Intrinsic cascade-free intramode scattering Brillouin laser

Brillouin lasers (BLs) with low-noise and narrow linewidth characteristics have been applied as an important approach for laser gyroscopes,^1,2 low-noise microwave signal generation,^3–5 and optical atomic clocks.⁶ Unlike conventional lasers, the Stokes gain arises from strong nonlinear light-sound coupling through the process of stimulated Brillouin scattering (SBS), which exceeds the strength of Kerr and Raman interactions in most transparent media.⁷ In a Brillouin platform, the combination of a high-Q cavity with the rapid damping of acoustic phonons provides a practical route to laser linewidths potentially lower than conventional single-frequency lasers.^2,8

Low threshold operation is achieved by tailoring a cavity to provide resonances at the pump and first Stokes frequencies. However, this generally also leads to good overlap of a cavity mode with the second Stokes so that its threshold is low and there is a small range of cascade-free operation.⁹ The limited single-frequency output power restricts the further narrowing of the BL linewidth in the adiabatic approximation.^2,10 In addition, the low power level prevents BLs from serving in high-power scenarios, such as quantum information processing and gravitational wave detection, thus limiting their further development slightly.^11,12

Efforts have been made to address the problem of single frequency power scaling of BLs. In the context of integrated waveguides, one method of suppressing the cascade has been through the use of inter-modal interactions. By tailoring the design to reduce the ratio of the coupling strengths for the second and first Stokes,^8,13 a single-frequency output power of 126 mW was achieved with an accompanying reduction in the Stokes linewidth to 0.245 Hz.¹⁴ The threshold of high-order Stokes will be increased while increasing the single-frequency Brillouin power by optimizing the coupling mirror reflectance. The corresponding design makes the single-frequency output power promising for approaching the limit of quantum conversion efficiency.^15–17 

Despite the impressive results of these studies, the problems that accompany BL development remain troubling. The miniaturized structure of the integrated BL causes detuning of the Stokes gain owing to the thermal accumulation of the cavity during the power boost, resulting in power clamping of the single-frequency BL power curve that occurs only when higher-order frequency components are generated.^2,18,19 This limits the ability of inter-mode scattering for power enhancement in high-power operation scenarios.¹⁴ Although the optimized coupling mirror reflectivity in spatially structured BLs achieves a single-frequency power improvement,¹⁴ the reduced Q value inevitably weakens the pump phase noise suppression and increases the intrinsic linewidth of the corresponding BLs.^20–22 All the above-mentioned problems restrict BL from achieving ultra-narrow linewidth high-power laser radiation to some extent.

In previous studies, it was observed that the suppression of higher-order Stokes frequency components to anticipate single-frequency power improvement is accomplished by regulating the mode structure of the Brillouin cavity; however, the key factor for the generation of the phase-matching condition is the matching of the free spectral range (FSR) with the phonon frequencies of the medium. Selecting Brillouin scattering properties for suppressing the Stokes cascade rather than manipulating the cavity mode structure can lead to stronger acousto-optical interactions, resulting in higher acousto-optical gain and laser conversion efficiency. Furthermore, the diversity of Brillouin gain material choices can mitigate gain detuning owing to thermal effects to a certain extent. It is promising to achieve BL single-frequency power scaling without sacrificing cavity Q or careful design of the intracavity mode structure.

This study provides a detailed analysis and experimental validation of the phase-matching conditions for cascade operation in a resonantly pumped intramode scattering BL as a function of the cavity and gain medium parameters. The remainder of this paper is organized as follows. Section II presents the maximum cascade order determined by the Brillouin platform in relation to the BL system parameters. Based on the analytical results, Sec. III demonstrates an intramode scattering high-power BL without Stokes cascade distress, and so forth, we analyzed and discussed the feasibility of the single-frequency operation of this laser over a wide range of cavity Q values.

The BL cascade is closely related to the corresponding cavity parameters and gain medium properties. In the adiabatic approximation, the dispersion of the Brillouin frequency shift is the dominant factor for the gain shift of the higher-order Stokes. Table I provides a comparison of the cascade orders of BLs reported in the literature and maximum cascade order calculated using the above equations. From Eqs. (6) and (7), the refractive index, sound velocity, and gain bandwidth determined the maximum order after the cavity parameters were established. The first material to realize micro-waveguide BL radiation, CaF₂, has parameters close to those of silica, but its narrow gain bandwidth, strict phase-matching conditions, and low gain coefficient lead to an experimentally reported obtainable cascade order of only the second order.⁸ Similarly, a disk-shaped fused-silica cavity with tightly controlled cavity length processing (FSR tolerance of 0.5 MHz) yields a ninth-order Stokes cascade limited by the pump power, as shown in Table I.^18,19 The Si₃N₄ waveguide cavity designed by Chauhan et al. was used only to confine the propagation of light, whereas the properties of Brillouin scattering depend more on the waveguide cladding (silica). This structure also caused the acoustic field to be significantly more attenuated than that in fused silica,² resulting in a Brillouin gain linewidth of ∼290 MHz, which also leads to a cascade order of 163 for this structure. Similarly, limited by the available pumping power, only first-order Stokes light output has been experimentally observed.¹⁰ 

