Doppler-free two-photon spectroscopy for monitoringstratospheric gases: an analysis

Jerry Gelbwachs

The application of Doppler-free two-photon electronic spectroscopy for the in situ monitoring of strato-spheric gases has been analyzed. Expressions have been derived for the optimum detection pressure andmaximum volumetric sensitivity. The results indicate that detection limits of the order of 105 to 107 mole-cules/cm 3 are feasible for molecular species with strong two-photon uv transitions that undergo efficientradiative relaxation from the excited state. The minimum detectable concentration of trace gas has beenplotted vs altitude.

1. Introduction

The possible depletion of stratospheric ozone byits chemical reaction (i) with free chlorine atoms pro-duced by the photolysis of chlorofluoromethanes in thestratosphere' and (ii) with the combustion productsfrom aircraft is of current concern. A reduction instratospheric ozone would permit more uv radiation toreach the earth's surface, which would deleteriouslyaffect biological species. Furthermore, modificationof the intensity and spectral distribution of solar energyreaching the lower portion of the atmosphere may causesevere climatic alterations. In an attempt to assess theextent of this problem, a committee of the NationalAcademy of Sciences-National Research Council rec-ommended that certain gases be measured as a functionof altitude and seasonal variations.2 The known at-mospheric concentrations of these gases range from 1012to 106 molecules/cm 3 . At 40 km, the latter moleculardensity corresponds to a volumetric concentration of10-11, i.e., 1 part in 1011; hence, sensitive monitoringapparatus is needed.

The in situ monitoring of trace gases in the strato-sphere by the Doppler-free two-photon excitation ofstrong uv transitions is discussed in this paper. Theimproved detection capacity of this method at reducedpressures warrants its consideration for this application.For a particular experimental configuration, the de-tection limit of the method is calculated as a functionof altitude and radiative lifetime of the two-photontransition. The results indicate that detection limitsof the order of 105 to 107 molecules/cm 3 are feasible.

The author is with Aerospace Corporation, P.O. Box 92957, Los

Angeles, California 90009.Received 31 January 1976.

Furthermore, the extremely narrow absorption line-widths that can be obtained at stratospheric pressuresin the absence of Doppler broadening minimize inter-ference effects.

II. Description of Method

Doppler-free two-photon spectroscopy involves theirradiation of a gas sample with oppositely directedoptical beams at a frequency that corresponds to one-half of the molecular transition frequency. Simulta-neous absorption of one photon from each of the coun-terpropagating beams yields an absorption spectrumfree of Doppler broadening. The counterpropagat-ing-beam two-photon absorption profiles are muchnarrower and exhibit more intense peaks than theDoppler-broadened two-photon absorption profiles.The two-photon absorption enhancement is observedonly when the primary line-broadening mechanism isthe result of the Doppler effect. At the ambient pres-sure found at sea level, pressure broadening is thedominant line-broadening mechanism, and the effec-tiveness of the method is reduced. However, in thestratosphere, broadening of uv molecular spectra isprimarily the result of the Doppler effect. Hence, thestratosphere provides an ideal environment in which toperform trace gas detection by the Doppler-free two-photon method.

The uv is a highly desirable spectral region in whichto monitor trace gases since most molecules exhibit richspectra in this region. The utilization of the two-pho-ton process to induce an uv transition requires that thephoton energies correspond to visible wavelengths. Thecommercial availability of tunable narrow-linewidth dyelasers at visible wavelengths is an important operationaladvantage.

The monitoring of the two-photon absorption can beaccomplished by the photoelectronic detection of flu-

2654 APPLIED OPTICS / Vol. 15, No. 11 / November 1976

orescence emission when the decay process is radiative.Since the fluorescence occurs at wavelengths shorterthan the excitation wavelength, sensitive dark-cur-rent-limited photodetection is possible. Molecules thatrelax by nonradiative processes can be monitored by thephotoacoustic method.3

The elimination of the Doppler effect by a counter-propagating-beam two-photon method was originallysuggested in 1970.4 In 1974, various groups applied themethod to study atomic5-7 and ir8 molecular spectra.The results indicate that a hundredfold reduction inlinewidth, compared with the Doppler width, is possible.In 1975, the method was extended to the electronic stateof molecules. Gelbwachs et al.9 observed absorption-line narrowing to values less than the Doppler width forNO and recorded resolvable spectral features in thebenzene absorption spectrum that had line spacings lessthan the Doppler width.

111. Sensitivity Calculation

The minimum detectable concentration of a gas in thestratosphere is calculated for Doppler-free two-photondetection in this section. The ratio of absorptioncoefficients per unit concentration for the counterpro-pagating-beam two-photon process 2w to the one forthe one-photon process 0,3, is given by'0

The radiative emission near the two-photon frequencyis collected and focused onto the cathode of a sensitivephotomultiplier tube (PMT) that is operating in thephoton-counting mode and is placed perpendicular tothe optical axis. An optical filter is inserted in front ofthe photocathode to reject radiation at the laser fre-quency and pass the shorter wavelength molecularemission. Dark-current-limited photodetection is thuseffected.

