Key words: Stimulated Raman scattering, four-wave mixing, UV Raman shifter, beam quality,differential absorption lidar in the UV.
1. Introduction
Raman cells in the UV that are pumped by quadru-pled Nd:YAG or KrF excimer lasers are used in ap-plications such as differential absorption lidar1–5
~DIAL! or laser ranging.6–8 Although solid-statepowerful tunable sources in the UV are being devel-oped, Raman cells remain the preferable wavelengthshifters for DIAL measurements of troposphericozone9 because of the high efficiency and simplicity ofthe setup. In the configuration considered here, thepump beam is focused in a cell that contains theRaman-active gas and is recollimated at the exit aftera single pass. Photon conversion efficiencies of sev-eral tens of percent are reported up to the thirdStokes beam with commercial high-power lasers ~the
L. Schoulepnikoff and V. Mitev are with the Observatory ofNeuchatel, Rue Observatoire 58, Neuchatel CH 2000, Switzerland.V. Simeonov, B. Calpini, and H. van den Bergh are with the SwissFederal Institute of Technology, Laboratory for Air and Soil Pol-lution, Lausanne, Switzerland.
Received 29 August 1996; revised manuscript received 6 Janu-ary 1997.
5026 APPLIED OPTICS y Vol. 36, No. 21 y 20 July 1997
Stokes or anti-Stokes number refers to the number oftimes the pump beam has been frequency downcon-verted or upconverted, respectively!.
The optimization process for obtaining the highestconversion efficiency and beam quality dependsmainly on the pressure of the Raman-active gas, thetype and pressure of the added inert gas ~below thisis called the buffer gas!, the cell-lens focal length, andthe quality and the power of the pump beam. Theoptimization of the conversion efficiency for a pumplaser in the visible or the UV has been reported byChu et al.5 @Nd:YAG second harmonic ~532 nm! in H2,D2 and CH4, with lens focal lengths of f 5 0.5, 0.75,and 1 m#, Sentrayan et al.10 @Nd:YAG third harmonic~355 nm! in H2, f 5 0.1 m#, Haner and McDermid1
@Nd:YAG fourth harmonic ~266 nm! in D2 and HD, f 52 m#, Trainor et al.11 @XeF ~353 nm! in H2, f 5 1.35,3.6, and 5.1 m#, Luches et al.12 @XeCl ~308 nm! in H2with He, Ne, Ar, or N2 buffer, f 5 1 m#, Bosenberg etal.9 @KrF ~248 nm! and Nd:YAG fourth harmonic inH2 and D2 with He or Ar buffer, f 5 1 and 1.1 m#; thelatter includes the work of Sunesson and Apituley13
and Kempfer et al.14 Other studies deal with theStokes beam quality or the influence of the pumpbeam quality: van den Heuvel et al.15 @Nd:YAG fun-damental ~1064 nm! in CH4, f 5 0.1 m#, Diebel et al.16
~KrF in H2 and D2 with a He buffer, f 5 0.675 and 0.9m#, and Cheng and Kobayashi17 ~XeCl in H2, f 5 0.25and 1 m!, and Cheng et al.18 ~XeCl in H2, f 5 1 m!.Most of the beam-quality studies in stimulated Ra-man scattering ~SRS! are performed in parallel ge-ometry19 ~in an oscillator–amplifier configurationtypically!. These works have a limited applicabilityto the configuration considered here because thebeam quality depends on the cell-lens focal length.17
This paper complements a number of aspects re-garding former investigations of single-pass Ramancells. We have made a parametric study by varyingthe cell parameters and measuring the Stokes con-version efficiency and beam quality ~M2 parameter!.The parameters that were varied are the pulse en-ergy at the cell input, the focal length of the cell lens,the type and the pressure of the Raman-active gas~H2, D2, or CH4!, and the type and the pressure of thebuffer gas ~He, Ne, or Ar!. The measurements areinterpreted with a model of SRS, four-wave-mixing~FWM!, buffer-gas Raman linewidth broadening, andtransient effects.20,21
