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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 12 — Jun. 4, 2012
  • pp: 12975–12986
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Experimental and numerical analysis of narrowband coherent Rayleigh–Brillouin scattering in atomic and molecular species

Barry M. Cornella, Sergey F. Gimelshein, Mikhail N. Shneider, Taylor C. Lilly, and Andrew D. Ketsdever  »View Author Affiliations


Optics Express, Vol. 20, Issue 12, pp. 12975-12986 (2012)
http://dx.doi.org/10.1364/OE.20.012975


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Abstract

Coherent Rayleigh–Brillouin scattering (CRBS) line shapes generated from all narrow-band pump experiment, Direct Simulation Monte-Carlo (DSMC) approach, and published kinetic line shape models are presented for argon, molecular nitrogen, and methane at 300 & 500 K and 1 atm. The kinetic line shape models require uncertain gas properties, such as bulk viscosity, and assume linearization of the kinetic equations from low intensities (<1 x 1015 W/m2) operating in the perturbative regime. DSMC, a statistical approach to the Boltzmann equation, requires only basic gas parameters available in literature and simulates the forcing function from first principles without assumptions on laser intensity. The narrow band experiments show similar results to broadband experiments and validate the use of DSMC for the prediction of CRBS line shapes.

© 2012 OSA

1. Introduction

Laser-gas interactions within pulsed optical lattices have proven to be a useful tool in gas diagnostics and characterization. Coherent Rayleigh scattering (CRS) and coherent Rayleigh-Brillouin scattering (CRBS) utilize low intensity, relative to breakdown, laser pulses to form a light interference pattern referred to as an optical lattice [1

1. R. W. Boyd, Nonlinear Optics (Academic, 1992).

]. This optical potential pattern, in turn, induces a periodic density perturbation in a gas sample with a periodicity on the order of the laser wavelength [2

2. H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer-Verlag, 1999).

]. By scattering a probe laser off the density grating formed by the lattice, seen in Fig. 1
Fig. 1 Schematic of a one-dimensional optical lattice, as formed by a CRBS experiment.
, the returned signal can be spectroscopically connected to the thermodynamic properties and velocity distribution of the gas sample [3

3. J. H. Grinstead and P. F. Barker, “Coherent Rayleigh scattering,” Phys. Rev. Lett. 85(6), 1222–1225 (2000). [CrossRef] [PubMed]

,4

4. X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh-Brillouin scattering,” Phys. Rev. Lett. 89(18), 183001 (2002). [CrossRef] [PubMed]

]. The necessary intermediate step is predicting the strength of the density perturbation for a given set of laser and gas parameters.

CRBS, as a gas diagnostic technique, has proven its use for yielding information about a gas, such as temperature [5

5. X. Pan, P. F. Barker, A. V. Meschanov, R. B. Miles, and J. H. Grinstead, “Temperature measurements in plasmas using coherent Rayleigh scattering,” in Proceedings of the Aerospace Sciences Meeting and Exhibit, AIAA-2001–0416 (Reno, NV, 2001).

,6

6. X. Pan, P. F. Barker, A. Meschanov, J. H. Grinstead, M. N. Shneider, and R. B. Miles, “Temperature measurements by coherent Rayleigh scattering,” Opt. Lett. 27(3), 161–163 (2002). [CrossRef] [PubMed]

] and bulk viscosity [7

7. X. P. Pan, M. N. Shneider, and R. B. Miles, “Power spectrum of coherent Rayleigh-Brillouin scattering in carbon dioxide,” Phys. Rev. A 71(4), 045801 (2005). [CrossRef]

,8

8. M. Vieitez, E. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A. de Wijn, N. Dam, and W. van de Water, “Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A 82(4), 043836 (2010). [CrossRef]

]. Since the pump lasers affect the gas at a kinetic level the connection between the experimentally obtained line shape signal and the gas condition, generally requires a solution to the Boltzmann equation. Currently, several kinetic line shape models are available that do not attempt to solve the Boltzmann equation directly, but use some approximations. Depending on the assumptions made, e.g. gas pressure, laser intensity, or species, separate kinetic line shape models have been developed for the collisionless [3

3. J. H. Grinstead and P. F. Barker, “Coherent Rayleigh scattering,” Phys. Rev. Lett. 85(6), 1222–1225 (2000). [CrossRef] [PubMed]

] or weakly collisional case of CRS and for the collisional case of CRBS [9

9. X. Pan, “Coherent Rayleigh–Brillouin scattering,” Princeton University (Ph.D. Thesis, 2003).

]. The latter requires further separation based on species, yielding a kinetic line shape model for the CRBS line shape based on the linearized Bhatnagar-Gross-Krook (for atomic species) or Wang-Chang-Uhlenbeck (molecular species) approximations to the 1-D Boltzmann equation. All of the models assume a near equilibrium condition and require bulk viscosity, and other gas transport properties, as an input. Of the input parameters used in these models (shear viscosity, bulk viscosity, thermal conductivity), the bulk viscosity is crucial in that it, so far, can only be measured at acoustic frequencies (not at the GHz employed in CRBS) and yet is necessary for accurate model treatment of internal energy relaxation. Because of the difficulty of working with this parameter [8

8. M. Vieitez, E. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A. de Wijn, N. Dam, and W. van de Water, “Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A 82(4), 043836 (2010). [CrossRef]

], a simulation technique such as DSMC, which does not require bulk viscosity as an input; may be more versatile than existing kinetic line shape models.