Among the materials for which BLs have been realized, diamond has a far greater refractive index and velocity of sound than other materials.²⁸ Diamond-based BLs have obtained radiation from the visible to near-infrared wavelengths.^16,27 Assuming that the second-order Stokes also satisfies the phase-matching condition, the power model of the spatially structured cascaded BL shows that the second-order Stokes threshold is four times that of the first-order Stokes threshold.¹⁵ The corresponding power output curve exhibited no clamping when the pump power reached four times the first-order Stokes light threshold while operating in the visible range.²⁷ The difference between the gain center frequency of the second-order Stokes and cavity mode, ∆_S,2, can be calculated using the corresponding parameters to reach 51 MHz, which far exceeds the full width of the diamond Brillouin gain corresponding to this band (0.85 × 16.9 MHz). At 1064 nm pumping, the difference between the gain center frequency of the second-order Stokes and cavity mode, ∆_S,2, also reaches 21 MHz, which is more than half of the full gain linewidth (0.85 × 5.3 MHz). The Brillouin gain coefficient of diamond in the NIR region is smaller than that in the visible band, which leads to a threshold power of ∼30 W.¹⁶ The available pump power failed to meet the theoretical excitation threshold (∼120 W) for second-order Stokes phase matching, suggesting that the power curve without clamping was not sufficient to indicate that a higher-order Stokes frequency component was not generated. In addition, the corresponding forward output spectra were not rigorously verified in previous experiments. Therefore, the corresponding conclusions must be verified by actively increasing the reflectivity of the coupling mirror and then verifying whether the corresponding first-order power output curve is clamped and whether the corresponding forward output has a second-order spectrum.

The laser setup and spectral measurement configuration used to verify the cascade characteristics of the diamond BL are illustrated in Fig. 2. An optical diagram of the BL system is shown in Fig. 2(a), where the pump laser is obtained based on a narrow-linewidth single-frequency seed laser amplified to reach the cavity with a maximum available power of 60 W and a linewidth of 7.36 kHz. The Brillouin cavity was a ring cavity with an FSR of ∼560 MHz. The pump light was injected into the cavity after passing through the focusing lens sets f1 and f2 to coincide with the TEM₀₀ mode inside the cavity. The diamond in the cavity is placed on top of a purple copper heat sink, and the temperature is actively controlled to 20 °C by an electric cooling element. The double resonance point of pump and Stokes is found by adjusting the length of the cavity. At the current FSR, the double resonance points of the appear every 3.8 mm.^16,26 The resonant frequency of the cavity was aligned with the injected pump frequency by PDH active-frequency stabilization to achieve intracavity resonance enhancement of the pump, lower the BL threshold, and improve the corresponding Stokes conversion efficiency.²⁹ The light reflected from the cavity contains a pump and an even-order Stokes output. Light from the backward output (after ISO separation) contains an odd-order Stokes output. Figure 2(b) shows the spectral measurement structure, where the forward and backward outputs from the cavity are coupled into the fiber through a collimator, combined by a 3 dB coupler and fed to the optical spectrometer for measurement.

Experimentally, to obtain a high-order Stokes output at the available pump power, the reflectivity of the coupling mirror must be increased to minimize the threshold as much as possible. The passive loss L₀ in the cavity was ∼1.5% because of the incomplete reflection of the cavity and presence of the Brewster element. There may be some differences in the corresponding passive losses because of the requirement for readjustment of the resonant cavity after each coupling mirror replacement. The resonant positions of the corresponding pump and Stokes signals remain unchanged after the coupling mirror is replaced. Hence, the corresponding beam waist sizes are still ∼76 µm. To ensure that the corresponding Stokes thresholds predicted by the model matched the actual threshold power, we measured the pump loss through the remaining optical elements after removing the coupling mirror at the end of the experiment. The corresponding data were used to calculate the first- and second-order Stokes thresholds corresponding to different reflectivity coupling mirrors and were compared with the experimental data shown in Table II.

The second-order Stokes light thresholds corresponding to 96% and 97% reflectance reached 108 and 96.3 W, respectively, thus failing to excite the second-order Stokes light at the available pump power (60 W). The corresponding second-order Stokes threshold was 44.6 W when the coupling mirror reflectance was 98.5%. Considering the impedance matching of the cavity, a further increase in the coupling mirror reflectivity cannot lower the second-order Stokes threshold because the passive loss of the system is ∼1.5%. The experimentally obtained first-order Stokes thresholds corresponding to the three sets of reflectivity-coupled mirrors differed slightly from the model predictions such that the predicted corresponding second-order Stokes thresholds were valid. The first-order Stokes optical power output curves corresponding to the three sets of reflectivity-coupling mirrors are shown in Fig. 3.

