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Experimental and Numerical Analysis of Narrowband Coherent Rayleigh-Brillouin 5b. GRANT NUMBER

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6. AUTHOR(S)Barry M. Cornell; Sergey F. Gimelshein; Mikhail N. Schneider; Taylor C. Lilly; and

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Andrew Ketsdever

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14. ABSTRACT

Coherent Rayleigh-Brillouin scattering (CRBS) lineshapes generated from an all narrow-band pump experiment, a Direct Simulation Monte-Carlo (DSMC) approach, and published simplified models are presented for argon, molecular nitrogen, and methane at 300 & 500 K and 1 atm. The simplified 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 lineshapes.

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19a. NAME OF RESPONSIBLE PERSON Marcus P. Young

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Experimental and numerical analysis of narrowband Coherent Rayleigh-Brillouin Scattering in atomic and molecular species

Barry M. Cornella,1 Sergey F. Gimelshein,1 Mikhail N. Shneider,2 Taylor C. Lilly,3,* and Andrew D. Ketsdever4

1 ERC Inc., Edwards AFB, CA 93524, USA 2 Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA

3 Department of Mechanical and Aerospace Engineering, University of Colorado Colorado Springs, Colorado Springs, CO 80918, USA

4 Air Force Research Laboratory, Edwards AFB, CA 93524, USA *tlilly@uccs.edu

Abstract: Coherent Rayleigh-Brillouin scattering (CRBS) lineshapes generated from an all narrow-band pump experiment, a Direct Simulation Monte-Carlo (DSMC) approach, and published simplified models are presented for argon, molecular nitrogen, and methane at 300 & 500 K and 1 atm. The simplified 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 lineshapes. ©2010 Optical Society of America OCIS codes: 190.2055 Dynamic gratings, 190.4380 Nonlinear optics, four-wave mixing, 290.5820 Scattering measurements, 290.5830 Scattering, Brillouin, 290.5870 Scattering, Rayleigh, 300.6240 Spectroscopy, coherent transient

References and links 1. R. W. Boyd, Nonlinear Optics, (Academic, Boston, 1992). 2. H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping, (Springer-Verlag, New York, 1999). 3. J. H. Grinstead and P. F. Barker, “Coherent Rayleigh Scattering,” Phys. Rev. Lett., 85, 1222 (2000). 4. X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh-Brillouin Scattering,” Phys. Rev. Lett., 89,

183001 (2002). 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, 161. (2002).

7. X.P. Pan, M.N. Shneider, R.B. Miles, “Power spectrum of Coherent Rayleigh-Brillouin Scattering in Carbon Dioxide,” Phys.Rev. A 71, 045801 (2005).

8. M. O. Vieitez, E. J. van Duijn, W. Ubachs, A. Meijer, A. S. de Wijn, N. J. Dam, B. Witschas, and W. van de Water, “Coherent and Spontaneous Rayleigh-Brillouin Scattering in Atomic and Molecular Gases and Gas Mixtures,” Phys. Rev. A 82, 043836 (2010).

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, 571 (2006). 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, 2008, T. Abe ed. (AIP, New York, 2009), pg. 533.

Approved for public release; distribution unlimited.

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, 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 (2011).

14. M. N. Shneider and P. F. Barker, “Optical Landau Damping,” Phys. Rev. A 71 (5), 053403 (2005). 15. M. N.Shneider, P. F. Barker and S. F. Gimelshein, “Molecular Transport in Pulsed Optical Lattices,”Appl.

Phys. A 89 (2), 337-350 (2007). 16. A. Stampanoni-Panariello, D. N. Kozlov, P. P. Radi, and B. Hemmerling, “Gas-Phase Diagnostics by

Laser-Induced Gratings I,” Appl. Phys. B 81, 101 (2005). 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, 113 (2005). 18. H. Eichler, P. Gunter, and D. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1986). 19. X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh-Brillouin Scattering in Molecular Gases,”

Phys. Rev. A 69, 033814 (2004). 20. H. Bookey, A. Bishop, M. N. Shneider, and P. Barker, “Narrow-Band Coherent Rayleigh Scattering,” J.