The use of a statistical approach (DSMC) to the Boltzmann equation allows for the same information to be predicted for various gas and laser conditions, mainly the magnitude of the induced density perturbation, using a first principles approach to the simulation process. A modified version of the DSMC code, SMILE, was used to calculate the magnitude of the density perturbations caused by non-resonant pulsed optical lattices in a configuration consistent with the performed CRBS experiments. The DSMC method has previously been applied to spontaneous Rayleigh-Brillouin spectra in atomic gases [10

10. D. Bruno, M. Capitelli, S. Longo, and P. Minelli, “Monte Carlo simulation of light scattering spectra in atomic gases,” Chem. Phys. Lett. 422(4-6), 571–574 (2006). [CrossRef]

], though not previously compared with experiments, and now is applied to scattering in a localized potential field which induces forced density perturbations (CRBS). SMILE has been used to predict the modification of a neutral gas by several laser configurations [11

11. T. Lilly, S. Gimelshein, A. Ketsdever, and M. Shneider, “Energy deposition into a collisional gas from optical lattices formed in an optical cavity,” in Proceedings of the 26th International Symposium on Rarefied Gas Dynamics, 533–538, 2008, T. Abe ed. (AIP, New York, 2009).

13

13. T. Lilly, “Simulated nonresonant pulsed laser manipulation of a nitrogen flow,” Appl. Phys. B 104(4), 961–968 (2011). [CrossRef]

] and is compared directly with an experiment in this investigation. The line shapes obtained experimentally and numerically are further compared against published atomic and molecular (s6) [9

9. X. Pan, “Coherent Rayleigh–Brillouin scattering,” Princeton University (Ph.D. Thesis, 2003).

] kinetic line shape models. It should be noted that the s6 model used in this work is a modified version of the Tenti model, originally derived for spontaneous Rayleigh-Brillouin spectra, for more information can be found in [9

9. X. Pan, “Coherent Rayleigh–Brillouin scattering,” Princeton University (Ph.D. Thesis, 2003).

] and the references within.

2. Theoretical framework

E2(x,t)=E12cos2(k1xω1t)+E22cos2(k2xω2t)+E1E2[cos((k1k2)x(ω1ω2)t)+cos((k1+k2)x(ω1+ω2)t)]
(2)

In Eq. (2), E1 and E2 represent the electric field amplitudes [V m−1] of laser pulses 1 and 2 respectively, k1 and k2 represent the two pulses’ wave numbers [rad m−1], and ω1 and ω2 represent the pulses’ angular frequency [rad s−1]. When k1≈-k2 and ω1≈ω2, the interference term of the field has two components: one with a relatively long spatial and short temporal period, and the other with a short spatial and long temporal period. When the gradient of Eq. (2) is taken per Eq. (1), the portion with the long spatial period has a negligible impact. In addition, the fast oscillating terms (cos2) can be time averaged to a constant value of 1/2. The resulting force acting on a particle within the potential region is given by
F=U=(αq/2)E1E2sin(qxΩt)
(3)
where q = k1-k2 is the lattice (interference pattern) wave number [rad m−1] and Ω = ω12 is the lattice angular frequency [rad s−1]. Note that q and Ω define the velocity of the lattice, ξ = Ω/q [m s−1]. The sign of Ω defines the direction of ξ. The intensity of the two laser pulses is assumed to have a Gaussian shape in both space (radial) and time which is described by
I(r,t)=Imaxexp(4ln(2)[(tto)2/τ2+r2/D2])E02=2I/cϵ0
(4)
where Imax is the on-axis peak intensity [W m−2], τ is the laser pulse width (FWHM of I) [s] and D is the laser beam diameter (FWHM of I) [m]. By substituting the laser intensity for the electric field magnitude, Eq. (3) in the axial direction becomes
Fx(x,r,t)=αq/cϵ0I1(r,t)I2(r,t) sin(qxΩt)
(5)
It should be noted that a gradient in the axial intensity profile caused by the temporal Gaussian shape can be neglected as (2π/q)/(c τfwhm)<<1. This equation gives the force on an individual particle based on its location in space and time relative to the center of the laser pulse’s temporal envelope.

δρ2Ipump1Ipump2
(7)

3. Experimental setup

Two Q-switched, frequency doubled, injection seeded, Nd:YAG lasers, each with ~5 ns pulses, generated the two narrowband pumps (~180 MHz line width). The two pump pulses passed through a set of 500 mm focal length lenses and crossed to form the interaction region with a diameter of approximately 100 µm. The crossing angle was 178° ± 0.5° as measured by spatial locations on the crossing lenses. A probe beam was split from pump 1, rotated in polarization orthogonal to the pump beams so not to interfere with the lattice interaction, and separately sent to the interaction region. This configuration required the signal to also be orthogonal in polarization to the pump beams, allowing it to be extracted using a thin film polarizer. The timing of the lasers was controlled by high precision delay generators. Care was taken in matching the path length of the probe to pump 1 and determining the timing of pump 2 to ensure the all three beams arrived at the interaction region simultaneously. The coherence length of the two pulses was approximately 1.6 m based on the speed of light over the line width [22

22. E. Hecht, Optics (Addison Wesley, 2002).

], c/Δf. For a path length matching to within 0.3 m, the interaction region was well within the coherence length, creating deep monochromatic potential wells. Therefore, the lattice interaction was both coherent and correlated.