Interestingly, when the coupling mirror reflectivity was 98.5%, the pump optical power exceeded the theoretically predicted second-order Stokes threshold (44.6 W), and the corresponding Stokes output curve did not show a clamp phenomenon, as predicted by the model after reaching 10.9 W. As the pumping power increased to 60 W, the Stokes output power reaches a level of 13.6 W. To further illustrate that no second-order Stokes optical frequency components were generated, we acquired the forward and backward output spectra of the BL system pumped at 60 W with locked and unlocked pump frequencies, as shown in Fig. 4. After locking, the intensity of the pump reflected from the cavity decreases, at which time the intensity of the first-order Stokes light is comparable to the remaining pump power; however, there is no second-order Stokes frequency component presented. Therefore, the resonantly pumped diamond BLs do not perform cascade operations.

Note that the coupling mirror reflectivity of 98.5% corresponds to a cavity mode width of 2.68 MHz, which does not satisfy the adiabatic approximation compared with the Brillouin gain width of 5.3 MHz. However, because diamond has the highest refractive index and speed of sound among all Brillouin gain materials, the difference between the second-order Stokes mode and gain center frequency reaches a level of 21 MHz even without considering the frequency pulling effect, which is much larger than half the full width of the gain; therefore, second-order Stokes is not generated at the current Q value of the cavity and higher Q values. Increasing the cavity mode linewidth by decreasing the Q value to achieve a corresponding second-order Stokes phase match does not work because of the increase in the second-order Stokes threshold owing to the reduced reflectivity of the coupling mirror.^15,30 Consequently, diamond BLs can be parameter modulated over a wide range of Q values that are not plagued by the Stokes cascade.

The output parameters of Brillouin lasers for several different materials using inter-mode and intra mode scattering are given in Table III. As the first Brillouin laser realized in silicon, the corresponding Stokes output power is only 0.15 mW due to the high loss of the silicon material and the low power density of the antisymmetric mode. In contrast, a Stokes light output of 126 mW was achieved using the resonance of the fundamental mode combined with a low-loss silica resonator. It can also be seen that the output power of conventional intramode scattering is limited by the higher-order Stokes frequency generation, resulting in a single-frequency output power in the milliwatt level. Finally, the diamond Brillouin laser demonstrated in this work enables an even higher power outputs owing to the inherent cascade-free nature of diamond. It is also worth mentioning that the linewidth of the diamond Brillouin laser is consistent with the previously reported ones, which is about 1.7 kHz.²² 

Benefiting from the inherently high Brillouin gain coefficient of diamond (80 cm/GW at 532 nm) and high thermal conductivity (>2000 W/K), the use of diamond as a gain medium combined with advanced integration processes gives diamond BLs the potential to achieve high-power ultra-narrow linewidth laser radiation on an integrated platform.³¹ Furthermore, the transmission range (>0.23 µm), which is much larger than that of Si₃N₄ material, provides new insights into narrow linewidth laser generation for a wider range of special wavelengths for integrated platforms.³² 

In this study, we analyze the fundamental factors of the cascade operation generation of resonantly pumped BLs and the corresponding higher-order Stokes light suppression methods from the perspective of the cascade phase matching of intra-mode-scattering BLs. Using a Brillouin gain medium with a large refractive index, a large sound velocity and narrow gain linewidth have been shown to significantly reduce the Stokes cascade order. The BLs using diamond as the gain medium yielded no higher-order Stokes radiation over a wide range of Q values when the cavity FSR was significantly larger than the Brillouin gain linewidth. The experimental results show that the corresponding power curves do not exhibit clamping phenomena and that there is no second-order Stokes frequency component in the output spectra when collecting the forward and backward output spectra under pumping conditions after exceeding the second-order Stokes threshold. This study provides a possibility for the realization of high power ultra-narrow linewidth single frequency Brillouin lasers. Furthermore, combined with advanced processing and integration processes, the use of diamond as a Brillouin medium can provide a novel perspective for laser radiation at special wavelengths with high power and narrow linewidths on integrated platforms.

This work received funding from the National Natural Science Foundation of China (Grant No. 61927815), the Natural Science Foundation of Tianjin City (Grant Nos. 22JCYBJC01100, and 20JCZDJC00430), the Program of State Key Laboratory of Quantum Optics and Quantum Optics Devices (Grant No. KF202201), and the Funds for Basic Scientific Research of Hebei University of Technology (Grant No. JBKYTD2201).

D.J. acknowledges the support from the China Scholarship Council (CSC) (Grant No. 202206707003). R.P.M. acknowledges the support from the Asian Office of Aerospace Research and Development (AOARD).

The authors have no conflicts to disclose.

Duo Jin: Conceptualization (lead); Investigation (lead); Writing – original draft (lead); Writing – review & editing (lead). Zhenxu Bai: Conceptualization (equal); Investigation (equal); Methodology (equal); Supervision (lead). Yifu Chen: Investigation (equal); Software (equal). Wenqiang Fan: Investigation (equal). Yulei Wang: Conceptualization (equal); Investigation (equal); Methodology (equal); Project administration (equal). Zhiwei Lu: Conceptualization (equal); Project administration (equal); Supervision (equal).

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