Raman Spectrosc. 37, 655 (2006). 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, 173903 (2011). 22. E. Hecht, Optics (Addison Wesley, San Francisco, 2002). 23. T. X. Phuoc, “Laser Spark Ignition Experimental Determination of Laser-Induced Breakdown Thresholds

of Combustion Gases,” Opt. Comm. 175, 419 (2000). 24. H. T. Bookey, M. N. Shneider, and P. F. Barker, “Spectral Narrowing in Coherent Rayleigh

Scattering,”Phys. Rev. Lett. 99, 133001 (2007). 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 (2003), pp. 339-348.

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

27. M. S. Ivanov, A. V. Kashkovsky, S. F. Gimelshein, G. N. Markelov, Thermophysics and Aeromechanics 4 (3), 251 (1997).

28. C. Borgnakke and P. Larsen, “Statistical Collision Model for Monte Carlo Simulation of Polyatomic Gas Mixture,” J. Comput. Phys. 18, 405 (1975).

29. J.G. Parker, “Rotational and Vibrational Relaxation in Diatomic Gases.” Phys. Fluids 2(4), 449 (1959). 30. R. C. Millikan, and D. R. White, “Systematics of Vibrational Relaxation,” J. Chem. Phys. 39(12), 3209

(1966). 31. S. F. Gimelshein, I. D. Boyd, and M. S. Ivanov, “DSMC Modeling of Vibration-Translation Energy

Transfer in Hypersonic Rarefied Flows,” AIAA Paper 99-3451 (1999). 32. N. E. Gimelshein, D. A. Levin, and S. F. Gimelshein, “Hydroxyl Formation Mechanisms and Models in

High-Altitude Hypersonic Flows,” AIAA Journal 41(7), 1323 (2003). 33. R. Jansen, S. Gimelshein, M. Zeifman, I. Wysong, and U. Buck, “Nonequilibrium Numerical Model of

Homogeneous Condensation in Argon and Water Vapor Expansions,” J. Chem. Phys. 132, 244105 (2010). 34. CRC Handbook of Chemistry and Physics, 90th ed., D. R. Lide ed. (CRC, Boca Raton, FL, 2009). 35. 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, 278 (Amsterdam, 1973). 36. G. Emanuel, “Bulk Viscosity of a Dilute Polyatomic Gas,” Phys. Fluids A 2, 2252 (1990).

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]. 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]. By scattering a probe laser off the density grating formed by the lattice, seen in Fig. 1, the returned signal can be connected spectroscopically to the thermodynamic properties and velocity distribution of the gas sample [3,4]. The necessary

intermediate sand gas param

CRBS, as a gsuch as tempekinetic level, from the gas solve the Boltattempt to soDepending onsimplified moCRS and for species, yieldBhatnagar-Grapproximationcondition and

The present stcreating deeptedious scannultimately havpumps create function in thSimulation Massumptions ffind gas paramthat it is mere

The use of a information toinduced densimodified versdensity pertuconsistent witapplied to spocompared witforced densityneutral gas b

step is predictimeters.

Fig. 1. Schemat

as diagnostic terature [5,6] anthe connectiondensity perturbtzmann equatioolve the Boltzn the assumptiodels have beenthe collisional

ding a simplifross-Krook (forns to the 1-D Brequire bulk v

tudy uses all naer potential we

ning of the puve use in morea monochrom

he numerical aMonte Carlo (Dfound in simplmeters, such asly perturbative

statistical appo be predicted ity perturbationsion of the DS

urbations causeth the performontaneous Raylth experiment, y perturbationsby several las

ing the strength

tic of a one-dimene

technique, has nd bulk viscosn between thebations, and thon. Currently,zmann equatioions made, e.gn developed focase of CRBS

fied model for atomic speciBoltzmann equviscosity as an

arrowband laseells than thoseump frequenc

e than purely diatic potential wapproach put fDSMC) approlified models.

