August 1984 / Vol. 9, No. 8 / OPTICS LETTERS 341

Experimental comparison of broadband rotational coherentanti-Stokes Raman scattering (CARS) and broadband vibrational

CARS in a flame

Jia-biao Zheng,* Judith B. Snow, Daniel V. Murphy,t Alfred Leipertz,t and Richard K. Chang

Section of Applied Physics and Center for Laser Diagnostics, Yale University, New Haven, Connecticut 06520

Roger L. Farrow

Sandia National Laboratories, Livermore, California 94550

Received February 7, 1984; accepted May 21, 1984

Broadband rotational coherent and anti-Stokes Raman scattering (CARS) and vibrational CARS measurementshave been performed to determine the N2 temperature in a flame (1800-2000 K). Comparisons between these twoCARS approaches indicate that, despite loss of signal strength with increasing temperature, rotational CARS is apotentially viable technique for flame-temperature measurements.

Coherent anti-Stokes Raman scattering (CARS) hasbeen used extensively as a diagnostic technique fortemperature measurement in combustion systems.1-5The relative intensities of the vibrational bands of N2gas provide a sensitive temperature probe at flametemperatures. Pure rotational CARS is superior tovibrational CARS for thermometry of N2 gas at roomtemperature and below,6'7 since the spectra are easilyresolvable (8 cm-1 between adjacent rotational peaks)compared with the congestion of the rotational lines inthe vibrational bands of the Q-branch spectra. Eventhough the rotational Raman cross section for rotationalCARS is larger than the vibrational CARS cross sec-tion,8 rotational CARS signal intensities are substan-tially reduced at higher temperatures as the populationdifference factor between the initial and final states forthe CARS process approaches zero. We present herean experimental comparison of rotational and vibra-tional CARS techniques, under similar conditions in thesame laboratory, that demonstrates that rotationalCARS may be viable for flame-temperature measure-ments up to 2000 K.

The flame was generated with a flat-flame burnerusing a premixed flow of CH4 and air. The thermo-couple was fabricated from a 50-gim-diameter Pt andPt-13% Rh wire yielding a junction bead diameter of-150 gm.9 We used a broadband CARS techniquesin which the entire rotational or vibrational CARSspectrum is generated in a single laser pulse and de-tected by an optical multichannel analyzer (OMA).The second harmonic (532 nm) of a Nd:YAG laser wasused as the pump radiation (1 cm-1 FWHM). For therotational CARS, the third harmonic of the Nd:YAGlaser (355 nm) was used to pump a coumarin 500broadband dye laser (532-538 nm). For the vibrationalCARS, a portion of the 532-nm beam was used to pumpa broadband Rhodamine 610 broadband dye laser(600-610 nm).

A small-angle three-dimensional phase-matching

geometry7' 9"1 ",12 was used to isolate the CARS signalspatially from the pump and Stokes beams. Becausethe broadband dye laser is characterized by sharp,random intensity variations with wavelength, a proce-dure is required to normalize the CARS signal with re-spect to the dye-laser spectral profile. A cell of Ar at9.5 atm was used to generate a nonresonant referenceCARS signal [see Fig. .1(a)] that essentially mimicked

CO

z

C)

(a}

(h)

LkJL AIJA r

WI/ 2 NORMAL

(d)

uJ

IZED

CALCULATED

iiJ = 16 18 20 22 24 26 28 30 32 34

RAMAN SHIFT A

Fig. 1. Pure rotational CARS spectrum of N2, including (a)the nonresonant CARS of the Ar reference, (b) the unnor-malized experimental CARS of N2 in a flame, (c) the corre-sponding normalized CARS, and (d) the calculated CARS.Experimental spectra are the average of 16 laser pulses. Thebest least-squares-fit CARS temperature was 2060 K.