The influence of the pump beam quality is studiedwith two models of quadrupled Nd:YAG lasers withdifferent M2 parameters, as well as with a KrF exci-mer laser with a stable resonator characterized by anM2 that is 10 to 100 times higher ~for the direction ofthe smallest and the biggest dimensions, respec-tively, of the beam!. The study of this excimer con-figuration cannot be fully generalized to excimerlasers with unstable resonators ~which is the usualchoice for high-power excimer-pumped Raman cellsbecause of the higher beam quality!. The effects ofadding He, Ne, or Ar are compared ~as reported pre-viously in the case of H2 with XeCl pumping12!. Theinfluence of the lens focal length is studied ~as previ-ously outlined in the case of the Nd:YAG second har-monic5 and XeF11 pumping!. CH4 is investigated asan alternative to D2 because both molecules havesimilar Raman shifts ~2917 and 2987 cm21, respec-tively!, but CH4 is cheaper and possibly brings ahigher first Stokes conversion efficiency. The mix-ture of H2 and D2 is investigated as a means of ob-taining similar energy in the first Stokes conversionefficiency of D2 and H2 from a single cell ~to ourknowledge this has not been reported yet!, which isuseful in, e.g., the DIAL measurement of troposphericozone.9
Diebel et al.16 and Bosenberg et al.9 reported themeasurement of the Stokes beam divergence in thecase of KrF pumping. In Ref. 18, Cheng et al. usedtwo models of a XeCl pump laser ~one with a stableresonator and the other one with an unstable reso-nator! and measured the Stokes beam divergence.In this paper characterizations of the Stokes beamand the residual pump beam are given by the mea-surement of the M2 parameter. In our experimentalsetup, laser-induced breakdown ~LIB! of the Raman-active and buffer gases is identified as a factor thatlimits the conversion efficiency and the Stokes beamquality. It has been previously noted by Yagi andHuo22 and Diebel et al.22 for KrF pumping.
The theoretical background is given in Section 2:Raman gain, transient effects, FWM, and how theseare affected by the addition of a buffer gas. Theexperimental setup is described in Section 3. Sec-tion 4 presents results with a single Raman-activegas. The aspects relevant to the conversion efficien-cies ~input-beam quality, lens focal length, buffer gas!are discussed in Subsection 4.A, whereas the Stokesbeam quality is discussed in Subsection 4.B. Themixture of H2 and D2 and, alternatively, a mixture ofH2 and CH4, and ethane are discussed in Section 5.The main results are summarized in the conclusion.
2. Theoretical Background
A. Raman Gain and Transient Gain Reduction
The ith Stokes, ith anti-Stokes, and output pumpbeams are denoted by Si, ASi, and P, their frequen-cies by ni
s, nias, and np, their wavelengths by li
s, lias, lp,
and their wave numbers by kis, ki
as, and kp, respec-tively. The Si and the ASi frequencies are given byni
s 5 np 2 inR and nias 5 np 1 inR, respectively, where
nR is the Raman transition frequency. The steady-state gain ~in units of meters per watt! for the P–S1SRS process is given by23
gp1 52~l1
s!2
hcn1s
NkB
pcDn Sds
dVD , (1)
where c is the speed of light, h is Planck’s constant, Nis the Raman-active molecule number density, kB isBoltzmann’s population factor, Dn is the Raman line-width ~FWHM!, and dsydV is the P–S1 differentialRaman cross section. gp1 as a function of pressure~at 295 K! for H2, D2, and CH4 is shown in Fig. 1, andthe corresponding cross section and linewidth dataare given in Table 1.
The condition for the validity of the steady-statedescription is tp .. GT2,23 where tp is the pump du-ration, T2 is the dephasing time @T2 5 1y~pDn!#, and
G 5Ip
Is
]Is
]Ip
Fig. 1. ~a! Steady-state Raman gain for H2, D2, and CH4 calcu-lated from the data in Table 1; ~b! wave-vector mismatch of theFWM process ~P, S1, S2, S3! for H2, D2 and CH4 calculated from thedata in Table 3 in Subsection 2.C.