s bulk viscositye to the equilibr

proach (DSMCfor various gan, using a firstSMC code, SMed by non-res

med CRBS expleigh-Brillouinand now is ap

s (CRBS). SMser configurat

h of the densit

nsional optical lattiexperiment.

proven its usesity [7,8]. Since experimentallhe gas conditio, several simpl

on directly, bug. gas pressureor the collisionS [9]. The latteor the CRBS es) or Wang-C

uation. All of tinput descripti

ers for the creae in broadbandcies to create iagnostic appliwell which canforth in this poach to predic

Common assy, or the impacrium condition

C) to the Boltzas and laser cont principles ap

MILE, was usesonant pulsederiments. The

n spectra in atoplied to scatter

MILE has been tions [11-13]

ty perturbation

ice, as formed by a

e for yielding ince the pump laly obtained linon, generally rlified models aut use some ae, laser intensinless [3] or weer requires furt

lineshape baChang-Uhlenbethe models assion of the gas.

ation of the gasd experiments.

a lineshape, ications. Addin be directly uspaper. This stct CRBS linessumptions incl

ct of the particln.

zmann equationditions, main

pproach to the ed to calculate

d optical lattice DSMC methmic gases [10]ring in a locali

n used to predicand is comp

n for a given se

a CRBS

nformation aboasers affect theneshape signalrequires an appare available thapproximationsity, or species,eakly collisionather separationased on the leck (molecularsume a near eq

s perturbation While requirthe configura

itionally all narsed as a particltudy also usesshapes withoulude values foe forcing funct

on allows for nly the magnitu

simulation proe the magnituces in a conf

hod has previou], though not pized potential fct the modifica

pared directly

et of laser

out a gas, e gas at a l returned proach to

hat do not s instead. , separate al case of

n based on linearized r species)

quilibrium

in CRBS, ring more ation may rrowband le forcing

s a Direct ut making or hard to tion, such

the same ude of the ocess. A de of the figuration usly been

previously field with ation of a

with an

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

2. Theoretical Framework

Detailed theory for the effect of an optical lattice on a collisional gas and the scattering of a probe beam off the resulting density perturbation formed by that interaction can be found in [3-4, 14-15]. Background material can be found in closely related fields such as laser induced grating spectroscopy (LIGS) [16,17] or a general book on the topic such as [1,18]. The force acting on a polarizable medium in a non-uniform electric field is given by Boyd [1] as

( )α 2E2F U= −∇ = ∇ (1)

where α is the directionally averaged static polarizabilty [C m2 V-1] of the particle and E is the electric field [V m-1]. For idealized anti-parallel, coherent, collimated laser pulses, the square of the electric field is calculated as the superposition of two plane waves.

( )

( ) ( )( )( ) ( )( )

2 2 21 1 1

2 22 2 2

1 2 1 21 2

1 2 1 2

, ( )

( )

cos t

E x t E cos k x t

E cos k x t

cos k k x tE E

k k x

ω

ωω ωω ω

= − +

− +⎡ ⎤− − − +⎢ ⎥⎢ ⎥+ − +⎢ ⎥⎣ ⎦

(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 k_1≈-k_2 and ω_1≈ω_2, 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 eqn. (2) is taken per eqn. (1), the portion with the long spatial period has a negligible impact. In addition, the fast oscillating terms (〖cos〗^2) 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

( ) ( )α 1 22 sin –F U q E E qx t= −∇ = − Ω (3)

where q=k_1-k_2 is the lattice (interference pattern) wave number [rad m-1] and Ω=ω_1-ω_2 is the lattice angular frequency [rad s-1]. Note that q and Ω define the velocity of the lattice, ξ= Ω/q. 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

( ) ( ) ( )( )2 2 2 2m 00ax

2, 4 lne p 2x 2oI Er t I t t r D cIτ⎡ ⇒ =⎤= − − +⎢ ⎥⎣ ⎦

ε (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, eqn. (3) in the axial direction becomes

( ) 0 1 2, , ( , ) ( , ) sin( )xF x r t q c I r t I r t qx tα= − − Ωε (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.

