We measure the coherent Rayleigh-Brillouin scattering (CRBS) signal integral as a function of the recorded gas pressure in He, Co2, SF6, and air, and we confirm the already established quadratic dependence of the signal on the gas density. We propose the use of CRBS as an effective diagnostic for the remote measurement of gas' density (pressure) and temperature, as well as polarizability, for gases of known composition.
Since its initial demonstration,1,2 Coherent Rayleigh-Brillouin Scattering (CRBS) has demonstrated the ability to measure important thermodynamic quantities in a gas or gas mixture, such as its temperature, speed of sound, and shear and bulk viscosity.3–8
Compared to Spontaneous Rayleigh-Brillouin Scattering (SRBS), in which the signal is scattered in a 4π solid angle, CRBS has the important advantage that the scattered signal is a coherent laser beam, allowing for measurements at a distance without a decrease in the signal to noise ratio (SNR). As a result of it being a four wave mixing process and the phasematching conditions, it offers a high degree of spatial localization, typically 100–200 μm. Utilizing the chirped lattice CRBS approach9 allows spectral acquisition times of 150 ns to be achieved. Finally, in SRBS, the intensity of the scattered light, IS, is linearly proportional to the number of scatterers N. In contrast, the CRBS signal intensity IS is proportional to the square of the induced refractive index modulation: , where I1 and I2 are the pump intensities, Ipr the probe intensity, and , with αeff being the effective polarizability of the gas particles (atoms or molecules) and ΔN the induced periodic density modulation.
Confirmation of this quadratic dependence would allow CRBS signal calibration for a known gas composition and pressure. This would allow extrapolation of the measured CRBS signal for gases with unknown pressures and would enable the use of CRBS for remote pressure measurement in atomic gases, molecular gases, or a mixture of gases at a known and constant composition. The N2 (and thus p2 since p = nkBT, where p is the pressure, T is the temperature, and n is the number density equal to n = N/V, where V is the volume) dependence of the CRBS signal has already been demonstrated in Ref. 10 for N2 and here we offer comprehensive validation of this dependence for a number of different gases. We believe that the method described can be an important tool for accurate, remote, and non-intrusive pressure and temperature measurements. Additionally, measuring the CRBS signal intensities for different gases at the same pressure allowed us to confirm the dependence of the CRBS signal intensity on the gas polarizability, as predicted in Ref. 11, thus demonstrating how the effective polarizability of a gaseous medium can be accurately estimated using CRBS.
Remote, non-perturbing measurements of gas parameters are of great utility to experimental fluid dynamics and aerodynamics, as well as other research areas. A diagnostic method that fulfills these criteria would be a significant improvement on perturbative gauges to measure the gas pressure, such as Pitot tubes, and would eliminate the need for the use of a gas cell in static pressure systems.
CRBS is a four-wave mixing technique in which two laser beams (called the pumps) of set frequency difference Δω and of wavelength λpump interfere within a medium to create, due to electrostriction, an optical lattice of wavelength and of phase velocity v given by , where is the half angle between the two pump beams (Fig. 1). If a third beam (called the probe) of wavelength λprobe is incident upon this lattice at the Bragg angle θ = sin−1(λprobe∕(2·λg)), then a fourth coherent beam, called the signal, is generated. The CRBS spectrum is the record of the intensity of the signal beam with respect to Δω and it consists of three distinct peaks. One is the Rayleigh peak, centered around Δω = 0, which is Doppler broadened due to the thermal motion of the medium. Equally shifted around it and centered at the speed of sound are the two Brillouin peaks due to acoustic (pressure) waves launched in the medium.