20 July 1997 y Vol. 36, No. 21 y APPLIED OPTICS 5027
Table 1. Parameters Used in the Calculation of the Raman Gain at 295 K @Eq. ~1!#a
aThe Raman-scattering cross section is given as a single resonance fit: dsydV 5 A~n1s!4y~ni
2 2 np2!2. pa is the Raman-active gas pressure
~in atmospheres!.
is the steady-state amplification factor, where Ip andIs are the pump and the Stokes intensities, respec-tively. In a focused geometry, G can be roughly es-timated as G 5 ~2z0!gp1Ip~zf !, which is denoted as Gf,where Ip~zf ! is the pump intensity at the waist invacuum and z0 is the Rayleigh range. Gf is esti-mated as Gf > 1300 for 10-atm H2 ~gp1 5 9.0 cmyGW!; with pump-beam parameters of 80-mJ pulseenergy at 266 nm, 5-ns pulse duration, 3-mm radiusat 86% power, M2 5 1, focused by a 50-cm focal-length lens to a waist radius of 15 mm, and a Rayleighrange of 2.8 mm, the pump intensity is estimatedassuming a top-hat temporal and spatial profile. Inthis case Gf .. tpDn ~and hence tp .. GfT2! since tpDn5 8.2 ~Dn 5 17.4 3 1023 cm21 at 10-atm H2; Table 1!,which indicates that the SRS is transient eventhough tp .. T2 ~T2 5 0.6 ns!. When the pulse en-ergy is taken to be ten times less ~10 mJ! and the M2
parameter of the pump is taken to be ten times larger~M2 5 10! ~w0 and z0 are proportional to M2!, then Gf5 16, which is still larger than tpDn.
In a previous numerical study21 the transient ef-fects were taken into account by a gain-reductionformalism in the steady-state description. WhenG . Dntp and GtpDn .. 1 ~i.e., high gain!, Eq. ~2! givesthe factor R by which the steady-state gain is multi-plied ~yielding the transient gain!:
R 51
ÎG F~tpDn!1y2 21
4ÎGG , (2)
which follows the plane-wave undepleted pump theoryof Wang,28 which has been verified experimentally in afocused geometry at threshold by Heeman and God-fried.29 An injection-seeded single-longitudinal-mode
5028 APPLIED OPTICS y Vol. 36, No. 21 y 20 July 1997
laser was used in Ref. 29, whereas the lasers used inthe present study do not have any line-narrowingmechanism. In high-gain single-pass Raman cells,the transient effects are expected to arise mainly fromthe high amplification rate of the Stokes beams and donot depend critically on the pump bandwidth. Be-cause GtpDn .. 1, R is approximated by R > ~tpDnyG!1y2. At a wavelength of 266 nm and a temperatureof 300 K, the steady-state Raman gain of H2 or D2 hasreached 95% of its saturation value at 11.7 or 4.5 atm,respectively @Fig. 1~a!#. In the pressure-broadeningregime ~i.e., .2.7 or 1.0 atm for H2 or D2, respectively;Table 1! the Raman linewidth increases with pressure,and thus the transient gain continues to grow withpressure ~because of the dependence of R on the line-width!, even though the steady-state gain has alreadyreached saturation @Eq. ~1!#. The gain reduction R asa function of pressure for two values of tp and thetransient Raman gain gt, which is defined as thesteady-state Raman gain multiplied by R, are shown inFig. 2.
When the SRS is considered to be steady state,with the pump beam parameters as given above, ananalytical model that is valid at threshold30 predicts0.17 mJ for the S1 threshold energy at 10-atm H2~which is defined as the pulse energy that corre-sponds to Gf 5 25!. This value agrees with a nu-merical modeling21 that yields 0.12 mJ. Themodeling predicts that the peak conversion efficiencyof S1 occurs at 0.29 mJ. Experimental S1 thresholdvalues for quadrupled Nd:YAG setups are in the1–10-mJ range ~5 mJ typically! at 10-atm H2 and thepeak conversion efficiency occurs above 20 mJ,1,9 bothof which are 1 order of magnitude higher than thosecalculated by the steady-state description. With the
gain reduction included @R 5 0.030; Eq. ~2!#, the an-alytical model and the numerical modeling yieldthreshold energies of 3.3 and 3.9 mJ, respectively,and the latter predicts the S1 maximum conversion at26 mJ, which lies in the range of values observedexperimentally.
