Brillouin lasers providing extremely narrow-linewidth are emerging as a powerful tool for microwave photonics, coherent communications, quantum processors, and spectroscopy. So far, laser performance and applications have been investigated for a handful of select materials and using guided-wave structures such as micro-resonators, optical fibers, and chip-based waveguides. Here, we report a Brillouin laser based on free-space laser action in an extreme optical material. Continuous-wave lasing 167 GHz from a 532 nm pump is demonstrated in diamond using a doubly resonant ring cavity, generating a pump-limited output power of 11 W. The Brillouin gain coefficient is measured to be 79 cm GW−1 with a linewidth of 12 MHz. These properties, along with an exceptionally high Brillouin frequency and wide transmission range, make diamond Brillouin lasers a promising high-power source of narrow-linewidth output and mm-wave beat notes.

Brillouin lasers rely on the optical gain by stimulated inelastic scattering from an induced hypersonic wave in a material.1 This effect brings forth a range of interesting gain properties set well apart from inversion lasers including sub-GHz gain linewidths and an inbuilt mechanism for reducing phase noise.2–5 The frequency shift is typically in the tens of GHz range, which provides a path toward photonic-based microwave synthesis,6 as well as a lasing process with exceptionally low loss (≪1%) through the quantum defect (hνphνs, where h is the Planck constant and νp and νs are the frequencies of pump and Stokes, respectively) compared to that of inversion lasers and Raman lasers. Some of these features have been applied in narrow-linewidth fiber lasers7–9 and more recently as on-chip lasers for narrow-linewidth microlasers and a diverse range of other functions in microwave photonics,6,10,11 optical gyroscopes,12 frequency metrology,13 and spectroscopy.14 One disadvantage associated with Brillouin lasers is that the gain is through a third-order nonlinear process so that coupling is typically much weaker compared to that of second-order. As a result, devices have been restricted to select materials such as chalcogenide,15–17 silica,18,19 CaF2,20 AlN,21 Si3N4,4 and silicon1 and combined with low-loss waveguides to attain threshold.

Diamond possesses a range of extraordinarily features including a high thermal conductivity (2000 W/mK), high optical damage threshold (>1 GW cm−2), and wide transparency range (225–3800 nm).22 The Brillouin frequency ΔνB = 2nvaνp/c for backscattering is markedly higher than all other optical materials due to its high refractive index (n ∼ 2.4), high acoustic velocity (va ∼ 18 km s−1), and compatibility for pumping at high frequencies νp.23 By tuning the pump frequency up to the bandgap, Brillouin frequencies into and across the entire mm-wave band (up to 300 GHz) are feasible where there are important applications in high frequency radar24 and high bandwidth wireless communications.25 In contrast, Brillouin frequencies for other stimulated Brillouin scattering (SBS) materials are typically constrained to the microwave band (<30 GHz). Therefore, diamond is an interesting candidate for high-power and low-threshold Brillouin lasers operating across a large range of the optical spectrum while providing frequency side bands spanning the mm-wave region. Recently, a diamond Brillouin laser (DBL) was demonstrated using the intense intracavity pump field in a diamond Raman laser, exhibiting a diverse array of output behavior including cascaded Brillouin lines, anti-Stokes comb, and quasi-cw output power up to 40 W (on-time power for 0.2 ms).23,26 This work increased the possibility for low-threshold and high-power DBLs, including designs that could avoid the Raman pumping intermediate step.

In this Letter, we report an external-cavity DBL in a free-space optical format. Using a 5 mm diamond in a stabilized ring-cavity frequency-locked to the pump laser, output powers up to 11 W are attained. A value for the Brillouin gain coefficient is determined for the first time using the laser threshold. The Brillouin gain linewidth of diamond is determined via two methods—using the gain coefficient with published photo-elastic coefficients and a novel frequency scanning method. The combination of a high frequency pump and the high Brillouin frequency of diamond produces a single Stokes sideband in the mm-wave band at 167 GHz. The demonstration of the free-space operation provides future options for conceptually simple Brillouin designs for beam coupling, resonator mirrors, and intracavity incorporation of other optical elements, as well as provides a first-step toward diamond waveguide Brillouin lasers.