The phase matching condition is shown in Fig. 3
Fig. 3 Phase matching condition for signal backscatter along the path of pump 2.
. Because the probe beam and pump 1 were degenerate, the probe beam was set to directly counter-propagate pump 1. This configuration required the scattered signal to propagate counter to pump 2, independent of the frequency difference between the two lasers. The center frequency of pump 2 was varied by a voltage input to the injection seed laser allowing explicit control over the lattice velocity. The frequency was scanned such that the range of the frequency differences varied from ~0 to ~3-5 GHz, in increments of ~15 MHz. Due to the symmetric nature of the line shapes, only the positive frequency differences were scanned to ensure consistency of the laser system over the temporal extent of the run. Temperature and pressure of the gases were verified at each data point. Small fractions of each seed laser (1064 nm) were interfered and the beat frequency measured on a fast amplified InGaAs photodiode. The measurements were taken on a 7 GHz oscilloscope, yielding a direct measurement of the frequency difference of the pumps at each increment (Δfpump = 2Δfseed).

Three nominal gases were selected for comparison: argon (monatomic), molecular nitrogen (diatomic), and methane (polyatomic). The experiments were performed for gas temperatures of 300 K and 500 K. A small vacuum chamber, which included 532 nm anti-reflective coated windows, was placed at the interaction region and back-filled with the test gas to 1 atm. A diagram of the chamber setup is shown in Fig. 4
Fig. 4 Diagram of the test chamber.
. Each pump energy was set to approximately 18 mJ, corresponding to a combined intensity value at the axis at the interaction region (3.0 x 1014 W/m2) well below the breakdown threshold for the test gases (2.0 x 1016 W/m2) [23

23. T. X. Phuoc, “Laser spark ignition experimental determination of laser-induced breakdown thresholds of combustion gases,” Opt. Commun. 175(4-6), 419–423 (2000). [CrossRef]

] and within the small perturbation regime for the lattice-gas interaction [24

24. H. T. Bookey, M. N. Shneider, and P. F. Barker, “Spectral narrowing in coherent Rayleigh scattering,” Phys. Rev. Lett. 99(13), 133001 (2007). [CrossRef] [PubMed]

]. For tests at 500 K, a resistive heater was wrapped around the outside of the chamber. The heater was controlled using a variable transformer and the temperature was measured using a J-type thermocouple. At each frequency point, the scattered beam was detected on a high speed GaAs photodiode and the signal averaged over 100 shots on the oscilloscope. The peak of the averaged signal was then recorded by a LabView interface along with data pertaining to the beat frequency, signal, and temperature.

4. Numerical setup

The force acting on the molecules directly affects the velocity distribution of the flow, requiring a kinetic approach to model the impact of the laser-species interaction on species trajectories. The kinetic approach chosen was the DSMC code SMILE. The code was modified to include the non-resonant laser interaction described by Eq. (5). This modification used a Newtonian integration scheme to approximate the force on a molecule as a temporally and spatially varying acceleration, which was considered constant over the duration of a simulation time step. Time steps were therefore reduced such that the species did not traverse appreciable fractions of the laser field or temporal pulse width in one time step. The SMILE code has been broadly applied and experimentally validated; see [25

25. M. S. Ivanov and S. F. Gimelshein, “Current status and prospects of the DSMC modeling of near-continuum flows of non-reacting and reacting gases,” in Proceedings of the 23rd International Symposium on Rarefied Gas Dynamics, 2002, A. Ketsdever, ed. (AIP, 2003), pp. 339–348.

] and the references therein. The variable hard sphere (VHS) model [26

26. G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford University Press, 1994).

] and majorant frequency scheme [27

27. M. S. Ivanov, A. V. Kashkovsky, S. F. Gimelshein, and G. N. Markelov, “Statistical simulation of hypersonic flows from free-molecular to near-continuum regimes,” Thermophys. Aeromechanics 4, 251–268 (1997).

] were employed for modeling molecular collisions. The latter feature was particularly important for maintaining fidelity while reducing the time step to satisfy the laser interaction conditions. The Larsen-Borgnakke model [28

28. C. Borgnakke and P. Larsen, “Statistical collision model for Monte Carlo simulation of polyatomic gas mixture,” J. Comput. Phys. 18(4), 405–420 (1975). [CrossRef]

] with temperature-dependent rotational and vibrational relaxation numbers was utilized for rotation/vibration-translation energy transfer.

