Intense Brillouin amplification in gas using hollow-core waveguides

Abstract

Among all the nonlinear effects stimulated Brillouin scattering offers the highest gain in solid materials and has demonstrated advanced photonics functionalities in waveguides. The large compressibility of gases suggests that stimulated Brillouin scattering may gain in efficiency with respect to condensed materials. Here, by using a gas-filled hollow-core fibre at high pressure, we achieve a strong Brillouin amplification per unit length, exceeding by six times the gain observed in fibres with a solid silica core. This large amplification benefits from a higher molecular density and a lower acoustic attenuation at higher pressure, combined with a tight light confinement. Using this approach, we demonstrate the capability to perform large optical amplifications in hollow-core waveguides. The implementations of a low-threshold gas Brillouin fibre laser and a high-performance distributed temperature sensor, intrinsically free of strain cross-sensitivity, illustrate the potential for hollow-core fibres, paving the way to their integration into lasing, sensing and signal processing.

Stimulated Brillouin scattering (SBS) is a third-order optical nonlinear effect that manifests itself in a coherent light–sound coupling^1–4. It is usually the strongest nonlinear effect in amorphous materials¹ and has been observed in many platforms^5–18.

Gas is an attractive medium for nonlinear optics because, unlike condensed matter, it is not subject to optical damage at high intensities (with the notable exception of photochemical dissociation for some molecular gases). It shows a potentially wider transparency window from the vacuum-ultraviolet to the mid-infrared region^19,20. Various nonlinear effects have been demonstrated in gases, including supercontinuum generation²¹, high-harmonic generation²², filamentation²³, Raman and Brillouin scattering¹⁶.

So far, backward SBS in gases has been exclusively observed using free-space interactions^16,17. The scattering efficiency remains limited owing to the weak light confinement over a sizeable interaction length, so that high-power laser pulses (megawatt peak power) are needed to eventually observe a moderate SBS signal^16,17.

Hollow-core fibres (HCFs), including hollow-core photonic bandgap fibres, Kagome-style HCFs and single-ring antiresonant fibres, show low loss and diffractionless optical transmission (state-of-the-art loss: 0.28 dB km⁻¹ (ref. ²⁴)). They are therefore the ideal candidate to drastically increase the light–sound interaction length in a gaseous medium and thereby achieve an efficient coupling between interacting waves^19,20,25.

In gas-filled HCFs, the effective interaction length (L_eff) can actually reach more than 10 km, neglecting potential gas absorption. Additionally, considering a mode field diameter typically ranging from 10 to 40 μm, the nonlinear gain in gas-filled HCFs may be six orders of magnitude larger than in free space in the near-infrared region. Incidentally, the threshold for nonlinear effects, such as stimulated Raman scattering^26,27, has been proven to be several orders of magnitude lower than using free-space optics.

Nevertheless, it should be mentioned that an opto-acoustic interaction, in this case forward SBS, has recently been demonstrated in a HCF filled with atmospheric air²⁸. In this work, the peak gain coefficient reached 4 × 10⁻¹⁴ m W⁻¹, which is 1,000 times smaller than the peak backward Brillouin gain coefficient in fibres with a solid silica core (single-mode fibre (SMF)). No strong Brillouin interaction in gaseous media has been reported so far.

Here, we report a considerable optical amplification by using backward SBS in a gas-filled HCF. We achieved 0.32 dB of signal amplification per milliwatt of pump power inside a 50-m-long HCF filled with carbon dioxide (CO₂) at a pressure of 41 bar. This large gain results from two causes. Firstly, the peak Brillouin gain coefficient shows a quadratic dependence on the gas pressure, in contrast with stimulated Raman scattering¹⁹ and Kerr nonlinearity²⁰ in which the nonlinear coefficients are typically proportional to the gas pressure. The Brillouin gain coefficient can therefore be drastically enhanced in the backward SBS configuration by raising the gas pressure. Secondly, the simultaneous tight confinement of light and gas in a HCF offers altogether an ultra-long interaction length and a small effective beam cross-section.

Using this platform we demonstrate two original and specific implementations: a low-threshold (33 mW) continuous-wave single-frequency laser in a HCF that can in principle operate at any wavelength, and a distributed temperature sensor of unprecedented performance showing zero strain cross-sensitivity.