0146-9592/84/080341-03$2.00/0 © 1984, Optical Society of America

RFFFvl:KllF1UlMDC1-1 -1-1

timn-,MAiE FLAME..

f_%

342 OPTICS LETTERS / Vol. 9, No. 8 / August 1984

Inzw

In

22~ 2350

RAMAN SHIFT (cm')

Fig. 2. Vibrational CARS spectra of the N2 Q-branch inwhich the solid line is the experimental spectrum and thedashed line is the theoretical spectrum. The best least-squares-fit CARS temperature was 1864 K.

the spectral-intensity variations of the dye laser. TheCARS of N2 in the flame and the nonresonant CARS ofthe Ar reference were dispersed by a spectrograph anddetected simultaneously on spatially distinct portionsof the two-dimensional vidicon detector of the OMA.The spectral resolution of the spectrograph and vidiconsystem was 2.7 cm-'. The N2 and Ar CARS signalswere corrected individually for the vidicon backgroundand for the overall system response. The corrected N2signal was then normalized by the corrected Ar refer-ence signal.

The pure rotational CARS spectra of N2 in a flameare presented in Fig. 1 for the rotational peaks J =16-35. The CARS spectrum of Ar is shown in Fig. 1(a).The unnormalized and normalized experimentally de-tected N2 flame spectra are shown in Figs. 1(b) and 1(c),respectively. The corresponding calculated spectrumis shown in Fig. 1(d). The temperature is deduced bya least-squares fit of the experimental and calculatedspectral-intensity distributions by using the total in-tegrated peak areas of the individual rotational lines.An average of 20 individual CARS spectra was used todetermine the temperature for three flame-temperatureranges. The standard deviation of the deduced tem-perature (±7, ±7, and ±9%) was measured for each ofthe temperature ranges ('1750, -1850, -1950 K). Therotational CARS-deduced temperatures were comparedwith the radiation-corrected thermocouple measure-ments for each of the temperature ranges and were inreasonable agreement (within -1, -4, and -1%).

A typical vibrational CARS spectrum of N2 in aflame, measured using the same burner and experi-mental arrangement, is presented in Fig. 2. The ex-perimentally detected and calculated spectra are rep-resented by the solid and dashed lines, respectively.The standard deviation for a series of 20 vibrationalCARS-deduced temperatures was -3%. The averagevibrational temperature for this temperature range(-1850 K) agreed with the thermocouple temperatureto within -1%.

The rotational N2 temperature is deduced by calcu-lating the relative integrated peak areas of all the Jpeaks over a sufficiently wide range of temperature and

then determining the least-squares difference betweenthe experimental and theoretical integrated intensityof all the J peaks.7 The influence of hot bands and ofinterference effects from the three adjacent lines oneither side of a given rotational line have been includedin the calculation. Vibrational temperatures were de-duced from nonlinear least-squares fits of theoreticalto experimental spectra. Theoretical spectra wereobtained by calculating the complex Raman suscepti-bility, adding the appropriate nonresonant suscepti-bility, and convoluting the squared modulus with aninstrumental line-shape function.9

For vibrational CARS, the total pump energy (WL +

C4') was 48 mJ, and the energy of the broadband Rho-damine dye laser (ws) was 3.4 mJ/pulse. For rotationalCARS, the total pump energy was 43 mJ, and the dye-laser energy was 1.3 mJ/pulse. The input-intensityadvantage for the vibrational CARS experiment was-3X.

The magnitude of the peak CARS intensity dependson the Raman cross section,8 on the spectral resolutionof the system, and on I(COL)I(wL')I(ws). Assuming thesame triple product and a spectral resolution equal to2.7 cm-', our calculated ratio of vibrational CARS peakintensity to rotational CARS peak intensity was 'vib/'rot= 1.6 at 300 K and Ivib/Irot = 4.2 at 1800 K. Using aresolution of 2.7 cm-1 and normalizing to the triple-

F-02zwu1--z02

cc

(a) REFERENCE

(b) FLAME

I pulse

1~6 IS 20 22 24 26 26 30 32 34

RAMAN SHIFT >

Fig. 3. Pure rotational CARS generated in a single 10-nseclaser pulse including (a) the nonresonant CARS of the Arreference and (b) the normalized CARS of N2 in a flame.