The nominal set of conditions and laser parameters were chosen to match those contained in the experiment. The nominal condition simulated a pair of 532 nm wavelength, 18 mJ, 100 μm (FWHM), 5 ns (FWHM) pulses interacting with each test gas. The simulation domain was modeled as axisymmetric around the optical axis of the two idealized anti-parallel, counter-propagating pulses. The lattice phase velocity in the forcing function described in Eq. (5) was varied in increments of 50 m/s through the range corresponding to the experiment. In order to cover the temporal shape of the pulses, each pulse simulation ran from -τ to + τ where τ was assumed to be 5 ns (FWHM). Therefore, the total time for each simulation was 10 ns. With a laser pulse spatial length of approximately 1.5 m, the axial domain boundaries were considered periodic. The radial domain boundary was considered specular and assumed to represent a sufficiently small cross-section at the center of the laser focus, such that the surrounding volume was equally affected. Also note that in the perturbative regime, there exists a linear relation between the square of the density perturbation and the scattering efficiency [19

19. X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh-Brillouin scattering in molecular gases,” Phys. Rev. A 69(3), 033814 (2004). [CrossRef]

]. This allows a representative portion of the optical interaction to be simulated and compared with experiment. The domain was nominally 6.65 nm tall and 532 nm wide. A diagram of the domain with an overlay of the maximum potential well depth (Tplot = −2U/k) is shown in Fig. 5(a)
Fig. 5 (a) SMILE simulation domain and maximum potential well depth [K] for an intensity of 3 x 1014 W/m2 [30] and (b) simulated density for a lattice velocity of 450 m/s.
.

The first step in the simulation procedure was to populate the domain in the baseline ambient configuration with the appropriate gas properties. Flow field properties were sampled every 1/20th of a run, 1/10th of a pulse width, in order to yield a time-dependent evolution of the gas in the simulation domain. With approximately 7,500,000 simulated particles per sample cell, the average statistical error is estimated at approximately 0.1%. The numerical density perturbation was found by a non-linear least squares fit of the axial domain density to a cosine as seen in Fig. 5(b). The magnitude of the cosine fit was used as the magnitude of the density perturbation. As discussed above, the square of the density perturbation is proportional to the magnitude of the scattered signal. The axial domain density perturbation shown in Fig. 5(b) corresponds to the circled point in the numerical/experimental comparison with a lattice velocity of 450 m/s.

An atomic model, formulated by Pan [9

9. X. Pan, “Coherent Rayleigh–Brillouin scattering,” Princeton University (Ph.D. Thesis, 2003).

], was used to predict the CRBS line shape for argon, whereas a six moment (s6) model for polyatomic molecules, also formulated by Pan [9

9. X. Pan, “Coherent Rayleigh–Brillouin scattering,” Princeton University (Ph.D. Thesis, 2003).

], was utilized for comparison with nitrogen, methane, and water. The input gas parameters for the kinetic line shape models are given in Table 2

Table 2. List of Gas Parameters for Kinetic Line Shape Models

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, including the y-parameter, defined as [4

4. X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh-Brillouin scattering,” Phys. Rev. Lett. 89(18), 183001 (2002). [CrossRef] [PubMed]

]
y=832πρ0kbT0/Mηq
(8)
where kb is Boltzmann’s constant [J/K], η is the sheer viscosity [Pa s], and M, ρ0 and T0 are the gas molecular mass [kg], density [kg/m3], and temperature [K]. The value for the bulk viscosity of nitrogen used in this work is suggested from Pan [9

9. X. Pan, “Coherent Rayleigh–Brillouin scattering,” Princeton University (Ph.D. Thesis, 2003).

], but it should be noted that other values for the bulk viscosity, such as one a factor of 2 higher in [8

8. M. Vieitez, E. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A. de Wijn, N. Dam, and W. van de Water, “Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A 82(4), 043836 (2010). [CrossRef]

], have also been experimentally suggested. At pressures near 1 atm, the effect of the bulk viscosity, for values within an order of magnitude, on these line shapes is small, e.g. see Fig. 8(c)
Fig. 8 Comparison of numerical and kinetic line shape results for (a) varying N2 pressure, (b) water vapor using s6 & ηb/η = 1000, and (c) water vapor using s6 & various ηb/η. Upper figure shows normalized signal, lower figure shows residual between values and kinetic line shape model.
.

5. Results and discussion

The results for the CRBS experimental runs and numerical simulations for argon, molecular nitrogen, and methane at 300 K are shown in Fig. 6
Fig. 6 Comparison of low intensity CRBS line shapes for Ar, N2, and CH4 at 300 K. Upper figure shows normalized signal, lower figure shows residual between values and kinetic line shape model.
. While the magnitude of the density perturbation is not directly measured by the experimental setup, the relative change in the erturbation (squared) is characterized by a corresponding change in signal intensity as described in Eq. (8). The maxima of the experimentally recorded (averaged) scattered signal are compared to the numerically simulated density perturbations (squared). Each set of results was normalized such that the area under the line shape for common frequencies is equal. Some experimental sets do not fully reach 0 GHz due to laser frequency control, while some numerical sets do not extend to reach 0 signal; areas were matched for the extent of the data in common. Comparison of the results obtained in this investigation with previously validated kinetic line shape models provides verification of both the presented numerical method, as well as the narrowband experimental technique.