The photoelectronic counts C recorded in this con-figuration are given by

C = 02(,,nL Pt 'ic2hVL 7fk

(2)

where n = molecular number density,L = interaction length,t = integration time,

P = average intracavity laser power,VL = laser frequency,7f = quantum efficiency for fluorescence, and77 = optical collection efficiency.

For dark-current-limited photodetection, the mini-mum detectable counts Cm are approximately 1count/sec cm2. For a nominal 1-cm2 photocathode andintegration time t (sec),

112w/(!elE)2 AVD I AVD

X. heel oY ' 7(1)

where el = transition dipole moment to an inter-mediate electronic state,

h = Planck's constant,Vel = electronic frequency,E = amplitude of optical electric field,

AVD = Doppler linewidth,o = linewidth from other processes,I = optical field intensity, and

I = a normalized intensity defined in termsOf Ael and Vel.

The well-defined parity of atomic electronic statesprohibits one-photon transitions and two-photontransitions between the same pair of states throughelectronic dipole coupling. Most molecules, however,lack an inversion center so that both types of processesare permitted between any pair of electronic levels. Asa consequence of the lack of well-defined parity ofstates, the fluorescence yields from levels excited byboth one-photon and two-photon processes will be thesame for most molecules.

A monitoring configuration is shown in Fig. 1. A dyelaser is tuned to exactly one-half the frequency of themolecular uv transition of interest. The sample cell isplaced inside the laser cavity to (i) increase the effi-ciency of two-photon absorption by taking advantageof the intense optical fields that exist there and (ii) en-sure the alignment of the counterpropagating beams.It is assumed for calculation purposes that some of theexcited-state molecules decay through photon emission.

Cm = t/2 (3)

By the use of Eqs. (1)-(3), the minimum detectablemolecular concentration nm can be expressed as

2hvLIonm = (AVD/Y)#(L/A)p2 t1/2,f7c (4)

where A is the optical-beam area. For a laser operatingin the TEMoo mode,

L _ __ = VL

A C

where c is the speed of light and X is wavelength.Substitution of Eq. (5) into Eq. (4) yields

2hcIo,=( AD/Y)flnfp2t 1277

(5)

(6)

Equation (6) indicates that molecules with transitionshaving large absorption coefficients, small naturallinewidths, and large fluorescence quantum efficienciesare ideal candidates for detection by this method.

TO PHOTON-COUNTINGINSTRUMENTS

OPTICAL FILTER

LENS II DIELL

EXHAUST INTAKE

Fig. 1. Experimental configuration for Doppler-free two-photondetection of stratospheric gases.

November 1976 / Vol. 15, No. 11 / APPLIED OPTICS 2655

In the absence of Doppler broadening, the transitionlinewidth of atmospheric gases is determined by pres-sure broadening, radiative decay, and internal non-radiative processes. For this case,

-y =kip +- (7)7rn

andT/TrOf= , ~~~~~~~~~(8)

1 + Tk2p(

where k1 is the pressure-broadening coefficient, p is thepressure, is the natural lifetime, Tr is the radiativelifetime, and k2 is the collisional deactivation rateconstant. Substitution of Eqs. (7) and (8) into Eq. (6)yields

n= 2hc 0 Tr (kip +-) (1 + rk 2p). (9)

For molecules with long-lived states, pressure broad-ening determines y, and nm decreases with increasingaltitude.

The pressure dependence of the detection sensitivityis investigated to determine the ambient pressure thatmaximizes volumetric sensitivity S. It is related to nmby

nm (0

3.5 x 16(10)

where p is expressed in Torr.The maximization of S with respect to p allows the

optimum pressure p0 for Doppler-free two-photon de-tection to be determined. This value is

P.=( 1 T21/2P= (Tk 2 2)"2 (11)

and depends solely upon parameters of the moleculartransition.

The maximum volumetric sensitivity Sm is found bythe substitution of po for p in Eq. (10), which yields

Sm = 2c rr[(irk112 + k21' 2]2. (12)