Results

Theoretical analysis of the Brillouin gain

Stimulated Brillouin scattering in a gas-filled HCF is a process in which pump and probe optical waves with a slightly different frequency counter-propagate along a HCF and their interference produces a longitudinally moving fringe pattern. When a strict phase-matching condition is met, dictated by the relative velocities of light and sound in the medium, the fringe pattern gives rise, via electrostriction, to a travelling longitudinal acoustic wave in the gas, as illustrated in Fig. 1a. In turn, this wave periodically modifies the medium’s optical density, inducing a Bragg-type coupling between pump and probe. We assume the frequency of the pump light to be higher than that of the probe. In this case, the probe is amplified by the pump when their frequency difference matches the Brillouin frequency shift (that is, the frequency for perfect phase matching), given by v _B = 2n _eff v _a/λ, where n _eff is the effective refractive index of the optical mode, v_a is the gas acoustic velocity and λ is the pump wavelength. Note that Brillouin amplification in gas can be implemented in any hollow-core waveguide, including microstructured fibres, capillary fibres and metal-coated waveguides, as well as slot waveguides. In our demonstration, we opted for a 50-m-long commercial HCF (see Methods), since it shows a relatively small optical effective mode area (51 μm²), leading to a higher Brillouin coefficient. A scanning electron microscope image of its cross-section is shown in Fig. 1b. This fibre guides light inside its hollow core by virtue of the photonic bandgap in the periodically patterned cladding region.

Fig. 1. Principle of the generation of SBS in gas-filled HCFs.

a, Conceptual view of the interacting waves in the SBS process: the pump and probe optical waves are separately launched into each HCF end and counter-propagate. Their interference creates an intensity beat pattern that slowly moves along the fibre owing to their slight frequency difference. The electrostrictive force on the gas molecules causes periodic density fluctuations thanks to the gas compressibility. This periodic density distribution is experienced as a moving refractive index grating by the optical waves that are consequently coupled. The process turns resonant when the beat pattern moves exactly at the sound velocity in the medium, which is realized for a well-defined frequency difference between the optical waves. In this case, a strong unidirectional energy transfer is observed from pump to probe and the probe is amplified. b, Scanning electron microscope image of the HCF used in this work. c,d, Spatial distributions of the intensity of the fundamental optical mode (c) and the acoustic amplitude of the first excited radial acoustic mode (d) in the HCF. The SBS efficiency is scaled by the overlap integral between these two distributions, which is highest for the two presented modes. e, Transmission of the HCF gas cell filled with air at atmospheric pressure (blue) and with 41 bar CO₂ (red).

During the SBS interaction, the probe wave is amplified with a peak gain given by⁴:

$$g_{\text{B}}=\frac{{\gamma }_{\text{e}}^2{\omega }^2}{\rho n{v}_{\text{a}}{c}^3{\Gamma }_{\text{B}}{A}_{\text{eff}}^{\text{ao}}},$$ (1)

where γ_e is the electrostrictive constant in the gas medium, ω is the light angular frequency, ρ is the gas density, n is the gas refractive index, c is the light velocity in vacuum, Γ _B/2π is the gain spectrum linewidth (full-width at half-maximum (FWHM)), directly related to the acoustic attenuation, and $A_{\text{eff }}^{\text{ao }}$ is the acousto-optic overlap effective area, as defined and calculated in Supplementary Section 4. Figures 1c and d show the spatial distributions of the fundamental optical and first excited radial acoustic eigenmodes, respectively (obtained by a finite-element method). $A_{\text{eff }}^{\text{ao }}$ is calculated from the overlap integral between these two distributions. In this work, we consider only the first excited radial acoustic mode, since the Brillouin interaction involving higher acoustic modes is more than two orders of magnitude smaller. Figure 1e shows the transmission spectrum of the HCF gas cell (see Methods for the detailed fabrication process) before and after filling with 41 bar CO₂ gas. At a wavelength of 1.55 μm, the total loss of the HCF gas cell filled with atmospheric air is 8.5 dB (≤4 dB SMF–HCF coupling losses at the two extremities as well as 0.8 dB transmission loss of the 50-m-long HCF). An additional ~0.5 dB loss at 1.55 μm was induced by gas absorption once the HCF was filled with CO₂ at 41 bar. The back-reflection at the SMF–HCF coupling point was measured to be about −34 dB at each end. The backscattering coefficient of the HCF itself (filled with air at atmospheric pressure) was measured to be ten times higher than the Rayleigh scattering coefficient in a standard SMF²⁹.

The acoustic velocity is given by $v_{\text{a}}=1/\sqrt{{\beta }_{\text{s}}\rho }$, independent of pressure for an ideal gas, where β _s is the adiabatic compressibility. As the compressibility coefficient of gases (for example, at 40 bar) is four orders of magnitude larger than that of solid materials (for example, fused silica) and the density of gases (at 40 bar) is some 30 times smaller than that of a condensed material, the acoustic velocity is about 20 times smaller. This leads to a 20-fold increase in gain, as shown by equation (1), as well as a Brillouin frequency shift ν _B lying in the sub-gigahertz range (for example, ~320 MHz for CO₂ at a pump wavelength of 1.55 μm).

Next we discuss the two key parameters contributing to the quadratic dependence of the Brillouin gain coefficient on gas pressure: the electrostrictive constant, γ_e, and the acoustic attenuation coefficient, Γ _B.