Signal in Fig. 6 is shown versus the frequency difference of the two pump beams. For 532 nm pump lasers, the conversion from frequency difference between the pumps to the velocity of the lattice, from above ξ = Ω/q, is approximately 0.38 GHz per 100 m/s. Because the CRBS scheme operates in the perturbative regime, the expected width of the line shape curve (half width half maximum) is on the order of (and should vary with) the mean thermal speed of each species, as indicated by the kinetic line shape models. Shown in Fig. 6, the numerical results, DSMC, compare favorably to experimental results as well as kinetic line shape models for all three gases. Scatter in the experimental data arises from laser pointing instabilities in both space and time. In particular, spatial movement due to the frequency locking control loop in each pump cavity and seed laser was occasionally observed to cause fluctuations in signal intensity, similar to those shown in Fig. 6, at various frequency points. However, Fig. 6 reflects that the prominent features, such as overall shape and line width, are retained in the experimental data within the scatter. Likewise, the numerical results also capture the general features of the line shape for each gas within the simulation error.

Using the same gas dynamic parameters in Fig. 6, the kinetic line shape model was applied to all three gases at an elevated temperature and compared to results from the numerical simulations and the experiment. Figure 7
Fig. 7 Comparison of low intensity CRBS line shapes for Ar, N2, and CH4 at 500 K. Upper figure shows normalized signal, lower figure shows residual between values and kinetic line shape model.
shows the CRBS results at 500 K. Since the CRBS line shape in the perturbative regime is dictated by collisional gas dynamic phenomena, it follows that the line shape width increases with the square root of temperature which can be seen in all three cases of Fig. 7. Again, the experimental and numerical results compare favorably to the predicted kinetic line shape model. For a given lattice potential well depth (intensity), less of the gas is affected as the velocity distribution broadens. Thus, as the temperature of the gas increases, the magnitude of density perturbation created by the lattice decreases for the same pump intensities. Consequently, an increase in relative experimental data scatter occurs due to an overall decrease in signal intensity. As a result, the fluctuations in the higher temperature experimental data are more pronounced. The error associated with determining the density perturbation in the numerical simulations also increases with temperature due to the decrease in signal to noise ratio. However, as was the case for the lower temperature data sets, both the experimental and numerical results were able to capture both the general line shape, as well quantifiably determine a line width.

DSMC simulations were further applied to two additional scenarios: varying pressure and a polar molecule. Figure 8(a) shows the comparison of the DSMC numerical predictions for the CRBS line at 1 atm (left) and 5 atm (right), with the line shape predicted by [9

9. X. Pan, “Coherent Rayleigh–Brillouin scattering,” Princeton University (Ph.D. Thesis, 2003).

]. Both curves are normalized as above with equal area for common frequencies. As shown in Fig. 8(a), Brillouin peaks become much more prominent at higher pressures than at 1 atm and occur at lattice velocities on the order of the speed of sound [4

4. X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh-Brillouin scattering,” Phys. Rev. Lett. 89(18), 183001 (2002). [CrossRef] [PubMed]

]. The DSMC predictions accurately predict the location of the Brillouin peaks as well as the magnitude (~150% larger than the center Rayleigh peak) for nitrogen at 5 atm. Figure 8(b) shows the comparison of DSMC simulation to predicted line shape for water vapor at 400 K. A ratio of bulk viscosity to shear viscosity was assumed to be 1000 in the kinetic line shape model due to a lack of readily available published data on the value. Figure 8(c) shows several kinetic line shape model lines, using various bulk/shear ratios to show the possibility of using the DSMC to find the bulk viscosity for a gas with well understood internal degrees of freedom. Figure 8 illustrates that the proposed numerical simulation method can be applied to predicting CRBS spectra for varying pressures as well as for naturally polar species, assuming the permanent dipole moment is less influential than the induced moment for this application.

6. Conclusion

Acknowledgments

This work was supported by the Air Force Office of Scientific Research (AFOSR). The authors would like to thank Dr. Mitat Birkan (AFOSR/RSA) for his support of numerical efforts and Dr. Tatjana Curcic (AFOSR/RSE) for her support of experimental efforts. This work was also supported, in part, by a grant of computer time from the DOD High Performance Computing Modernization Program at the U.S. Army Engineer Research and Development Center DoD Supercomputing Resource Center (ERDC DSRC).

References and links

1.

R. W. Boyd, Nonlinear Optics (Academic, 1992).

2.

H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer-Verlag, 1999).

3.

J. H. Grinstead and P. F. Barker, “Coherent Rayleigh scattering,” Phys. Rev. Lett. 85(6), 1222–1225 (2000). [CrossRef] [PubMed]

4.

X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh-Brillouin scattering,” Phys. Rev. Lett. 89(18), 183001 (2002). [CrossRef] [PubMed]

5.

X. Pan, P. F. Barker, A. V. Meschanov, R. B. Miles, and J. H. Grinstead, “Temperature measurements in plasmas using coherent Rayleigh scattering,” in Proceedings of the Aerospace Sciences Meeting and Exhibit, AIAA-2001–0416 (Reno, NV, 2001).

6.

X. Pan, P. F. Barker, A. Meschanov, J. H. Grinstead, M. N. Shneider, and R. B. Miles, “Temperature measurements by coherent Rayleigh scattering,” Opt. Lett. 27(3), 161–163 (2002). [CrossRef] [PubMed]

7.