B. Four-Wave Mixing
FWM is a third-order nonlinear process that coexistswith SRS.21,23,31 At low pressure or pump energy,the conversion to S1 proceeds by SRS. When S1reaches the threshold for S2 generation, the latter isproduced by SRS and the FWM process, which mod-ifies the S2 electric field in agreement with
2ik2s]ze2
s 5 i~k2
s!2
~k1sk2
s!1y2
gp112
2~e1
s!2ep* exp~izDk11p2!, (3)
where the indices of the electric field e follow the samerule as that for k, gp112 5 ~gp1g12!1y2 is the FWM gain,and Dk11p2 5 2k1
s 2 kp 2 k2s determines its wave-
vector mismatch. The third Stokes generation isproduced from P, S1, and S2 through the FWM pro-cesses ~e2
s!2e1s* exp~izDk2213! and ep*e1
se2s exp~izDk12p3!.
Fig. 2. ~Left panel! transient plane-wave gain reduction for H2,D2, and CH4 as calculated from Eq. ~2! with G taken as Gf; ~rightpanel! transient Raman gain for H2, D2, and CH4, which is definedas the steady-state Raman gain times the transient gain reduction.The pump beam parameters are pulse durations of 5 ns ~solidcurves! or 20 ns ~dashed curves!, 80-mJ pulse energy, 3-mm radius~at 86% power!, and M2 5 1. The pump beam is focused by a50-cm lens, which yields a waist of 15 mm and a Rayleigh range of2.8 mm.
The higher the Stokes order, the more FWM pro-cesses lead to it, and hence the FWM-to-SRS ratioincreases. When n Stokes and anti-Stokes beamsare present ~total number, including the pump!, thereis a total of ~n 2 1!~n 2 2!y2 distinct FWM processesamong them. Without the averaging effect of FWM,all the energy would be shared by, at most, two beams~P–S1, S1–S2, . . . ,!.21 The FWM is reduced by anincrease in the pressure ~and hence the wave-vectormismatch!. Figure 1~b! shows that the wave-vectormismatch in CH4 is roughly twice that in H2, which istwice that in D2. The dispersion relation of thegases used in this study is given in Table 2.
The FWM phase matching expresses the conserva-tion of momentum and is also written as a vectorrelation Dkjlmn 5 kj 1 kl 2 km 2 kn. The vectorphase matching shows more clearly than its scalarcounterpart in Eq. ~3! that the FWM is optimized atdefinite angles of propagation. Consequently theFWM strength decreases when the lens focal lengthincreases because of the reduced potential of vectorphase matching that is due to the reduced numericalaperture.
C. Buffer-Gas Influence
The addition of buffer gas simultaneously reduces theFWM @by increasing the wave-vector mismatch, Eq.~3!# and the gain ~by increasing the Raman linewidthby a factor that increases with the molecular mass ofthe gas!. The Raman linewidth of a gas mixture canbe approximated by34
Dn 5 Dn0 1 gpb, (4)
where Dn0 is the self-broadened linewidth, g is thebroadening coefficient, and pb is the buffer-gas partialpressure. The underlying assumptions of Eq. ~4! arethat, first, the self-broadening occurs independentlyof the buffer-gas broadening and, second, there is noshift of the molecule vibrational frequency. Thebroadening coefficients of the buffer gases used in thisstudy are found in Table 3.
Figure 3 shows the Raman gain and wave-vectormismatch that occur when buffer gas is added to5-atm H2. The gain decays sharply at a low buffer-
Table 2. Resonance Fit Parameters at 272 K and 1 atm of the Dispersion Relationa
where n is the index of refraction and l is the wavelength in centimeters.
20 July 1997 y Vol. 36, No. 21 y APPLIED OPTICS 5029
gas pressure and eventually tends asymptotically to aconstant value. The gain reduction is seen to beapproximately proportional to the buffer-gas molecu-lar mass. The ratio among the wave-vector mis-match of He, Ne, and Ar is 1.0:1.1:3.8, respectively, at10-atm buffer-gas pressure and 1.0:1.3:7.8, respec-tively, at 30-atm buffer-gas pressure.
3. Experimental Setup
The fourth harmonic of a 10-Hz Q-switched Nd:YAG~266-nm! laser from Continuum, either a Powerlite8010 ~oscillator–amplifier! ~hereafter denoted as Po!or a Surelite III ~single oscillator! laser ~hereafterdenoted as Su!, was used as the pump source. Inboth cases the harmonics are separated by dichroicmirrors. Alternatively we used a Lumonics Excimer500 laser ~operated at 10 Hz! with a stable resonator~hereafter denoted as Ex!. This type of excimer la-ser is a much less common choice for high-powerRaman cells because of its bad beam quality andtherefore a loose focusing capability that results inlow conversion efficiencies. The excimer configura-tion is studied in order to investigate the dependenceon the pump beam quality.