The electrostrictive constant is defined as the normalized rate of change of the relative permittivity є_r in response to a change in the density ρ (ref. ³⁰):

$${\gamma }_{\text{e}}=\rho \frac{\partial {ϵ}_{\text{r}}}{\partial \rho }=\rho \frac{\partial \chi }{\partial \rho },$$ (2)

where χ is the electric susceptibility. At the pressure ranges considered in this work, the electric susceptibility of CO₂ shows a linear dependence on density: χ = Aρ, where A ≈ 5 × 10⁻⁴ m³ kg⁻¹ for CO₂. As a result, the electrostrictive constant

$${\gamma }_{\text{e}}=A\rho$$ (3)

is directly proportional to the density, hence to the pressure in the ideal gas approximation.

The acoustic attenuation of a sound wave in CO₂ at megahertz frequencies arises mainly from two dissipative phenomena: viscous forces and thermal conductivity³¹. Thermal conductivity and viscosity have very similar origins: they arise from energy and momentum diffusion, respectively, driven by thermal motion of the gas molecules that compensates for any temperature and velocity gradient, respectively. Hence, the strength of thermal conductivity and viscosity is proportional to the temperature and velocity gradient, respectively. In order to intuitively grasp the pressure dependence in these two processes, let’s consider an acoustic plane wave propagating along the x axis in a gas that is globally at rest. Such a wave consists of similar periodic variations of density, pressure, velocity and temperature. In particular, we express the velocity of the gas volume elements as: u(x, t) = u ₀ cos(qx – Ωt), where x is the position, t is the time, u ₀ is the velocity amplitude, and Ω and q are the wave angular frequency and wavenumber, respectively (for backward SBS, q ≈ 2nω/c). The intensity of the acoustic plane wave is expressed as:

$$I_{\text{ac}}=\frac{1}{2}\rho v_{\text{a}}{u}_0^2.$$ (4)

Within the ideal gas model, it can be shown that the temperature oscillations of the acoustic wave are given by³¹:

$$T(x,t)=\frac{T_0}{v_{\text{a}}}(\gamma -1)u_0\cos (qx-\Omega t),$$ (5)

where T ₀ is the average ambient temperature and γ is the adiabatic index, namely the ratio of specific heats at constant pressure and volume, respectively. Thus, for a constant intensity, both gas velocity and temperature periodic variations (and hence, their gradient) decrease for an increasing density ρ. As a consequence, both thermal diffusion and viscosity forces are equally reduced. It can be more formally shown that the dissipated energy caused by each process is proportional to $u_0^2$ and the acoustic attenuation coefficient is therefore proportional to 1/ρ, expressed as³²:

$${\Gamma }_{\text{B}}=\frac{q^2}{\rho }\left[\frac{4}{3}{\eta }_{\text{s}}+{\eta }_{\text{b}}+\frac{\kappa }{C_{\text{P}}}(\gamma -1)\right],$$ (6)

where η _s and η _b are the shear and bulk viscosity respectively, ĸ is the thermal conductivity and C _P is the specific heat at constant pressure. By inserting equations (3) and (6) into equation (1), it can be shown that the Brillouin gain coefficient increases quadratically with the density, thus the pressure in the ideal gas approximation.

SBS gain coefficient measurement

The CO₂ Brillouin gain coefficient at atmospheric pressure is about 10⁻¹³ m W⁻¹. In order to measure such a small gain, a lock-in detection technique is the preferred approach to separate the gain signal from the background noise and spurious signals. The experimental set-up is detailed in Supplementary Section 1.1. The loss of our HCF filled with 41 bar CO₂ is 26 dB km⁻¹ (16 dB km⁻¹ due to fibre loss and an additional 10 dB km⁻¹ due to molecular absorption) at our working vacuum wavelength of 1.55 μm. All the experiments were performed at an environmental temperature of 24 ± 1 °C. Figure 2a shows the measured backward SBS gain spectra of the HCF filled with CO₂ at different pressures and, for comparison purposes, of a standard SMF with a solid silica core of very similar diameter. The detailed analysis of the system response is presented in Supplementary Section 1. It can be observed that the Brillouin gain coefficient exceeds that of the standard SMF for pressures above ~20 bar. Remarkably, when the pressure reaches 41 bar, the measured Brillouin gain coefficient is 1.68 m⁻¹ W⁻¹, which turns out to be 6 times higher than in a standard SMF and 20 times higher than the largest Raman gain achievable in gas-filled HCFs at a wavelength of 1.55 μm (that is, at pressures above 10 bar, the peak Raman gain from the hydrogen Q(1) transition saturates to 0.08 m⁻¹ W⁻¹, see Supplementary Section 5 for a comparative Raman gain analysis). Since the acoustic velocity is of the order of hundreds of metres per second in gaseous media, the Brillouin frequency shift lies in the sub-gigahertz range, in contrast with the ~11 GHz in silica. Note that the acoustic velocity derived from the Brillouin frequency shift shown in Fig. 2a decreases with rising pressure (see Supplementary Section 6 for the detailed analysis), caused by a moderate departing from the ideal gas model.