The CRBS experiment used in this work is shown in Fig. 2. The laser system is largely based on the setup used in Ref. 9. Therefore, we provide only a short description of it here. The ∼15 mW single-mode, continuous-wave (CW) output of a custom made Nd:YVO4 microchip laser (called the master), which hosts an intracavity LiTaO3 electro-optic modulator (EOM), is injection seeded on a commercial laser diode emitting ∼20 mW, single-mode at 1064 nm (called the slave). The output of the slave is further amplified to 1 W by a commercial fiber amplifier (IPG Photonics YAR-1 K-1064-LP-SF). This CW beam is then split into two, and the resulting beams propagate through two intensity modulators (Jenoptik AM1064b) which chop the CW beams into pulses. When the first pulse has passed through the intensity modulator, a voltage signal is sent to the master laser's EOM in order to change the frequency of the second pulse with respect to the first one. When the resulting two pulses interfere, they create chirped optical lattices within a medium. The two pulses are further amplified through two custom made, triple stage, diode-pumped ND:YAG amplifiers. With this system, we obtain flat-top pulses of 10–1000 ns duration, with measured energies up to 250 mJ/pulse and chirps exceeding 1 GHz. Since the CRBS spectral range is inversely proportional to the molecular weight and dependent on the scattering angle, larger chirp rates may be needed to measure the CRBS profiles of lighter particles.
The main advantage of this setup compared to other CRBS implementations is that, by employing chirped optical lattices, i.e., lattices in which Δω is chirped for the duration of the pulse, it allows for a very fast acquisition of a CRBS spectrum in a single laser pulse. By comparison, it takes conventional CRBS implementations between 5 and 20 min for the acquisition of a CRBS spectrum.
Part of both beams is heterodyned on a fast photodiode (Hamamatsu Photonics G6854–01), and we use the analysis technique of Fee et al.12 to determine the instantaneous frequency f(t) of the beat signal across the pulse duration. The temporal spread of the resulting CRBS profile will be a function of the temporal profile of the induced chirp. A linear chirp rate is then preferential since the effective phase velocity is linearly mapped with the chirp rate. The heterodyne detection we are performing aids to verify, and correct if necessary, the chirp we are inducing. This way, we can determine the effective phase velocity across the pulse duration. The probe beam is derived from pump 1 through a thin film polarizer (TFP), and thus its polarization is normal to that of the pumps and it does not interfere with them. All beams have an energy of ∼130 mJ/pulse and a duration of ∼200 ns which, when focused to a spot of ∼150 μm diameter, corresponds to an intensity of ∼1.2 × 1014 W m−2.
The signal beam counterpropagates pump 2 and is separated from it through a TFP since it retains the polarization of the probe. It propagates for a long distance (8–10 m) in order to minimize the contribution of background light, before it is being detected. Since CRBS is a coherent process, the contribution of any incoherent components to the signal will decrease quadratically with distance. At high pressures, the signal is strong enough to be detected via a simple CCD camera (Thorlabs DCC1545M). This is the detector used for an initial optimization of the CRBS signal after which, a fast, unamplified photodiode (Hamamatsu Photonics G6854–01) can be used to spectrally resolve the CRBS signal on the oscilloscope. Figure 3 presents the CRBS signal averaged over 20 pulses from SF6 gas, at atmospheric pressure and room temperature. There is almost perfect agreement between the spectral location of the Brillouin peaks and the speed of sound in SF6, allowing us to be confident about the validity of the CRBS spectrum.
For low intensity measurements, the unamplified photodiode is replaced with an avalanche photodiode (APD). The APD used (Hamamatsu C5460–01) has a low bandwidth, resulting in a slow response (on the order of a few μs) which does not allow spectral resolution of the CRBS spectrum as was the case with the unamplified photodiode. However, we can record the integral of the signal, which is linearly proportional to the signal intensity, thus not altering the calibration procedure. This allows us to verify the N2 dependence of the integrated signal, similar to the verification of the integrated signal being proportional to N in spontaneous Rayleigh scattering.13
Figure 4 is a plot of the recorded values of the CRBS spectrally integrated signal for various pressures and for four different gases as measured with the APD, with the background subtracted for each data point. Also plotted is the quadratic fit to each experimental curve, normalized to the largest experimental value, in order to illustrate the quadratic dependence of the CRBS signal intensity with respect to pressure. It is apparent that there is ideal quadratic dependence of the measured signal with respect to pressure for all gases, confirming the findings in Ref. 10. A small disagreement can only be observed at very low signal levels (for air and CO2, inset of Fig. 4), which is attributed to the gain nonlinearity of the APD at low signal levels. Consequently, we propose that CRBS can be used for an accurate measurement of gas pressure in environments where one cannot simply use a pressure gauge, such as in combustion and transient flow environments. If one calibrates the measurement system at a known pressure, then one can measure at an area of unknown pressure and extrapolate the pressure with relative ease, with an estimated error of ∼5% as it emerges from the error bars in Fig. 4. Additionally, given the high spatial resolution of CRBS, typically between 100 and 200 μm, one can expect that this method could potentially be utilized for mapping out pressure in turbulent and laminar flows. Furthermore, as Fig. 4 suggests, the method is applicable to both molecular and atomic gases, as well as gas mixtures. The only constraint for the validity of the method would be that, for a gas mixture, the ratio of the constituent gases has to remain unchanged.