With the force on the particles within the gas evaluated, it can be inferred that the periodic nature of the force will induce a local area of higher density at the anti-nodes of the interference pattern [1]. This perturbation in turn causes a periodic structure in the index of refraction of the gas, which is related to its density, effectively creating a grating which will scatter light. Given the CRS/CRBS experimental parameters, such as the angle of the

crossing pumps and the wavelength of the lasers, the scattered light will evolve as a coherent scatter off the grating, increasing the signal significantly over a spontaneous processes [3,4]. It has been shown that the intensity of the returned light in a CRS/CRBS experiment is proportional to the intensity of the probing light and the square of the density perturbations in the gas [3,19]

2sig probeI I δρ∝ (6)

For low intensity (perturbative) interactions, it has also been shown that the magnitude of the density perturbation is proportional to the product of the pump laser intensities [3,19]

2pump1 pump2I Iδρ ∝ (7)

3. Experimental Setup

CRBS experiment was performed to directly compare with published simplified models and numerical DSMC results. The experimental setup is shown in Fig. 2 and was modeled after previous narrowband CRS setups [20], though used for CRBS lineshapes. It should be noted that this experiment uses all narrowband lasers for CRBS, simplifying the correlation of the two pulses within their coherence distance. The use of all narrowband lasers yields the same results as the use of broadband CRBS pumps, but requires scanning of one of the pump beam’s frequency to cover the desired spectral range, instead of the use of an etalon [4] for spectral resolution from a broadband return. Commenting on a recent article which notes “spectral narrowing” when within the coherence distance of the lasers [21], it is understood that if the pump lasers are interfered within their coherence distance, a single interference pattern will form, creating a single frequency density perturbation. Thus, the spectral makeup of the signal, scattered off that single frequency grating, will be close to that of the probe beam. This does not make the configuration useful as a straightforward gas diagnostic technique, the predominant use for CRBS, due to the necessity for long sweeps of the pump laser frequency in order to create a full line shape. However, it does directly relate to the simulated condition of a single frequency optical interference pattern and validates the similarity between narrow- and broadband pumped signals. Lastly, this configuration translates well to future experimental applications requiring deep potential wells, such as gas heating, impossible with broadband pumps.

Two Q-switched, frequency doubled, injection seeded, Nd:YAG lasers, each with ~5 ns pulses, generated the two narrowband pumps (~180 MHz linewidth). 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 approximately 178°. 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 sound over the linewidth [22], c/??. 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 madegenerate, threquired the sdifference betinput to the frequency waGHz on the lointerfered andmeasurementsfrequency diff

Three nomina(diatomic), anof 300 K and windows, wasdiagram of the18 mJ, corresW/m2) well perturbation rwas wrapped transformer afrequency poisignal averagerecorded by atemperature.

atching conditihe probe beam scattered signatween the two injection seed

as scanned suchonger runs, at d the beat freqs were taken oference of the p

Fig. 3. Phase ma

al gases were nd methane (po500 K. A smas placed at thee chamber setusponding to anbelow the bre

regime for the around the ou

and the tempeint, the scattereed over 100 sha LabView inte

Fig. 2. Schema

on is shown inwas set to dire

al to propagatelasers. The c

d laser allowinh that the rangincrements of quency measuon a 7 GHz opumps at each

atching condition f

selected for coolyatomic). Tall vacuum chae interaction reup is shown in n intensity valueakdown threslattice-gas inte

utside of the cherature was med beam was d

hots on the oscierface along w

atic of experimenta

n Fig. 3. Becauectly counter-pe counter to puenter frequenc

ng explicit conge of the frequ~15 MHz. Sm

ured on a fast oscilloscope, yincrement (?f_

for signal backscat2.

omparison: argThe experimentamber, which inegion and backFig. 4. Each p

ue at the axis shold for all teraction [24]. hamber. The hmeasured usindetected on a illoscope. The

with data pertai

al setup.