The Raman cell experimental setup is standard~Fig. 4!. The pump beam passes through a Pellin–Broca prism ~in order to avoid backward-shifted ra-diation!; it is focused by a lens in the center of the cell,and the pump and the Stokes beams are recollimatedon exiting with a lens of the same type and dispersionby a prism. The pulse energies are measured afterthe prism with a calibrated pyroelectric detector~Gentec ED500 and EM-1! and averaged over 100shots. All the beams above the detector energy
Fig. 3. Steady-state Raman gain ~dashed curve! and the wave-vector mismatch Dk12p3 5 k1
s 1 k2s 2 kp 2 k3
s of the FWM processinvolving P, S1, S2, and S3 ~solid curve! for 5-atm H2.
Table 3. Broadening Coefficients g Used in the Calculation of theRaman Linewidth @Eq. ~4!#
5030 APPLIED OPTICS y Vol. 36, No. 21 y 20 July 1997
threshold ~0.2 mJ! are measured. Since the numberof photons is conserved by the Raman process, the ithStokes photon conversion efficiency hi
s is approxi-mated as
his 5
Pisyni
s
(j51
J
Pjynj
, (5)
where P is the pulse energy, n is the frequency, and Jis the number of beams above the detector thresholds~pump, Stokes, and anti-Stokes!.
The energy stability ~standard deviation! is of theorder of 5% for the Nd:YAG lasers ~at 266 nm! and 2%for the excimer laser. In a pure active gas, the en-ergy stability of the Stokes beam reproduced that ofthe pump beam at the pressure corresponding to theconversion efficiency maximum. At lower pressuresthe stability can reach more than three times that ofthe pump beam ~because the slope of the conversioncurve versus pressure is steep!, and at higher pres-sures it is roughly two times that of the pump.When a buffer gas is added, the Stokes energy stabil-ity improves when the conversion rises and degradesotherwise. As for pure active gas, the Stokes stabil-ity reproduces that of the pump at the buffer-gaspressure that yields the maximum conversion effi-ciency.
The M2 parameters of the input pump and theoutput Stokes beams are determined by the focusingwith either a 50- or a 75-cm focal-length lens and themeasurement of the beam width at various positionsbefore and after the waist. The knife-edge tech-nique with either the ~16%, 84%! or the ~10%, 90%!clip level is used to measure the beam size.38 Thesampled beam sizes are fitted to the curve
w2~z! 5 w02F1 1
~z 2 zf!2
z02 G , z0 5
pw02
M2l, (6)
where w~z! is the beam size at position z along theoptical axis and zf is the waist position. The uncer-tainty was estimated to be lower than 10%, from thedispersion of the measurement points around themodel curve of Eqs. ~6! and the difference between thetwo sets of clip levels. Figure 5 shows a typical ex-
Fig. 4. Experimental setup for the conversion efficiency andbeam-quality ~shaded elements! measurements: PB, Pellin–Broca prism; M’s, mirrors; L’s, lenses; P, prism; W, wedge plate;E’s, energy meters; K, knife edge. For the pump beam-qualitymeasurement, the setup comprising the shaded elements is put atthe exit of the laser.
ample of beam-size sampling along the optical axis.The curve fitting yields an uncertainty in M2 of ;5%from the dispersion of the measurement points and;5% difference between the ~16%, 84%! and ~10%,90%! clip level sets from which the total uncertaintyin M2 is estimated as 10%. The M2 parameters atthe laser output are measured to be 6.2 ~Su!, 3.9 ~Po!,and 260 3 25.4 ~Ex!; the values for the Ex lasercorrespond to the axes of the larger and the smallerdimension, respectively.
The pump pulse energy ~at 266 nm for the Nd:YAGlaser! at the cell input is 80 mJ ~unless otherwise stated!,with diameters ~at 86% power! of 8 mm ~Su!, 7 mm ~Po!,and 30 3 10 mm ~Ex! ~measured with the knife-edgetechnique!, and pulse durations of 4 ns ~Su!, 6 ns ~Po!,and 12 ns ~Ex! ~measured by the constructor!. The cellfocusing lenses have focal lengths of 25, 50, or 75 cm,along with a cell length that is twice the lens focal lengthat 266 nm. All mentioned focal lengths are defined atthe 587-nm wavelength. The lenses and the cell win-dows are antireflection coated ~a reflection coefficient ofless than 0.5% for 245–390 nm; 0° angle of incidence!.