Fig. 2. Experimental gains in gas by SBS.

a, Measured Brillouin gain spectra in a HCF filled with CO₂ at different pressures. The Brillouin spectrum of a solid silica-core SMF is also shown for comparison. Note that the horizontal scale is discontinued, but its intervals are kept constant. Inset: magnified view of the 41 bar CO₂-filled HCF gain spectrum, showing measured datapoints and Lorentzian fitting. b,c, Measured peak Brillouin gain coefficient (b) and FWHM linewidth (c) of SBS in a CO₂-filled HCF as a function of the gas pressure. The theoretical lines in b and c are calculated from equations (1) and (6), respectively. All the parameters used for these calculations are listed in Supplementary Section 4.

At 41 bar, the CO₂ Brillouin linewidth is measured to be 3.65 MHz using a Lorentzian fitting over the experimental spectrum, as shown in Fig. 2a inset. This value is ten times smaller than in a SMF, which means that the acoustic lifetime in the gas is ten times longer than in a silica core. Figures 2b and c show the Brillouin gain coefficient and linewidth measured as a function of pressure, respectively. The measured gain coefficients and linewidths match very well with the theoretical model given by equations (1) and (6): the gain is proportional to the square of the pressure, while the linewidth is inversely proportional to the pressure. In this study the maximum gain was obtained by pressurizing CO₂ to 41 bar in our 50-m-long HCF, thus this configuration was preferably used in subsequent experiments.

This HCF propagates several guided optical modes and is therefore not strictly single-moded. The light launching conditions make the fundamental mode to be more preferably populated, so that the conditions are close to a single-mode operation. This is indirectly evidenced by the symmetry and the absence of side peaks in the Brillouin gain spectra. If some light were ever to propagate in the higher-order modes, it would lead to an underestimation of the gain value at worst.

Signal amplification

A large gain value could be benefical for optical amplification within a HCF. To this end, we measured the amplification of a –34 dBm input probe beam as a function of pump power. The injected probe power is more than 40 dB smaller than the pump power, hence satisfying the small-signal amplification condition (that is, absence of pump depletion) at least up to 30 dB amplification. The detailed set-up is shown in Supplementary Section 2.

By scanning the pump-signal detuning frequency, the measured amplification spectra for different pump powers are shown in Fig. 3a, while the logarithmic peak amplification value in the HCF as a function of the pump power is plotted in Fig. 3b. The red line in Fig. 3b is calculated from the equation: G = exp (g _B P _pump L _eff – αL) using actual gas and fibre parameters, where G is the gain, g _B is the Brillouin linear gain calculated from equation (1), P _pump is the pump power at the input to the HCF (inside the HCF), L _eff is the effective length of the HCF, a is the fibre attenuation and L is the physical fibre length. It shows a slope of 0.32 dB mW⁻¹, indicative of the amplification efficiency normalized to the pump power. The experimental results are in perfect agreement with the theoretical prediction. A record 53 dB amplification was observed for a signal input power below –49 dBm and a pump power of 200 mW inside the HCF (pump-depleted regime). The maximum theoretical amplification (limited by the depletion due to the massive amplification of spontaneous Brillouin scattering) is calculated to be 80 dB in our 50-m-long HCF filled with 41 bar CO₂ by using equation (25) in ref.³³. This is lower than for a 50-m-long standard fibre-based Brillouin amplification system (~96 dB), but, in practice, spurious reflections and double scattering set the gain limit to some 50–60 dB in any configuration.

Fig. 3. Amplification of the probe wave as a function of the pump power in the HCF.

a, Probe amplification spectra for pump powers in the HCF of 40, 52, 59 and 71 mW. Noise from spontaneous scattering is visible in the wings of the gain spectra for high pump powers. b, Peak probe amplification on a logarithmic scale as a function of pump power inside the HCF on a linear scale. The dots are experimental results and the line is theoretically calculated from the equation G = exp(g _B P _pump L _eff – αL). All the parameters used for the theoretical calculation are listed in Supplementary Section 2.

A straightforward estimation shows that the amplification coefficient could be enhanced up to 1.2 dB mW⁻¹ by extending the effective length to 160 m using the same 41-bar CO₂-filled hollow-core photonic bandgap fibre (~10 μm core diameter).

The advantages and disadvantages of this Brillouin amplification in gas do not fundamentally differ from those extensively reported for silica-core fibres³⁴: very narrowband efficient amplification that can be spectrally enlarged by broadening the pump spectrum through modulation, at the expense of a lower efficiency, and a poor noise figure that has yet to be quantified in the case of amplification in a gas.