ause the probe propagate pumpump 2, indepecy of pump 2 wntrol over the

uency differencmall fractions amplified InG

yielding a dire_pump=2?f_se

tter along the path

gon (monatomt was performencluded 532 n

k-filled with thpump energy wat the interact

test gases [23] For tests at 5

heater was conng a J-type thigh speed Ga

e peak of the avining to the be

beam and pummp 1. This confendent of the fwas varied by e lattice velocces varied fromof each seed la

GaAs photodioect measuremeeed).

h of pump

mic), moleculared for gas tem

nm anti-reflectihe test gas to 1was set at approtion region (3.] and within t00 K, a resisti

ntrolled using athermocouple. aAs photodiodveraged signal

eat frequency s

mp 1 were figuration frequency a voltage ity. The

m 0 to ~5 aser were

ode. The ent of the

r nitrogen mperatures

ve coated 1 atm. A oximately .0 x 1014 the small ive heater a variable

At each de and the was then

signal and

4. Numerical

The force acrequiring a kintrajectories. Tinclude the nNewtonian inspatially varyitime step. Tappreciable frcode has beetherein. The vemployed for maintaining fThe Larsen-Brelaxation num

Assuming thedensity perturmolecular nitrused as the teand water vapthe creation oatm was not prevented waefforts have vspecies [7]. address the nu

The nominal the experimenμm (FWHM)was modeled counter-propaeqn. (5) wasexperiment. from -τ to + τsimulation wadomain boundspecular and afocus that theregime, there scattering effisimulated and

Setup

ting on the mnetic approach

The kinetic codnon-resonant lantegration scheing acceleratioTime steps wractions of the en broadly appvariable hard smodeling mol

fidelity while rBorgnakke mombers is utilize

e validity of eqrbation created rogen, and metst gases. Beyo

por was simulaof the gas cell,

feasible. Coater vapor fromvalidated the us

These two adumerical techni

set of conditiont. The nomin, 5 ns (FWHM

axisymmetricagating pulses.s varied in inIn order to coτ where τ was as 10 ns. Witdaries were coassumed to repe surrounding

exists a lineariciency [19]. Td compared wi

Fig. 4. Diagr

molecules direh to model the de chosen was aser interactio

eme to approxion which was cwere therefore

laser field or tplied and expesphere (VHS) mlecular collisionreducing the ti

odel [28] withed for rotation/v

qn. , the numeby the periodi

thane initially aond the experimated at 1 atm a the ability to

ondensation of m being experise of the simpldditional scenaiques usefulnes

ons and laser pnal condition sM) pulses intercally around t The lattice p

ncrements of over the tempo

assumed to beth a laser pulsonsidered periopresent a sufficvolume was er relation betwThis allows a rth experiment.

am of the test cham

ctly affects thimpact of the lthe DSMC cod

on described bimate the forceconsidered cons

reduced suchtemporal pulseerimentally vamodel [26] andns. The latter ime step to sa

h temperature-dvibration-trans

erical simulatioic force given bat 1 atm and tement, nitrogen

and 400 K. Duexperimentall

f water vapor imentally testelified models farios were coss with varying

parameters werimulated a pairacting with eahe optical axiphase velocity50 m/s throu

oral shape of te 5 ns (FWHMse spatial lengodic. The radciently small cqually affected

ween the squarrepresentative p. The domain

mber.

he velocity dilaser-species inde SMILE. Thby eqn. . The on a molecustant over the dh that the spe width in one alidated, see [d majorant freqfeature was pa

atisfy the laserdependent rotslation energy t

on package waby eqn. . As inemperatures ofn was simulatedue to the use oly increase theon the anti-re

ed. However,for varying gas

ompared to theg pressures and

re chosen to mir of 532 nm wach test gas. is of the two

y in the forcingugh the rangethe pulses, eac

M). Therefore,gth of approximdial domain bocross-section ad. Also note re of the densiportion of the owas nominally

istribution of nteraction on mhe code was mohis modificatioule as a tempoduration of a s

pecies did nottime step. Th25] and the rquency schemearticularly impr interaction cotational and vtransfer.