To reduce the Brillouin lasing threshold, the cavity length is adjusted so that both the pump and Stokes frequencies coincide with cavity resonances, as in Fig. 1(a). This condition corresponds to cavity lengths Lcav,
Lcav=mcΔνB,
(1)
where m is a positive integer and c is the speed of light. A ring cavity, allowing the counterpropagation of the pump and the Stokes fields, was adopted to avoid Kerr four-wave-mixing and cascaded SBS, as shown in Fig. 1(b). The pump laser was a 532 nm linearly polarized single-frequency fiber laser (IPG Photonics, GLR-100) with a linewidth of 1 MHz. A Brewster-cut single crystal CVD diamond (Element Six Ltd.) of length 5 mm was placed in a 50 cm-long ring-cavity that produced a 53 µm TEM00 mode radius in the diamond. The pump polarization angle and the Brewster facet were configured for polarization aligned to the diamond ⟨111⟩ axis. The pump was mode-matched into the cavity fundamental mode using a telescope, and the folding angle of the cavity was chosen according to the Brewster crystal used to compensate the cavity astigmatism. The cavity mirror M2 was mounted on a piezoelectric translator (PZT) for cavity scanning and locking. The cavity length was set manually first and then automatically stabilized using the Hänsch–Couillaud locking scheme so that the FSR matched an integer sub-multiple of the Brillouin frequency shift. Leakage of the pump and Brillouin laser from M4, which are spatially separated since they are counterpropagating, enabled the straightforward detection of the presence of the Brillouin laser and, from the known transmission, the determination of the intracavity pump intensity at threshold. The total round-trip loss was measured to be 6.0% ± 0.1% (including the 4% transmission of the input coupler).
FIG. 1.

(a) Schematic showing the double-resonance condition for the DBL cavity with the FSR about 600 MHz (cavity length ∼0.5 m). νp and νs are the frequencies of pump and Stokes, respectively. (b) The ring-cavity layout. T, telescope; λ/2, half-wave plate; M1, plane input/output-coupler mirror with R = 96% at 532 nm; M2, plane mirror with R = 99.98% at 532 nm; M3 and M4, concave mirrors with radius of curvature 100 mm and R = 99.98% at 532 nm; diamond, 4 × 1.2 × 5 mm3 Brewster-cut single crystal diamond; PZT, piezoelectric translation stage; M5, partial reflection mirror at 532 nm; λ/4, quarter-wave plate; PBS, polarizing beam splitter; PD1 and PD2, photodiodes; and PID, feedback controller circuit.

FIG. 1.

(a) Schematic showing the double-resonance condition for the DBL cavity with the FSR about 600 MHz (cavity length ∼0.5 m). νp and νs are the frequencies of pump and Stokes, respectively. (b) The ring-cavity layout. T, telescope; λ/2, half-wave plate; M1, plane input/output-coupler mirror with R = 96% at 532 nm; M2, plane mirror with R = 99.98% at 532 nm; M3 and M4, concave mirrors with radius of curvature 100 mm and R = 99.98% at 532 nm; diamond, 4 × 1.2 × 5 mm3 Brewster-cut single crystal diamond; PZT, piezoelectric translation stage; M5, partial reflection mirror at 532 nm; λ/4, quarter-wave plate; PBS, polarizing beam splitter; PD1 and PD2, photodiodes; and PID, feedback controller circuit.

Close modal

At the mirror position for dual-resonance, Brillouin lasing is observed in the back-scattered direction. We coupled the pump and SBS into a Fabry–Perot interferometer (FPI) with an FSR of 90 GHz and resolution 2 GHz at 532 nm to produce interferograms for off- [Fig. 2(a)] and on-resonance conditions [Fig. 2(b)]. The Brillouin frequency shift appears as a second-order fringe at 167 ± 1 GHz, consistent with the theoretical value 166.79 GHz using νp = 563 910 GHz, n = 2.43, and νs = 563 743 GHz for a longitudinal acoustic mode along the [110] direction.27 We expect the actual laser linewidth to be much less than the FPI resolution, dictated by the cavity noise properties, and potentially narrower than the pump linewidth.5,28

FIG. 2.

Fabry–Perot interferogram images and line-scans for (a) pump only and (b) pump plus Brillouin lasing. The Brillouin laser line appears as a second-order fringe.

FIG. 2.

Fabry–Perot interferogram images and line-scans for (a) pump only and (b) pump plus Brillouin lasing. The Brillouin laser line appears as a second-order fringe.