Gas Brillouin laser

This platform can be straightforwardly turned into a gas Brillouin laser by looping the 50-m-long gas-filled HCF, so as to form a fibre ring cavity. Figure 4a shows the detailed experimental implementation. The pump light is launched into the cavity through a circulator and, after one revolution, is stopped by that same circulator. Since the pump is not circulating in the cavity, it must not be resonant. In contrast, the Brillouin-amplified light freely circulates in the ring cavity. The total cavity length is 55 m, made of the 50-m-long HCF connected to 5 m of diverse SMF patch cords (circulator and coupler pigtails), so that the free spectral range of the cavity is 5 MHz, roughly equivalent to the Brillouin gain linewidth of CO₂ at 41 bar. Figure 4b shows the Stokes power as a function of the pump power evaluated inside the HCF. Brillouin lasing is turned on when the net Brillouin gain exceeds the round-trip loss of the fibre cavity (that is, 9 dB HCF insertion loss and 2 dB circulator and coupler loss, 11 dB altogether). The measured threshold is 33.2 mW, in good agreement with the theoretically estimated threshold of 34.9 mW. Considering the coupling losses, far from being optimized, this corresponds to a net pump power of 105 mW. Figure 4c shows the heterodyne electrical beating spectra between the frequency-shifted pump laser (as a local oscillator) and the amplified spontaneous Brillouin scattering (50-m-long HCF filled with 41 bar CO₂, single-pass backscattering through a non-looping cavity) when the pump power inside the HCF is 12 mW, as well as the beat note between the local oscillator and the Brillouin laser emission after closing the cavity, when the pump power inside the HCF is 44.6 mW. The beating spectrum linewidth (FWHM) between the Stokes signal and the local oscillator above threshold is measured to be 66 kHz, which is much narrower than the spontaneous spectrum (3.66 MHz). Since our lasing cavity is neither locked nor isolated from the environment, mode hopping constantly occurs during laser emission. In order to record the snapshot of the heterodyne spectrum during lasing, the resolution bandwidth of the radio-frequency spectrum analyser is set to 62 kHz to promptly scan a several-megahertz frequency range. The measured beating linewidth is therefore dominated by this resolution and does not represent the real lasing linewidth. The theoretical Brillouin linewidth defined by the Schawlow–Townes limit³⁵ is calculated to be in the sub-hertz range. However, in practice, the linewidth is limited by the acoustic and thermal fluctuations along the fibre loop cavity, so that silica Brillouin fibre lasers achieve an actual short-term linewidth of a few tens of hertz^36,37. Thus, we can reasonably speculate that the short-term linewidth of our laser is similar to that of silica Brillouin fibre lasers.

Fig. 4. Gas Brillouin lasing.

a, Experimental set-up. The continuous-wave output of an external-cavity diode laser (ECDL, 10 kHz linewidth) is split: one branch is amplified by an erbium-doped fibre amplifier (EDFA) and used to pump the laser and the other branch is frequency-shifted by an acousto-optic modulator (AOM) and combined with the cavity Stokes emission for heterodyne mixing. The radio-frequency (RF) spectrum analyser resolution and video bandwidth were set to 62 kHz and 160 kHz, respectively. b, Intracavity Stokes optical power as a function of pump power inside the HCF. c, Heterodyne electrical spectrum of the Brillouin lasing emission when the pump power is 44.6 mW (above threshold). Inset: zoomed-in view of the lasing spectrum. For comparison, the heterodyne beating spectrum of the amplified spontaneous Brillouin-scattered Stokes light is also shown (highly magnified), obtained using a single-pass set-up (opened cavity) when the pump power is 12 mW inside the HCF. The lasing beating linewidth (66 kHz) is much narrower than the spontaneous spectrum linewidth (3.66 MHz), though certainly not representing the real, much narrower, laser linewidth.

It should be mentioned that suppression of the mode hopping is possible using reported techniques, for instance by locking the pump–Stokes detuning frequency to a local radio-frequency oscillator³⁶.

Distributed temperature sensing

Temperature and strain cross-sensitivity is currently a crucial issue in all Brillouin-based sensing systems, because the acoustic velocity in a solid is indistinctly sensitive to both these quantities that will identically impact the Brillouin frequency shift. Many methods have been proposed to solve this issue by measuring two parameters showing distinct responses to temperature and strain³⁸. However, no solution, solely based on Brillouin scattering and showing intrinsic strain insensitivity, has been reported so far. The absence of cross-sensitivity is an essential quality of a sensing system.

Raman distributed sensing in silica fibre is known to show no strain cross-sensitivity. However, due to the weak response of spontaneous Raman scattering, the spatial resolution remains limited to ~1 m and the distance range to some 30 km (ref. ³⁸) for a reasonable integration time, far from competing with the performance of a Brillouin-based sensor.

Here, we demonstrate an intrinsically strain-insensitive system based on SBS in gas-filled HCFs. In our system, the optical signals are kept confined in the gaseous medium, meaning that this configuration offers unique properties that solid waveguides cannot. The absence of stiffness of the gaseous medium leads to an insensitivity to any strain applied to its surrounding walls. Here, we take advantage of this specific property, combined with the large Brillouin gain coefficient and its narrow linewidth to achieve high-performance strain-insensitive temperature measurements.