as used to calcn the experimef 300 K and 50d at a pressureof vacuum harde gas pressure eflective wind, previous exps pressure [4] e simplified md polar molecu

match those conwavelength, 18The simulationidealized anti

g function dese correspondinch pulse simul, the total timemately 1.5 m, oundary was coat the center ofthat in the per

ity perturbationoptical interacty 1064 nm tal

the flow, molecular odified to

on used a orally and imulation t traverse he SMILE references e [27] are

portant for onditions. ibrational

culate the nt, argon,

00 K were e of 5 atm dware for beyond 1

dows also perimental and polar

models to ules.

ntained in 8 mJ, 100 n domain i-parallel, scribed in ng to the lation ran e for each

the axial onsidered f the laser rturbative n and the tion to be l and 532

Gas Ar CH4 N2 H2O

nm wide. A (Tplot=-2U/k)

The first step configuration 20th of a run the simulationaverage statisperturbation was seen in Figperturbation. magnitude of corresponds tvelocity of 45

The values ofTable 1. Fonegligible, antranslation annumbers [29,vibrational ennumbers Zr=Zthe CRBS linalso formulateinput gas parparameter, def

where kb is Bdensity and te

Mass [kg] 6.630 x 10-26 2.656 x 10-26 4.650 x 10-26 2.990 x 10-26

diagram of th) is shown in F

Fig. 5. (a) SMILEan intensity of 3

in the simulatiwith the appro.10th of a puls

n domain. Witstical error is

was found by ag. 5(b). The ma

As discussed the scattered s

to the circled 0 m/s.

f the VHS modor methane annd the continuond rotation-tran,30]. For wnergies was uZv=10 [32]. Ae shape for arged by Pan et alrameters for tfined as [4]

y =

Boltzmann’s cemperature.

Table

Dia. [m] 4.170 x 10-1

4.830 x 10-1

4.170 x 10-1

6.200 x 10-1

Tab

he domain withFig. 5(a).

E simulation domax 1014 W/m2 and

ion procedure opriate gas prose width, in ordth approximates estimated a

a non-linear leaagnitude of theabove, the squsignal. The axpoint in the n

del [26] paramd nitrogen, vious Larsen-Bonslation energ

water, the discused [31], wi

An atomic modgon whereas a. [9], was utilizthe simplified

08

3 2

bkρ

ηπ=

constant and M

e 1. List of DSMC

Visc. Ind0 0.310 0 0.340 0 0.240 0 0.500

le 2. List of gas p

h an overlay o

ain and maximum d (b) simulated den

450 m/s.

was to populaoperties. Flowder to yield a tly 7,500,000 s

at approximateast squares fit oe cosine fit wasuare of the densxial domain denumerical/ exp

meters used in tibrational relaxorgnakke modegy transfer, wicrete Larsen-Bith constant r

del, formulateda six moment (zed for compar

d models are

0T M

qη

M, ρ0 and T0

C parameters for

dex Tref D273 273 273 2273

arameters for sim

of the maximu

potential well depnsity for a lattice v

ate the domain w field propertitime dependentsimulated particely 0.1%. Tof the axial doms used as the msity perturbatioensity perturbaperimental com

the DSMC comxation at tempel [28] was usith temperatur

Borgnakke morotational and d by Pan et al. (s6) model forrison with nitrogiven in Tab

are the averag

each gas species.

DOFR θv [K- - 3 23602 337

3 -

mplified models.

um potential w

pth [K] for velocity of

in the baselineies were sampt evolution of tcles per sampleThe numericamain density to

magnitude of thon is proportioation shown in mparison with

mputations areperatures of ised to model vre-dependent rodel of rotati

vibrational r[9], was used t

r polyatomic mogen and meth

ble 2, includin

(7)

ge gas molecu

.

K] ZR∞

- 0 15.0 1 23.5 - 10.0

well depth

e ambient pled every the gas in e cell, the l density o a cosine he density onal to the

Fig. 5(b) h a lattice

e given in nterest is vibration-relaxation ional and relaxation to predict

molecules, hane. The ng the y-

ular mass,

T* Sour- 2100.0 291.0 210.0 3

rce 26 26 26

3

GAACCNNNH

Gas T [K] Ar 300 Ar 500 CH4 300 CH4 500 N2 300 N2 500 N2 300 H2O 400

5. Results and

The results fonitrogen, and perturbation iperturbation (described in Eare compared was normalizeobtained in verification oftechnique.