3.5 X Ol67r#P 2tl/ 2 ,7'iv D

The calculated dependence of the minimum detect-able molecular concentration upon altitude and radia-tive lifetime of the two-photon induced transition isshown in Fig. 2. Typical system parameters are P = 20W, t = 100 sec, and 77c = 3%. Typical molecular pa-rameters are ,, = 100 cm-1/atm, Io = 1015 W/cm 2 , andAVD = 3 GHz. The radiative lifetime of the two mo-lecular species is taken to be 100 nsec and 1 nsec, re-spectively, and it is assumed that the excited state de-cays primarily by radiative relaxation in the absence ofcollisions, i.e., XT Tr. Note that transitions with radi-ative lifetimes that fall between 1 nsec and 100 nsec havehomogeneous linewidths in the range of 300 MHz to 3MHz, respectively. Commercial cw dye lasers exhibitspectral bandwidths of -1 MHz so that effective exci-tation of the two-photon transition can be readily ac-complished with existing laser systems. For both gases,a representative value for the pressure-broadeningcoefficient of 10 MHz/Torr is selected, and thequenching of the excited state by collisions with other

molecules is assumed to proceed with unit efficiency andto occur at the gas-kinetic rate. The values of ambientpressure as a function of altitude were taken from Ref.11.

An interpretation of the results shown in Fig. 2 is nowgiven. For long-lived species, pressure broadening ofthe absorption lines and severe quenching hamper de-tection at low altitudes. At higher altitudes, pressurebroadening and quenching effects are diminished, andthe detection limit improves and approaches a value of105 molecules/cm3. The reduced effect of quenchingupon the fluorescence yield of the short-lived speciescompared with the long-lived one provides greater de-tection sensitivity at lower altitudes. However, near30 km, the natural linewidth caused by spontaneousemission and the broadening caused by pressure arecomparable; thus no further enhancement of the two-photon absorption coefficient by the counterpropa-gating-beam geometry occurs above this height. Thus,at higher altitudes, the detection limit for the short-lived species remains constant at 107 molecules/cm 3 .

For this example, the maximum volumetric sensi-tivity is achieved at a total sample pressure of 0.56 Torrfor the long-lived species and 56 Torr for the short-livedone. For both species, Sm = 2 X 10-11, i.e., 0.02 partsper billion.

The dashed curve in Fig. 2 represents the minimumdetectable molecular concentration as a function of al-titude when the pressure inside the sample cell ismaintained at p. It is the same for both molecularspecies since Sm is independent of Tr for T Tr. Thedashed curve is tangent to the solid curves at the alti-tude ho at which the ambient pressure is pO; ho corre-sponds to 17 km and 52 km for the short-lived and

11

E 9

8 ~ %

EE 779\ r = a nsec

6 \ ;10 nsec

5-

4

I I l l l I0 10 20 30 40 50 60 70

ALTITUDE (km)

Fig. 2. Minimum detectable molecular concentration vs altitude formolecular species with radiative lifetimes of 100 nsec and 1 nsec. Thesolid curves correspond to detection at ambient pressure. The dashedcurve represents the detection limit when the pressure inside the

sample cell is maintained at pa (see text).

2656 APPLIED OPTICS / Vol. 15, No. 11 / November 1976

long-lived species, respectively. To achieve maximumvolumetric detection sensitivity for p0 < 760 Torr, it isnecessary to have a vacuum pump below ho and acompressor above ho. The detection limit improve-ment for monitoring the short-lived and long-livedspecies at sea level corresponds to a factor of 10 and1000, respectively, when the gas cell is operated at p0rather than at 760 Torr (Fig. 2).

IV. Summary

The feasibility of Doppler-free two-photon spec-troscopy for the in situ detection of stratospheric gaseswas analyzed. A value of pressure was found thatmaximizes the volumetric detection sensitivity. Theminimum detectable molecular concentration wasplotted vs altitude for representative atmosphericmolecules.

References1. F. S. Rowland and M. J. Molina, Rev. Geophys. Space Phys. 13,

1 (1975).2. G. B. Lubkin, Phys. Today 28, 34 (Oct. 1975).3. L. B. Kreuzer, J. Appl. Phys. 42, 2934 (1971).4. L. S. Vasilenko, V. P. Chebotaev, and A. V. Shishaev, JETP Lett.

12, 133 (1970).5. M. P. Levenson and N. Bloembergen, Phys. Rev. Lett. 32, 645

(1974).6. F. Biraben, B. Cagnac, and G. Grynberg, Phys. Rev. Lett. 32,643

(1974).7. T. W. Hansch, K. Harvey, G. Meisel, and A. L. Schawlow, Opt.

Commun., 11, 50 (1974).8. W. K. Bischel, P. J. Kelley, and C. K. Rhodes, Phys. Rev. Lett.

34, 300 (1975).9. J. A. Gelbwachs, P. F. Jones, and J. E. Wessel, App. Phys. Lett.

27, 551 (1975).10. P. L. Kelley, H. Kildal, and H. R. Schlossberg, Chem. Phys. Lett.

27, 62 (1974).11. S. Valley, Ed., Handbook of Geophysics (MacMillan, New York,

1960), Chap. 1.

International Conferenceon Integrated Optics andOptical Fiber Communication (IOOC'77)

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November 1976 / Vol. 15, No. 11 / APPLIED OPTICS 2657