We used the same 50-m-long HCF filled with 41 bar CO₂ and set up a phase-modulated Brillouin optical correlation-domain analysis system³⁹ (the detailed set-up is shown in Supplementary Section 3). The Brillouin dynamic grating position is scanned all along the fibre to measure the local Brillouin gain spectrum at each position. A strain applied on the HCF has a negligible impact on both the gas pressure and the effective optical refractive index and therefore presents no observable effect on the Brillouin frequency shift (see Supplementary Section 7 for the detailed simulation and analysis). In contrast, a change in temperature substantially modifies the acoustic velocity⁴⁰ and hence shifts the Brillouin frequency.

Our sensing system is depicted in Fig. 5a. For the sake of comparison, identical lengths of HCF and solid-core SMF are jointly placed on a test bench consisting of a 4 cm thermoelectric element positioned in the middle of a 15 cm variable-strain stage. This enables us to simultaneously apply strain and temperature changes over the same segment and identically for the two fibre types. The small size of the thermoelectric element is suitable to validate the system’s high spatial resolution. For each fibre, the spatial resolution was set to the highest value to secure a signal-to-noise ratio in excess of 10 at the peak gain value. The resulting spatial resolution was 1.28 cm and 2.32 cm for the HCF and SMF, respectively (calculated as the inverse of the bit duration), reflecting the difference in gain in the two media, despite a higher total loss through the HCF. Measurement spectra were recorded using a 7.8 Hz equivalent noise bandwidth and their peak gain frequency was estimated using a quadratic fitting. The repeatability for the HCF and the SMF is experimentally estimated to be 0.3 °C and 0.4 °C, respectively (see Supplementary Section 3.7 for additional details). Figure 5b shows the longitudinal distribution of the Brillouin frequency shift for various preset temperatures in the HCF. The slightly different positioning of the step transitions is due to the uncertainty in the central frequency determination when two Brillouin gain spectra overlap in the presence of noise. The average Brillouin frequency shift in the HCF along the thermoelectric element as a function of the preset temperature is shown in Fig. 5c. It should be pointed out that the response is not perfectly linear but shows an average slope of 1.2 MHz °C⁻¹, which, conveniently, is slightly larger than for silica. The slope is higher for lower temperatures (in Fig. 5c), as a result of the closer vicinity to the liquefaction temperature (~8 °C at 41 bar), in agreement with a previous work⁴⁰. Note that this nonlinear monotonic response is specific to a given gas and can be calibrated, with no notable impact on the sensor performances. Figure 5d,e compare the response of each fibre at a preset temperature of 35 °C and under different applied strains: 0 μє, 2,000 με and 4,000 με. As expected, a strong strain dependence is observed for the SMF, but no change is visible for the HCF, validating the absence of observable cross-sensitivity, which was subsequently confirmed up to 1% elongation. This experimental result consolidates the numerical simulations predicting this strain insensitivity (Supplementary Section 7).

Fig. 5. Distributed temperature sensing with no strain cross-sensitivity.

a, Sensing test bench. Preset strains and temperatures can be applied on the same segment of a gas-filled HCF and a solid silica-core SMF, so that each fibre can be alternately measured under the same conditions for a fully demonstrative comparison. b, Longitudinal distribution of the Brillouin frequency shift in the HCF in the region of the thermoelectric element for several preset temperatures and no applied strain. c, Brillouin frequency shift as a function of the preset temperature, showing a quasi-linear dependence with a typical slope of ~1.2 MHz °C⁻¹ for the HCF and a linear dependence with a slope of 1.09 MHz °C⁻¹ for the SMF. d, Longitudinal distribution of the Brillouin frequency shift in the HCF in the region of the strained section at a preset temperature of 35 °C and under different applied strains, demonstrating a non-observable cross-sensitivity. e, Same as d but for the SMF under identical experimental conditions, showing the presence of a massive cross-sensitivity (larger vertical scale). v _B0 is the Brillouin frequency shift of the fibre in ambient conditions.

Discussion

The large light–sound interaction in a gas-filled HCF reported here leads to a measured gain nearly six orders of magnitude larger than in previous works using free-space optics. From the fibre perspective, the increased compressibility of gases and their lower acoustic attenuation compared with solid materials result in a measured Brillouin gain coefficient in our 41-bar CO₂ gas-filled HCF six times larger than in a standard SMF.

Realizing optical amplification in HCFs has led to sustained efforts. Interesting results have been reported so far, mostly using molecular or atomic transitions in a low-pressure gas⁴¹ (as in classical gas lasers) or Raman gain in hydrogen²⁶. The obtained gains remain modest in both cases when compared with solid-core solutions, with the specific penalties of amplification at fixed wavelengths for molecular or atomic transitions and the issue of hydrogen permeation through the glass walls for Raman amplification. In contrast, our approach offers an efficient alternative to amplify signals since it shows a gain 20 times larger than the highest achievable Raman gain at 1.55 μm. Moreover, this amplification scheme operates at any wavelength from the ultraviolet to the mid-infrared region, limited only by the transmission windows of the HCFs.