F-UJw

z

ccC,

1600 K1700KL 1800 K1900 K2000 K

j 1 LII IIILLLJ = 16 18 20 22 24 26 28 30 32 34 36

RAMAN SHIFT -

Fig. 4. Theoretical rotational CARS intensity distributionof N2 for temperatures from 1600 to 2000 K in increments of100 K.

I pulse

August 1984 / Vol. 9, No.8 / OPTICS LETTERS 343

Z (/)

2250 2270 2290 2310 2330 2350

RAMAN SHIFT (cm-')

Fig. 5. Theoretical vibrational CARS spectra of N2 fortemperatures from 1600 to 2000 K in increments of 100 K.

intensity product, we found that the correspondingexperimental result (-1800 K) was Ivib/Irot = 1 (witha random error of -20%3. However, systematic errorsproduced by factors such as varying spatial and tem-poral beam overlap and beam profile could explain thedifference between the calculated and measured ra-tios.

Figure 3 demonstrates that the signal intensity ofrotational CARS of N2 in a flame is sufficient for a single10-nsec laser-pulse measurement. The Ar CARS ref-erence is shown in Fig. 3(a), and the rotational CARSof N2 in a flame is shown in Fig. 3(b). The flame tem-perature was estimated from the CARS spectrum to be1300-1500 K, although no attempt was made to deducethe N2 temperature by a least-squares fit.

In addition to signal intensity, the sensitivity of therotational and vibrational CARS spectra to temperaturechanges must be considered. Figure 4 presents thetheoretical rotational CARS integrated intensity ofdifferent J transitions for T = 1600 K to T = 2000 K inincrements of 100 K. Figure 5 presents the theoreticalline shapes for vibrational CARS in the same temper-ature range. In the rotational CARS distribution, theless intense peaks are more sensitive to temperaturechanges, and the most intense peaks (J = 22-26) are theleast sensitive. Note that, even for the most-temper-ature-sensitive peaks, the intensity change is less thana factor of 2 when the temperature varies from 1600 to2000 K. In contrast, the peak height of the hot band (v= 1) of the vibrational CARS spectra changes by morethan a factor of 2 in this temperature range. However,as the temperature is lowered significantly from 1600K, the signal strength of this hot band drops rapidly, sothat temperature information must then be derivedfrom the v = 0 band alone, requiring higher spectralresolution.

The primary source of inaccuracy encountered withrotational CARS measurements is associated with theintensity normalization of the CARS spectrum relativeto the spectral input of the broadband dye laser. Anyspectral structure in the dye-laser output tends to in-fluence the intensities of the isolated rotational lines

(-2 cm-1 FWHM) much more critically than those ofthe broader vibrational band. Even though, in princi-ple, the random spectral structure in the dye-laseroutput can be accounted for in the nonresonant CARSreference spectra shown in Figs. 1(a) and 3(a), distor-tions in the optical system (spectrograph and vidicon)do not permit an accurate correspondence between thesignal and reference channels with respect to wave-length.

Our results indicate that rotational CARS has po-tential as an alternative technique for the measurementof flame temperatures. Rotational CARS has the ad-vantage of requiring spectral resolution no higher than3 cm-1 , since the peaks are adequately separated andonly the integrated peak area for each J is required.Vibrational CARS thermometry demands more-com-plex line-shape fitting procedures and requires higherresolution for accuracy at temperatures below 900 K.If the difficulties with dye-laser normalization can besolved, rotational CARS will be particularly advanta-geous for systems requiring the measurement of a widerange of temperatures (77-1900 K) with the same ex-perimental apparatus.

We gratefully acknowledge the partial support of thisresearch by the U.S. Department of Energy, Office ofBasic Energy Sciences, at Sandia National Laboratoriesand at Yale University (grant no. DE-AC02-81ER10969).

* Present address, Department of Physics, FudanUniversity, Shanghai, China.

t Present address, Lincoln Laboratory, Massachu-setts Institute of Technology, Lexington, Massachusetts02173.

t Present address, Institut fur Thermo- und Fluid-dynamik, Ruhr-Universitat Bochum, D-4630 Bochum1, Federal Republic of Germany.

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