p₄₁ = 0.151 (ref. ⁴³) determine the SBS gain coefficients for p–p polarization conversion, s–s polarization conversion and cross-polarized conversion (p–s or s–p polarization conversion)³², respectively.

SBS gain property calculation

Assuming both pump and SBL modes are with their fundamental mode (HG₀₀ mode), the SBL output P_B in a free-space cavity is given by⁵³

where

P_in is the input pump power, w₀ = 50 μm is the beam radius inside the crystal, R = 0.9897 is the reflectivity of the optical coupler mirror, L = 0.004 is the other total passive intracavity loss, η_oo is the optical mode overlap between the pump and SBL mode (we use 0.9 for the cross-polarized case due to astigmatism and use 0.95 for the co-polarized cases), g_B is the Brillouin gain coefficient and l_eff is the effective SBS interaction length, which is determined by

where l = 25 mm is the LN crystal length and b is the confocal parameter given by

Here n is the refractive index and λ_p = 1.55 μm is the pump wavelength. By substituting the experimental input pump and output SBL power into equation (3) and conducting a fitting, we can obtain the Brillouin gain coefficient.

With the Brillouin gain coefficient, we can calculate the spontaneous Brillouin gain bandwidth through⁷¹

where η_oa = 0.95 is the estimated overlap integral between the optical-mode- and acoustic-mode-induced density change, p is the photoelastic coefficient characterizing the SBS process, c is the speed of light, ρ = 4,647 kg m^–3 is the density, v_B is the Brillouin frequency shift and Δv_B is the Brillouin gain bandwidth.

The Brillouin frequency shift can be calculated as

where υ_s = 6,572 m s^–1 is the speed of the longitudinal acoustic wave in LN crystals^33,72. In the case of the co-polarized case with p–p polarization conversion, n = n_o = 2.2118 and Ω_B is calculated to be 18.755 GHz. In the case of the co-polarized case with s–s polarization conversion, n = n_e = 2.1376 and Ω_B is calculated to be 18.126 GHz. In the case of the cross-polarized case, n = (n_o + n_e)/2 = 2.1747 and Ω_B is calculated to be 18.435 GHz.

Measurement of fundamental linewidth

Two self-heterodyne frequency discriminators using a fibre-based unbalanced MZI and a balanced photodetector are used to measure the laser phase noise and fundamental linewidth for SBL and its SH, respectively. For both discriminators, one arm of the unbalanced MZI is made of a 250-m-long single-mode fibre, whereas the other arm consists of an acousto-optic frequency shifter with a frequency shift of 200 MHz and a polarization controller for a high-voltage output. The FSRs of the unbalanced MZI are 0.85 MHz and 0.81 MHz for 1,550 nm and 775 nm, respectively. The two 50:50 outputs of the unbalanced MZI are connected to a balanced photodetector with a bandwidth of 400 MHz to reduce the impact of detector intensity fluctuations. The balanced output is then analysed by a phase noise analyser (NTS-1000A, RDL). We do not measure the linewidth of the generated visible Turing comb due to the lack of an optical filter. According to the measured results at ~1,545 nm, the visible comb linewidth should have the same fundamental linewidth with its pump (SH of the generated SBL), which is 6 dB larger than the generated SBL.

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