Gas Brillouin lasing has not yet been reported due to the extremely low scattering efficiency in free-space implementations. Using a gas-filled HCF, we have demonstrated a continuous-wave gas Brillouin laser with only 33 mW of threshold power, despite the high cavity round-trip loss. The lasing threshold can be further decreased by dynamically matching the cavity resonance to the pump frequency in a doubly resonant configuration (both pump and Stokes are resonant). In addition, by changing the gas pressure, we showed that not only can we scale the gain but that we can also modify the acoustic lifetime, which is an important feature for building gas Brillouin photon or phonon lasers⁴². As clarified below, the nature of the gas is not important, thus it would be possible to realize a gas Brillouin laser simply using compressed air as the amplifying medium.

From a different perspective, we also demonstrated a high-performance distributed temperature sensor showing spatial and temperature resolutions of 1.28 cm and 0.3 °C, respectively. Note that, since we used a correlation-domain technique, the ten times narrower linewidth (that is, longer acoustic lifetime) compared with the silica-core SMF has no impact on the spatial resolution, but substantially improves the temperature resolution⁴³. Our distributed temperature sensor is immune to high-energy radiation (for example, in spaceborne situations or inside a nuclear reactor) where conventional solid-glass fibres are subject to photodarkening⁴⁴. The sensing range may be potentially extended to several tens of kilometres by using low-loss HCFs²⁴ filled with gases free of absorption in the C-band (such as nitrogen or noble gases).

A question naturally arises as to how the nature of the gas influences the Brillouin gain coefficient. Our theoretical analysis shows that the gain coefficient depends quadratically on the gas density, so that heavier molecules are expected to present a larger amplification potential. We observed SBS in a HCF filled with different types of gas, namely CO₂, sulfur hexafluoride (SF₆), nitrogen (N₂) and methane (CH₄). The Brillouin gain spectra for these four gases under specific pressures are plotted in Fig. 6. The acoustic velocity, and hence the Brillouin frequency shift, usually scales inversely to the square root of the gas molecular mass (Fig. 6). CO₂ was selected in this work for four main reasons: (1) its absorption at a wavelength of 1.55 μm remains limited below 41 bar; (2) it has a relatively large density, leading to a Brillouin gain coefficient six times and three times larger than N₂ and CH₄, respectively, at the same pressure; (3) compared with SF₆, CO₂ shows a higher liquefaction pressure at room temperature, which results in a higher achievable gain (even though the Brillouin gain coefficient of CO₂ is three times lower than that of SF₆ at the same pressure (for example 10 bar)); and (4) it is widely available, does not permeate through glass and can be handled with no potential hazards.

Fig. 6. Experimental Brillouin gain spectra for the HCF filled with different types of gas.

Measured Brillouin gain spectra for 37 bar CO₂, 80 bar N₂, 10.4 bar SF₆ and 10 bar CH₄. The molar masses of the four gases are also indicated.

In our experiments, the maximum pressure used for CO₂ is 41 bar, which is not a physical limitation of the HCF, since such fibres can easily sustain a pressure in the kilobar range by virtue of their small core diameter and thick glass sheath¹⁹. This maximum pressure lies below the onset of substantial light absorption at 1.55 μm. As observed at pressures above 41 bar, the substantial light absorption due to pressure broadening impairs the HCF transmission and hence decreases the Brillouin signal. As a result, it should be mentioned that the use of complex heavy molecules is eventually of limited relevance, since such molecules normally present broad and ubiquitous absorption bands and frequently liquefy at moderate pressure (for example 61 bar for CO₂ and 22 bar for SF₆) at room temperature. Using simpler molecules such as nitrogen, oxygen or noble gases opens the possibility of increasing the pressure without risk of liquefaction; their smaller intrinsic gains can be compensated by higher pressures. Such gases are normally also totally free of spectral absorption lines in the regions of interest. For instance, a theoretical gain up to 30 m⁻¹ W⁻¹ is anticipated in a xenon-filled HCF for a pressure above 130 bar. This gain is more than 100 times larger than in a solid-core silica fibre.

Our platform is also suitable for the investigation of light–sound interactions in gases close to their critical point or in the supercritical region, as well as for the study of the bulk viscosity at high frequency, which, so far, is poorly documented. It should be pointed out that the gas volume in a 50-m-long HCF with its core and cladding filled with 1 kbar gas is equivalent to only about 200 ml at atmospheric pressure, thanks to the microscopic size of the structure. In a more practical approach, the gas-filled HCF can be hermetically sealed by splicing both ends to standard SMFs (with a typical splicing loss of 3 dB and −60 dB reflection using angled splicing⁴⁵), thereby making a perfectly airtight compact all-fibre gas cell⁴⁶ that can be flexibly and safely handled.