Signal in Fig. pump lasers, tthe lattice is aperturbative ron the order othe simplifiedexperimental experimental spatial movemlaser was occshown in Figfeatures, suchscatter. Likeweach gas withi

Using the samthree gases at and the exper

P [atm] 1 1 1 1 1 1 5 1

d Discussion

or the CRBS emethane at 3

is not directly (squared) is cEq. (7). The mto the numericed such that ththis investiga

f both the pres

Fig. 6. Compari

6 is shown verthe conversion

approximatley 0egime, the exp

of, and should vd models. Sho

results as wedata arises fro

ment due to thcasionally obs

g. 6, at varioush as overall shawise, the numein the simulatio

me gas dynaman elevated temiment. Fig. 7

y η [Pa0.46 22.740.23 34.080.70 11.130.35 16.920.57 17.890.30 26.062.85 17.890.62 11.41

experimental ru00 K are showmeasured by

characterized bmaxima to thecally simulatedhe lineshape tration with psented numeric

son of low intensi

rsus the frequen from frequen0.38 GHz per pected width ofvary with, the wn in Fig. 6, tell as simplif

om laser pointihe frequency loerved to causs frequency poape and linewiderical results aon error.

mic parameters mperature andshows the CR

a s] ηb/η x 10-6 - x 10-6 - x 10-6 2.16 x 10-6 2.16 x 10-6 0.73 x 10-6 0.73 x 10-6 0.73 x 10-6 1000

uns and numerwn in Fig. 6. the experimen

by a correspoe experimentalld density perturrend at 0 m/s wpreviously valcal method as

ty CRBS line shap300 K.

ency differencency difference b100 m/s. Becaf the line shapmean thermal

the numerical rfied models fing instabilitieocking controle fluctuations oints. Howevedth, are retainelso capture the

in Fig. 6, thecompared to r

RBS results at 5

η k [W/mK17.84 x 126.73 x 1

6 34.19 x 16 68.34 x 13 25.97 x 13 39.04 x 13 25.97 x 10 19.76 x 1

rical simulation While the mantal setup, the

onding change ly recorded avrbations (squarwas unity. Colidated simpliwell as the na

pes for Ar, N2, and

e of the two pubetween the p

ause the CRBSe curve (half wspeed of eachresults, DSMC

for all three gs both space al loop in eachin signal inte

er, Fig. 6 refleed in the expere general featu

e simplified moresults from the500 K. Since t

K] cint S0-3 - 0-3 - 0-3 3/2 0-3 3/2 0-3 1 0-3 1 0-3 1 0-3 3/2

ns for argon, magnitude of th

e relative chan in signal int

veraged scatterred). Each set omparison of thified models arrowband exp

d CH4 at

ump beams. Foumps to the ve

S scheme operawidth half maxh species as indC, compare favgases. Scatteand time. In ph pump cavity ensity, similarects that the primental data w

ures of the line

odel was apple numerical simthe CRBS line

Source 34,9 34,9

34,35,7 34,35,7

34,9,35,36 34,9,35,36 34,9,35,36

34

molecular he density nge in the tensity as red signal of results he results provides

perimental

or 532 nm elocity of ates in the ximum) is dicated by vorably to er in the particular, and seed

r to those prominent within the eshape for

lied to all mulations e shape in

the perturbativline shape widcases of Fig. predicted simpis affected as the magnitudeintensities. Coverall decreaexperimental perturbation inin signal to noexperimental quantifiably d

DSMC simulapolar moleculCRBS line at are normalizebecome muchon the order oof the Brilloufor nitrogen ashape for wate1000 in the siFig. 8(c) showpossibility of internal degrecan be appliedspecies, assumfor this applic

6. Conclusion

The experimeprevious meth

ve regime is ddth increases w7. Again, th

plified model. the velocity die of density p

Consequently, aase in signal idata set are mon the numerica

oise ratio. Howand numerical

determine a line

Fig. 7. Compari

ations were fule. Fig. 8(a) sh1 atm (left) an

ed such that thh more promineof the speed of in peaks as we

at 5 atm. Fig. 8er vapor at 400implified modws several simf using the DSees of freedom.d to predictingming the permcation.