Close modal

Figure 3 shows the output power and intracavity pump power as a function of input pump power. The lasing threshold (defined as the intercept of the slope efficiency) was 5 W, which corresponded to 150 W of the intracavity pump power. Above the threshold, the intracavity pump power remained nearly constant and the output power increased monotonically with slope efficiency 41%. At the maximum input pump power available, the output power from the input coupler M1 was 11 W with 34.4% conversion efficiency. To the best of our knowledge, the power is 10 times higher than the previous highest reported,29 for any continuous wave Brillouin laser. The inset of Fig. 3 is the near-field profile of the output beam showing a TEM00 mode. Considering the excellent thermal properties of diamond as well as the extremely low thermal load, higher output powers are anticipated when using higher pump powers. No cascading SBS is observed in our experiment even at the maximum pump power, despite the substantial Stokes intracavity power (>350 W). In our case, the two mechanisms for cascading, four-wave-mixing and higher-order Stokes generation, are both suppressed. Four wave mixing is suppressed as the pump and Stokes are counterpropagating in the ring laser, and therefore, the process is far from phase-matched.25 Higher-order Stokes modes are suppressed as the second Stokes is well displaced from the nearest longitudinal cavity mode as a result of the ΔνB dependence on the shifted drive frequency νp − ΔνB.26,30

FIG. 3.

Output Brillouin laser power and intracavity pump power as a function of pump power. Inset: beam profile of the DBL output.

FIG. 3.

Output Brillouin laser power and intracavity pump power as a function of pump power. Inset: beam profile of the DBL output.

Close modal
At the threshold, the overall gain g0IL is equal to the round-trip loss of the cavity, where g0 is the SBS gain coefficient, I is the pump intensity, and L is the length of diamond. Therefore, using the above values for the round-trip loss of the cavity, pump waist, and threshold intracavity power, the Brillouin gain coefficient is g0 = 60 ± 9 cm/GW. In terms of the photoelastic coefficient p, the steady-state Brillouin gain coefficient g0 is26,31
g0=n7p2ωs2ρvac3ΓB,
(2)
where ρ (=3.52 g cm−1) is the mass density, ωs is the Stokes angular frequency, and ΓB/(2π) is the Brillouin gain linewidth. For the present case of pump and Stokes polarizations aligned parallel to ⟨111⟩, the corresponding photoelastic coefficient p2 = 0.0153.27 Since p2 maximizes for pump and Stokes polarizations aligned to ⟨110⟩, as shown in Fig. 4, we deduce that Brillouin gain coefficients up to 79 ± 12 cm/GW can be obtained (p2 = 0.0202). We note that the tensor properties of the Brillouin gain coefficient are different from those of the Raman nonlinearity [see Fig. 1.12(d) in Ref. 22]. Hence, advanced devices may be configured to exploit either coupling or de-coupling of two nonlinearities through controlling polarization.
FIG. 4.

p2 as a function of pump and Stokes polarizations for Brillouin backscattering from longitudinal phonons propagating along [110].

FIG. 4.

p2 as a function of pump and Stokes polarizations for Brillouin backscattering from longitudinal phonons propagating along [110].

Close modal
As a means of measuring the Brillouin gain linewidth, we utilize the fact that scanning the cavity length enables a cavity mode to be scanned through the gain profile. The linewidth is then deduced by measuring the lasing threshold and therefore gain as a function of cavity length detuning. Figure 5(a) shows the detuning of the nearest mode from the gain peak as a function of cavity length, with the cavity resonant with the pump frequency (by monitoring the threshold only at these double resonance conditions). From Eq. (1), the scan length required to regain the double resonance condition is ΔL = c/ΔνB, which is 1.8 mm in our experiment. The longitudinal-mode-spacing (cavity FSR) is 600 MHz, as also indicated in Fig. 5(a), so that the slope k of the frequency offset with cavity length, given by
k=c/Lcavc/υpυs=ΔυBLcav,
(3)
is −0.33 MHz/μm. Hence, as shown in the inset of Fig. 5(a), a cavity length change of ΔLcav corresponding to the transition from the minimum threshold (maximum gain) to twice the minimum (half gain) yields
ΓB=kΔLcav.
(4)
The cavity length was adjusted by translating M2 over a range of approximately 30 µm (60 µm cavity length change) with 1 µm resolution, corresponding to a frequency scan range of 20 MHz. The Brillouin gain line shape gν) and intracavity threshold power as a function of frequency offset are shown in Fig. 5(b), providing a value 23.7 ± 4.1 MHz (FWHM) based on the Lorentzian fit. Due to frequency pulling as the cavity resonance is detuning from the gain center, the Brillouin linewidth is the difference between this measured width and the cavity mode linewidth.32 Based on the finesse (101 ± 2) and length of the ring cavity, the cavity mode linewidth is 11.8 ± 0.2 MHz so that ΓB/2π = 11.9 ± 4.3 MHz. An independent calculation based on the gain coefficient value determined above and the literature value for p2 [Eq. (3)] yields 14.7 ± 2.2 MHz.
FIG. 5.