X. P. Pan, M. N. Shneider, and R. B. Miles, “Power spectrum of coherent Rayleigh-Brillouin scattering in carbon dioxide,” Phys. Rev. A 71(4), 045801 (2005). [CrossRef]

8.

M. Vieitez, E. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A. de Wijn, N. Dam, and W. van de Water, “Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A 82(4), 043836 (2010). [CrossRef]

9.

X. Pan, “Coherent Rayleigh–Brillouin scattering,” Princeton University (Ph.D. Thesis, 2003).

10.

D. Bruno, M. Capitelli, S. Longo, and P. Minelli, “Monte Carlo simulation of light scattering spectra in atomic gases,” Chem. Phys. Lett. 422(4-6), 571–574 (2006). [CrossRef]

11.

T. Lilly, S. Gimelshein, A. Ketsdever, and M. Shneider, “Energy deposition into a collisional gas from optical lattices formed in an optical cavity,” in Proceedings of the 26th International Symposium on Rarefied Gas Dynamics, 533–538, 2008, T. Abe ed. (AIP, New York, 2009).

12.

T. Lilly, A. Ketsdever, and S. Gimelshein, “Resonant laser manipulation of an atomic beam,” in Proceedings of the 27th International Symposium on Rarefied Gas Dynamics, 825–830, 2010, D. Levin ed. (AIP, New York, 2011).

13.

T. Lilly, “Simulated nonresonant pulsed laser manipulation of a nitrogen flow,” Appl. Phys. B 104(4), 961–968 (2011). [CrossRef]

14.

M. N. Shneider and P. F. Barker, “Optical Landau damping,” Phys. Rev. A 71(5), 053403 (2005). [CrossRef]

15.

M. N. Shneider, P. F. Barker, and S. F. Gimelshein, “Molecular transport in pulsed optical lattices,” Appl. Phys., A Mater. Sci. Process. 89(2), 337–350 (2007). [CrossRef]

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A. Stampanoni-Panariello, D. N. Kozlov, P. P. Radi, and B. Hemmerling, “Gas-phase diagnostics by laser-induced gratings I,” Appl. Phys. B 81(1), 101–111 (2005). [CrossRef]

17.

A. Stampanoni-Panariello, D. N. Kozlov, P. P. Radi, and B. Hemmerling, “Gas-phase diagnostics by laser-induced gratings II,” Appl. Phys. B 81(1), 113–129 (2005). [CrossRef]

18.

H. Eichler, P. Gunter, and D. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, 1986).

19.

X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh-Brillouin scattering in molecular gases,” Phys. Rev. A 69(3), 033814 (2004). [CrossRef]

20.

H. Bookey, A. Bishop, M. N. Shneider, and P. Barker, “Narrow-band Coherent Rayleigh scattering,” J. Raman Spectrosc. 37(6), 655–662 (2006). [CrossRef]

21.

A. Manteghi, N. J. Dam, A. S. Meijer, A. S. de Wijn, and W. van de Water, “Spectral narrowing in coherent Rayleigh-Brillouin scattering,” Phys. Rev. Lett. 107(17), 173903 (2011). [CrossRef] [PubMed]

22.

E. Hecht, Optics (Addison Wesley, 2002).

23.

T. X. Phuoc, “Laser spark ignition experimental determination of laser-induced breakdown thresholds of combustion gases,” Opt. Commun. 175(4-6), 419–423 (2000). [CrossRef]

24.

H. T. Bookey, M. N. Shneider, and P. F. Barker, “Spectral narrowing in coherent Rayleigh scattering,” Phys. Rev. Lett. 99(13), 133001 (2007). [CrossRef] [PubMed]

25.

M. S. Ivanov and S. F. Gimelshein, “Current status and prospects of the DSMC modeling of near-continuum flows of non-reacting and reacting gases,” in Proceedings of the 23rd International Symposium on Rarefied Gas Dynamics, 2002, A. Ketsdever, ed. (AIP, 2003), pp. 339–348.

26.

G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford University Press, 1994).

27.

M. S. Ivanov, A. V. Kashkovsky, S. F. Gimelshein, and G. N. Markelov, “Statistical simulation of hypersonic flows from free-molecular to near-continuum regimes,” Thermophys. Aeromechanics 4, 251–268 (1997).

28.

C. Borgnakke and P. Larsen, “Statistical collision model for Monte Carlo simulation of polyatomic gas mixture,” J. Comput. Phys. 18(4), 405–420 (1975). [CrossRef]

29.

A. S. Meijer, A. S. de Wijn, M. F. E. Peters, N. J. Dam, and W. van de Water, “Coherent Rayleigh-Brillouin scattering measurements of bulk viscosity of polar and nonpolar gases, and kinetic theory,” J. Chem. Phys. 133(16), 164315 (2010). [CrossRef] [PubMed]

30.

T. Lilly, A. Ketsdever, B. Cornella, T. Quiller, and S. Gimelshein, “Gas density perturbations induced by a pulsed optical lattice,” Appl. Phys. Lett. 99(12), 124101 (2011). [CrossRef]

31.