Fig. 7. Compapressure, (b) wate

n

ental CRBS thods, while usi

dictated by collwith the squarehe experimenta For a given lastribution broa

perturbation cran increase in ntensity. As ore pronouncedal simulations wever, as was tl results were e width.

son of low intensi

urther applied thows the compnd 5 atm (righthe maxima arent at higher p

f sound [4]. Thell as the magn8(b) shows the0 K. A ratio ofel due to a lac

mplified modelSMC to find t. Fig. 8 illustr

g CRBS spectraanent dipole m

arison of numericaer vapor using s6 &

v

technique presing narrowband

lisional gas dye root of tempeal and numericattice potentialadens. Thus, areated by the relative expera result, the fld. The error asalso increases

the case for theable to captur

ty CRBS line shap500 K.

to two additionparison of the t) with the linere unity. As ressures than a

he DSMC prednitude (~150% comparison of bulk viscosityck of readily al lines, using vthe bulk viscorates that the pra for varying pmoment is less

al and simplified re& ηb/η=1000, andarious ηb/η.

sented in thisd pumps. A ki

ynamic phenomerature which cal results coml well depth (in

as the temperatulattice decreas

rimental data sfluctuations in ssociated with with temperat

e lower temperre both the gen

pes for Ar, N2, and

nal scenarios: DSMC numer

e shape predictshown in Fig

at 1 atm and ocdictions accurat

larger than theof DSMC simuy to shear viscoavailable publivarious bulk/shosity for a gasroposed numer

pressures as wes influential tha

esults for (a) varyid (c) water vapor u

s investigationinetic numerica

mena, it followcan be seen inmpare favorabntensity), less oure of the gas ises for the samscatter occurs dthe higher temdetermining thture due to therature data setsneral line shap

d CH4 at

varying pressurical predictionted by [9]. Bog. 8(a), Brillouccur at lattice vtely predict thee center Rayle

ulations to predosity was assumshed data on thear ratios to s with well unrical simulatioell as for naturan the induced

ing N2 using s6 &

n follows the al simulation t

ws that the n all three bly to the of the gas increases, me pump due to an mperature he density e decrease s, both the pe as well

ure and a ns for the

oth curves uin peaks velocities e location

eigh peak) dicted line med to be the value. show the nderstood n method

rally polar d moment

spirit of echnique,

DSMC, was applied with laser and gas parameters that directly coincide with the presented experiment. Both the experiment and numerical simulations operated in the low intensity (perturbative) regime allowing comparison with the simplified models which are based on linear approximations to the 1-D Boltzmann equation. It can be assumed for dilute gases that the change in index of refraction, and therefore scattered light, varies with the square of the density perturbation formed by an optical dipole force. Thus, the density perturbation obtained from the simulations was taken as a measurement of the CRBS signal. It has been shown that a DSMC simulation technique can adequately capture the lineshapes of a CRBS experiment. Good agreement was shown for monatomic species as well as diatomic and polyatomic species where internal energies have an influence on the overall lineshape. At elevated temperatures, an expected broadening of the power spectra was shown and verified. Furthermore, DSMC was matched with the experimentally verified simplified models for varying pressure and the use of polar gas species. While current simplified models have adequately predicted CRS and CRBS line shapes for a wide variety of cases, multiple models are required to encompass all scenarios. Utilizing a DSMC approach for modeling CRBS lineshapes has the advantage of broad applicability over a wide variety of scenarios in the perturbative regime, but also the potential ability to determine CRBS line shapes beyond the perturbative regime as no assumption on the forcing function has been made. One such scenario in the perturbative regime is the calculation of line shapes in gas mixtures, for which no simplified model has been formulated.

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).