Another important finding from Fig. 4 is also the difference in scattering intensities for the different gases we measured at the same pressure. Indeed, since for the induced refractive index modulation Δn it holds that it would follow for the ratio of the scattered intensities from two different gases at the same pressure, that , as shown in Ref. 11 for optimal conditions, i.e., for when the phase velocity is optimal for the density perturbation of the i-th component and equal to , where Mi is the molecular mass. So for the SF6, CO2, air, and He gases we measured, with respective polarizabilities of 6.54, 2.507, 1.834 (effective), and 0.2 (all in units of 10−40 C m2 V−1), it is expected that the acquired signal intensity between two gases at a particular pressure would scale as the ratio of the polarizabilities to the same power. Hence, we have demonstrated the use of CRBS as a tool to validate and specify the effective polarizability in a gas, and more importantly a gas mixture, using another gas of established polarizability as a reference.
To date, the main efforts to provide such a pressure measurement tool have concentrated on the application of laser-induced thermal-acoustics (LITA) and laser-induced thermal grating spectroscopy (LITGS).14–19 Although these methods have successfully demonstrated their applicability in pressure and temperature measurement, they do have some limitations. More specifically, because they are dependent on the laser radiation absorption and subsequent acoustic wave generation, they work well at high pressures (typically above 2 atm) while only one such method has demonstrated its applicability at a pressure below 100 Torr.17 Finally, although the temperature measurement is trivial with these techniques (for a known gas composition), pressure derivation is in general model dependent and computationally complex and expensive, since it is derived from the fit to the obtained experimental data.15
We have verified for a range of gases the already established quadratic dependence of the obtained CRBS signal intensity on the gas density and thus pressure if the temperature is known. We have also shown that CRBS can be used for the measurement of temperature at high pressures by the spectral position of the Brillouin peaks since where γ is the adiabatic constant and M is the molecular mass of the gas. At low pressures, where the Brillouin peaks cannot be observed, the temperature can be derived by the lineshape of the Rayleigh peak as shown in previous works.1–3 Consequently, we have shown how this method can be used for remote, nonintrusive pressure, temperature and polarizability measurements in a gas or gas mixture of known composition. Of course, temperature and pressure cannot be simultaneously measured since one of these quantities is needed for the other to be retrieved. The results reported in the present letter are in agreement and in accordance with previous studies in the literature, in which accurate measurements of temperature in atomic and molecular gases,4 flames20 and weakly ionized plasmas21 as well as bulk viscocity7,8,22 and speed of sound6 have been reported. We have thus added pressure and polarizability in the list of quantities that can be measured with CRBS and, if one follows the chirped lattice approach shown here, shown how almost the full state of the free gas can be measured in a single laser pulse. Finally, it should be mentioned that measurements at pressures below 5 Torr should be possible using an APD with higher quantum efficiency than used here.
The authors would like to thank Dr. Y. Raitses and Dr. K. Hara of Princeton Plasma Physics Laboratory and Dr. A. Dogariu of Department of Mechanical and Aerospace Engineering, Princeton University for useful discussions. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. The digital data for this paper can be found at http://arks.princeton.edu/ark:/88435/dsp01x920g025r.