J. G. Parker, “Rotational and vibrational relaxation in diatomic gases,” Phys. Fluids 2(4), 449–462 (1959). [CrossRef]

32.

R. C. Millikan and D. R. White, “Systematics of vibrational relaxation,” J. Chem. Phys. 39(12), 3209–3213 (1963). [CrossRef]

33.

S. F. Gimelshein, I. D. Boyd, and M. S. Ivanov, “DSMC modeling of vibration-translation energy transfer in hypersonic rarefied flows,” in Proceedings of the 33rd AIAA Thermophysics Conference, AIAA-99–3451, 1999.

34.

N. E. Gimelshein, S. F. Gimelshein, and D. A. Levin, “Hydroxyl formation mechanisms and models in high-altitude hypersonic flows,” AIAA J. 41(7), 1323–1331 (2003). [CrossRef]

35.

G. L. Hill and T. G. Winter, “Effect of Temperature on the Rotational and Vibrational Relaxation Times of Some Hydrocarbons,” J. Chem. Phys. 49(1), 440–444 (1968). [CrossRef]

36.

J. A. Lordi and R. E. Mates, “Rotational Relaxation in Nonpolar Diatomic Gases,” Phys. Fluids 13(2), 291–308 (1970). [CrossRef]

37.

R. Jansen, I. Wysong, S. Gimelshein, M. Zeifman, and U. Buck, “Nonequilibrium numerical model of homogeneous condensation in argon and water vapor expansions,” J. Chem. Phys. 132(24), 244105 (2010). [CrossRef] [PubMed]

38.

D. R. Lide ed., CRC Handbook of Chemistry and Physics 90th ed. (CRC, 2009).

39.

G. J. Prangsma, A. H. Alberga, and J. J. M. Beenakker, “Ultrasonic determination of the volume viscosity of N2, CO, CH4 and CD4 between 77 and 300 K,” Physica 64(2), 278–288 (1973). [CrossRef]

40.

G. Emanuel, “Bulk viscosity of a dilute polyatomic gas,” Phys. Fluids A 2(12), 2252–2254 (1990). [CrossRef]

OCIS Codes
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(290.5820) Scattering : Scattering measurements
(290.5830) Scattering : Scattering, Brillouin
(290.5870) Scattering : Scattering, Rayleigh
(300.6240) Spectroscopy : Spectroscopy, coherent transient
(190.2055) Nonlinear optics : Dynamic gratings

ToC Category:
Scattering

History
Original Manuscript: February 17, 2012
Revised Manuscript: April 23, 2012
Manuscript Accepted: April 23, 2012
Published: May 24, 2012

Citation
Barry M. Cornella, Sergey F. Gimelshein, Mikhail N. Shneider, Taylor C. Lilly, and Andrew D. Ketsdever, "Experimental and numerical analysis of narrowband coherent Rayleigh–Brillouin scattering in atomic and molecular species," Opt. Express 20, 12975-12986 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-12-12975