Stimulated Brillouin scattering cannot be reduced to a mere amplification process, since it has demonstrated potential to realize advanced functions⁴⁷. This novel gas-based Brillouin platform can be the foundation of many potential applications: amplifiers, highly coherent Brillouin gas lasers, slow and fast light, microwave filters, tunable delay lines, light storage, all-optical calculus and sensing. The same functions can therefore be implemented in HCFs, some of which have been illustrated here, offering all the inherent advantages of fibre-based optics with the key advantage to realize the same response with the product pump power × fibre length potentially 100 times smaller than in SMFs. It must be noted that the reduced acoustic loss compared with silica results in a narrower gain resonance. At first glance, this may be seen as a drawback since it reduces the capacity for broadband amplification, however, it is a clear asset for most applications that benefit from a long-lasting vibration, for example optical storage, optical signal processing, precise selective spectral filtering, and sensing.

From a broader perspective, the concept introduced here can also be applied to other waveguiding structures. More specifically, although suspended silicon or silica waveguides can be designed to couple light and sound¹, the interaction between the evanescent field of their guided light and the surrounding gas has not yet been exploited and could lead to gains of practical interest. For instance, a small-dimension slot waveguide inducing an intense evanescent field⁴⁸ can be designed to offer a large light–sound interaction in gas. This shows that the Brillouin amplification in gases in hollow-core waveguides can be extended to other configurations.

Online content

Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41566-020-0676-z.

Methods

Fabrication of the HCF gas cell

Our HCF (HC-1550-02 from NKT Photonics) has a core diameter of 10.9 μm and a cladding diameter of 120 μm. Thanks to the similar core and cladding diameters of our HCF and a standard SMF (ITU G.652), the HCF gas cell can be formed by placing a segment of HCF between two SMF patch cords according to the following procedure. Firstly, two ceramic fibre ferrules with an inner diameter of 125 μm were inserted into a ceramic sleeve, keeping a 30 μm gap between the two ferrule tips. The ceramic sleeve’s side slot enables visual monitoring of the butt coupling at the fabrication stage and gas inlet (outlet) into (from) the HCF under operation. Secondly, an angled-cleaved SMF and a cleaved end of the HCF were inserted into the fibre ferrules and the coupling of the HCF–SMF was monitored using a microscope through the side slot. The HCF and SMF ends were brought closer to each other until they are separated by a few-micrometre gap. The other end of the HCF was coupled according to the same procedure. The total end-to-end loss for the assembled SMF–HCF–SMF was 9 dB. Thirdly, we inserted each joint into a metallic T-tube and sealed its two facing sides using epoxy glue. Gas could be vacuum-pumped out or pressurized into the HCF through the third port of the T-tubes.

Simulations

Simulations of the optical and acoustic modes were performed using COMSOL Multiphysics 2D ‘Electromagnetic waves’ and 2D ‘Pressure acoustics’ modules, respectively. The silica refractive index n _SiO2 = 1.444 and the gas refractive index n _gas = 1.01804 (for 41 bar CO₂) were entered into the calculation of the optical modes. The effective refractive index of the fundamental optical mode n _eff was calculated to be 1.0123 at a wavelength of 1.55 μm. The fundamental mode profile (optical intensity) is plotted in Fig. 1c. At 41 bar CO₂, the gas density ρ _gas = 72.77 kg m⁻³ (ideal gas approximation) and the speed of sound v _a = 243.6 m s⁻¹ (as deduced from the Brillouin frequency shift of our measurement) were used to calculate the acoustic mode in the fibre core, considering a sound hard boundary on the hollow tube wall. The acoustic mode profile (density) of the calculated first excited radial mode is shown in Fig. 1d with an out-of-plane wavevector of 8.228 × 10⁶ rad m⁻¹ at a resonant frequency of 320 MHz, which corresponds to the measured Brillouin frequency shift at 41 bar CO₂. Note that the scalar model has intrinsic limits since it considers co-polarization for pump and probe and does not take into account inter-polarization scattering. A vectorial model has been introduced in ref. ⁴⁹ to calculate the inter-polarization scattering induced by torsional–radial acoustic modes, among others. Inter-polarization scattering is generally forbidden in gases²⁸, but could originate from deformations of the honeycomb cladding. However, the radiation pressure at the core sidewalls as well as the vibrations of the honeycomb cladding can be reasonably neglected due to the negligible fraction of the light power in the silica (<1%). The large mode-field diameter of our HCF (~10 μm) compared with the optical wavelength also contributes to a small radiation pressure at the core sidewalls. In addition, the Brillouin-activated fundamental phonon modes in the silica part vibrate below 100 MHz (ref. ⁴⁹), which is not in the frequency range used in our gas SBS (that is, 150 MHz to 700 MHz). This is indirectly evidenced by the absence of side peaks in the Brillouin gain spectra.

Reporting Summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Supplementary Material

Supplementary Information

Supplementary information is available for this paper at https://doi.org/10.1038/s41566-020-0676-z

Data availability

The data that support the plots within this paper and other findings of this study are available on Zenodo (https://doi.org/10.5281/zenodo.3934070). All other data used in this study are available from the corresponding authors upon reasonable request.

Code availability

The simulation code of this study is available on Zenodo (https://doi.org/10.5281/zenodo.3934070).