(a) The frequency detuning of the nearest longitudinal cavity mode from the Brillouin gain peak as a function of cavity length (for the condition that the pump is also resonant with the cavity). Inset: schematic diagram of the Brillouin linewidth measurement principle based on the cavity tuning. (b) Threshold and Brillouin gain profile as functions of frequency detuning from the line center.

FIG. 5.

(a) The frequency detuning of the nearest longitudinal cavity mode from the Brillouin gain peak as a function of cavity length (for the condition that the pump is also resonant with the cavity). Inset: schematic diagram of the Brillouin linewidth measurement principle based on the cavity tuning. (b) Threshold and Brillouin gain profile as functions of frequency detuning from the line center.

Close modal

Comparing the Brillouin properties of diamond with other typical bulk SBS materials (Table I) shows that diamond possesses a g0 value at the high end compared to other media and second to TeO2, the highest reported to our knowledge. Diamond’s high gain coefficient is a result of the combination of high refractive index, high p coefficient, and small ΓB. The high gain, several hundred times higher than silicon, foreshadows good opportunities for low threshold Brillouin lasers. Meanwhile, diamond possesses a moderate Brillouin linewidth (larger than TeO2 but similar to fused silica) and a νB more than 2–3 times than all other investigated materials. In addition, diamond has a wide transparency range compared with other bulk materials. This combination of parameters, along with the outstanding capacity for heat dissipation and high Brillouin frequency, makes diamond an interesting material for greatly extending Brillouin laser capability.

TABLE I.

Comparison of Brillouin parameters of typical bulk SBS media.

MaterialTransparency range (μm)g0 (cm/GW)ΓB2π(MHz)νB (GHz) (@1550 nm)
Fused silica2,33 0.25–3.6 4.52 16 11 
CaF22  0.13–10 4.11 45.6 37.1 
TeO231,34 0.33–5 100 8.6 ± 2.4 11.4 ± 2.2 
As2S315,35,36 1–8 74 19 7.7 
Silicon37,38 >1.2 0.24 320 40 
Diamond >0.23 79 ± 12 11.9 ± 4.3 56 
MaterialTransparency range (μm)g0 (cm/GW)ΓB2π(MHz)νB (GHz) (@1550 nm)
Fused silica2,33 0.25–3.6 4.52 16 11 
CaF22  0.13–10 4.11 45.6 37.1 
TeO231,34 0.33–5 100 8.6 ± 2.4 11.4 ± 2.2 
As2S315,35,36 1–8 74 19 7.7 
Silicon37,38 >1.2 0.24 320 40 
Diamond >0.23 79 ± 12 11.9 ± 4.3 56 

In conclusion, we have demonstrated a ring-cavity Brillouin laser in diamond operating without the need of acoustic or optical guidance. The pump-limited output power of 11 W is, to our knowledge, the highest reported for any continuous wave Brillouin laser. The measured threshold enabled the Brillouin gain coefficient in diamond to be determined for the first time, yielding a value of 60 cm/GW for pump and Brillouin polarizations aligned parallel to the ⟨111⟩ crystallographic direction in diamond (determined by the cut of our diamond in this case). Analysis of the diamond photoelastic tensor shows that for polarization aligned to ⟨110⟩ for maximum gain, a coefficient of 79 ± 12 cm/GW is obtained, a value higher than most other media.

The low quantum defect and high thermal conductivity of diamond Brillouin systems are promising for an extremely wide range of achievable output powers free of thermal effects. The Brillouin laser produced a single Stokes sideband at 167 GHz, a frequency markedly higher than other Brillouin systems due to the combination of the high pump frequency and the fast speed of sound in diamond. The broad transmission of diamond provides a material for Brillouin lasing across ultraviolet-visible and infrared spectral regions and with Brillouin frequencies above 200 GHz. This combination of features points to an interesting new approach to narrow-linewidth lasers with diamond-introduced advantages of high-power handling capability, wide wavelength range, and direct optical access to mm-wave frequencies.

This work was supported by the Australian Research Council (ARC) (Grant Nos. DP150102054 and LP160101039), the Air Force Office of Scientific Research (AFOSR) (Grant No. FA2386-18-1-4117), and the National Natural Science Foundation of China (Grant No. 61905061).

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