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References

  1. R. W. Boyd, Nonlinear Optics (Academic, 1992).
  2. H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer-Verlag, 1999).
  3. J. H. Grinstead and P. F. Barker, “Coherent Rayleigh scattering,” Phys. Rev. Lett.85(6), 1222–1225 (2000). [CrossRef] [PubMed]
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  5. X. Pan, P. F. Barker, A. V. Meschanov, R. B. Miles, and J. H. Grinstead, “Temperature measurements in plasmas using coherent Rayleigh scattering,” in Proceedings of the Aerospace Sciences Meeting and Exhibit, AIAA-2001–0416 (Reno, NV, 2001).
  6. X. Pan, P. F. Barker, A. Meschanov, J. H. Grinstead, M. N. Shneider, and R. B. Miles, “Temperature measurements by coherent Rayleigh scattering,” Opt. Lett.27(3), 161–163 (2002). [CrossRef] [PubMed]
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  9. X. Pan, “Coherent Rayleigh–Brillouin scattering,” Princeton University (Ph.D. Thesis, 2003).
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  11. T. Lilly, S. Gimelshein, A. Ketsdever, and M. Shneider, “Energy deposition into a collisional gas from optical lattices formed in an optical cavity,” in Proceedings of the 26th International Symposium on Rarefied Gas Dynamics, 533–538, 2008, T. Abe ed. (AIP, New York, 2009).
  12. T. Lilly, A. Ketsdever, and S. Gimelshein, “Resonant laser manipulation of an atomic beam,” in Proceedings of the 27th International Symposium on Rarefied Gas Dynamics, 825–830, 2010, D. Levin ed. (AIP, New York, 2011).
  13. T. Lilly, “Simulated nonresonant pulsed laser manipulation of a nitrogen flow,” Appl. Phys. B104(4), 961–968 (2011). [CrossRef]
  14. M. N. Shneider and P. F. Barker, “Optical Landau damping,” Phys. Rev. A71(5), 053403 (2005). [CrossRef]
  15. M. N. Shneider, P. F. Barker, and S. F. Gimelshein, “Molecular transport in pulsed optical lattices,” Appl. Phys., A Mater. Sci. Process.89(2), 337–350 (2007). [CrossRef]
  16. A. Stampanoni-Panariello, D. N. Kozlov, P. P. Radi, and B. Hemmerling, “Gas-phase diagnostics by laser-induced gratings I,” Appl. Phys. B81(1), 101–111 (2005). [CrossRef]
  17. A. Stampanoni-Panariello, D. N. Kozlov, P. P. Radi, and B. Hemmerling, “Gas-phase diagnostics by laser-induced gratings II,” Appl. Phys. B81(1), 113–129 (2005). [CrossRef]
  18. H. Eichler, P. Gunter, and D. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, 1986).
  19. X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh-Brillouin scattering in molecular gases,” Phys. Rev. A69(3), 033814 (2004). [CrossRef]
  20. H. Bookey, A. Bishop, M. N. Shneider, and P. Barker, “Narrow-band Coherent Rayleigh scattering,” J. Raman Spectrosc.37(6), 655–662 (2006). [CrossRef]
  21. A. Manteghi, N. J. Dam, A. S. Meijer, A. S. de Wijn, and W. van de Water, “Spectral narrowing in coherent Rayleigh-Brillouin scattering,” Phys. Rev. Lett.107(17), 173903 (2011). [CrossRef] [PubMed]
  22. E. Hecht, Optics (Addison Wesley, 2002).
  23. T. X. Phuoc, “Laser spark ignition experimental determination of laser-induced breakdown thresholds of combustion gases,” Opt. Commun.175(4-6), 419–423 (2000). [CrossRef]
  24. H. T. Bookey, M. N. Shneider, and P. F. Barker, “Spectral narrowing in coherent Rayleigh scattering,” Phys. Rev. Lett.99(13), 133001 (2007). [CrossRef] [PubMed]
  25. M. S. Ivanov and S. F. Gimelshein, “Current status and prospects of the DSMC modeling of near-continuum flows of non-reacting and reacting gases,” in Proceedings of the 23rd International Symposium on Rarefied Gas Dynamics, 2002, A. Ketsdever, ed. (AIP, 2003), pp. 339–348.
  26. G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford University Press, 1994).
  27. M. S. Ivanov, A. V. Kashkovsky, S. F. Gimelshein, and G. N. Markelov, “Statistical simulation of hypersonic flows from free-molecular to near-continuum regimes,” Thermophys. Aeromechanics4, 251–268 (1997).
  28. C. Borgnakke and P. Larsen, “Statistical collision model for Monte Carlo simulation of polyatomic gas mixture,” J. Comput. Phys.18(4), 405–420 (1975). [CrossRef]
  29. A. S. Meijer, A. S. de Wijn, M. F. E. Peters, N. J. Dam, and W. van de Water, “Coherent Rayleigh-Brillouin scattering measurements of bulk viscosity of polar and nonpolar gases, and kinetic theory,” J. Chem. Phys.133(16), 164315 (2010). [CrossRef] [PubMed]
  30. T. Lilly, A. Ketsdever, B. Cornella, T. Quiller, and S. Gimelshein, “Gas density perturbations induced by a pulsed optical lattice,” Appl. Phys. Lett.99(12), 124101 (2011). [CrossRef]
  31. J. G. Parker, “Rotational and vibrational relaxation in diatomic gases,” Phys. Fluids2(4), 449–462 (1959). [CrossRef]
  32. R. C. Millikan and D. R. White, “Systematics of vibrational relaxation,” J. Chem. Phys.39(12), 3209–3213 (1963). [CrossRef]
  33. S. F. Gimelshein, I. D. Boyd, and M. S. Ivanov, “DSMC modeling of vibration-translation energy transfer in hypersonic rarefied flows,” in Proceedings of the 33rd AIAA Thermophysics Conference, AIAA-99–3451, 1999.
  34. N. E. Gimelshein, S. F. Gimelshein, and D. A. Levin, “Hydroxyl formation mechanisms and models in high-altitude hypersonic flows,” AIAA J.41(7), 1323–1331 (2003). [CrossRef]
  35. G. L. Hill and T. G. Winter, “Effect of Temperature on the Rotational and Vibrational Relaxation Times of Some Hydrocarbons,” J. Chem. Phys.49(1), 440–444 (1968). [CrossRef]
  36. J. A. Lordi and R. E. Mates, “Rotational Relaxation in Nonpolar Diatomic Gases,” Phys. Fluids13(2), 291–308 (1970). [CrossRef]
  37. R. Jansen, I. Wysong, S. Gimelshein, M. Zeifman, and U. Buck, “Nonequilibrium numerical model of homogeneous condensation in argon and water vapor expansions,” J. Chem. Phys.132(24), 244105 (2010). [CrossRef] [PubMed]
  38. D. R. Lide ed., CRC Handbook of Chemistry and Physics 90th ed. (CRC, 2009).
  39. G. J. Prangsma, A. H. Alberga, and J. J. M. Beenakker, “Ultrasonic determination of the volume viscosity of N2, CO, CH4 and CD4 between 77 and 300 K,” Physica64(2), 278–288 (1973). [CrossRef]
  40. G. Emanuel, “Bulk viscosity of a dilute polyatomic gas,” Phys. Fluids A2(12), 2252–2254 (1990). [CrossRef]

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