For the simple estimations that are carried outbelow, standard approximate formulas are used@rather than the beam sampling and the fit; Eqs. ~6!#to calculate w0 and z0 from the measured beam size atthe lens ~wL!:
w0 5lfM2
pwL, z0 5
lf 2M2
pL2 . (7)
w0 and z0 as calculated with Eqs. ~7!, were checked tobe within 25% of the values retrieved from the fit,Eqs. ~6!.
4. Single Raman-Active Gas
A. Conversion Efficiency
The threshold pressure ~at a given pump pulse ener-gy! is defined here as the one that corresponds to 1%
Fig. 5. M2 measurement at the output of the Po laser with a50-cm focal-length lens ~defined at 587 nm!. The beam width w isshown as a function of the distance z along the optical axis from thefocusing lens. The curve of Eqs. ~6! is fitted to the measured w~z!,which yields w0 5 0.051 6 0.005 mm, zf 5 446.5 6 1.0 mm, and M2
5 3.8 6 0.2 for the ~16%, 84%! clip levels, and w0 5 0.058 6 0.004mm, zf 5 446.1 6 0.8 mm, and M2 5 4.0 6 0.2 for the ~10%, 90%!clip levels. The uncertainties are determined from the dispersionof the measurement points around the model curve.
photon conversion efficiency ~ht! and is denoted bypt~Si! for the ith Stokes photon conversion efficiency.In Refs. 23 and 30, the authors use the thresholdconversion efficiency to define the threshold pumpintensity It by assuming that for It the product Itgp1z~which is the argument of the exponential amplifica-tion in a plane-wave description! lies between 20 and30. In a similar fashion, in a focused geometry weassume ~Subsection 2.B! that It is defined by Gf 5 25.In this paper we report investigations carried out ata constant pump pulse energy whose level ~80 mJ! isclose to the maximum available with high-powercommercial quadrupled Nd:YAG lasers ~;100 mJ!.Within this framework the definition of threshold aspressure rather than energy is more natural. Theith Stokes photon conversion efficiency is denoted byh~Si!, the peak pa~S3! that could be achieved is de-noted by h~Si!, and the active gas pressure at whichthe latter occurs is denoted by pa~Si!.
The excimer configuration at low energy ~inputpump pulse of 20 mJ, Fig. 6! best shows the effect ofthe transient gain that increases with pressure, eventhough the steady-state gain is in the saturation re-gime. Between 15- and 25-atm pressure, the steady-state gain gp1 increases from 9.5 to 9.7 cmyGW, whichcannot solely explain the S1 and S2 photon conversionefficiency increases from 17% to 21% ~S1! and from4% to 5% ~S2!. At such a pump energy, the anti-Stokes and the higher Stokes ~.S2! beams are underthe detector threshold, so that the increase in the S1and S2 photon conversion efficiencies with pressurecannot be attributed to a backconversion that is dueto a FWM decrease. This effect is therefore inter-preted as the dependence of the transient gain reduc-tion on pressure. At a higher pump energy, thedependence of the FWM with pressure dominates.
Figure 7 shows the photon conversion efficienciesin pure H2, D2, and CH4 for the Po laser ~similarcurves are obtained with the Su laser!. The highergain of H2 with respect to D2 makes, for H2, h~S1!higher and pt lower for Si ~1 # i # 4!. The transientgain of CH4 is the highest ~Fig. 2!, and consequentlypt~Si!, 1 # i # 4, is lower than that for D2 and quitesimilar to that of H2. h~S1! in CH4 is lower than thatin H2 and D2, despite the highest transient gain,which is attributed to a more pronounced LIB in CH4~see Subsection 4.A.1!. In agreement with the h~S1!
Fig. 6. Photon conversion efficiencies in H2 for the excimer laserwith a pump pulse energy of 20 mJ and a lens focal length of 75 cm.
20 July 1997 y Vol. 36, No. 21 y APPLIED OPTICS 5031
dependence, the residual pump is seen to be the mostdepleted in H2, followed by D2 and CH4 @at 3 atm, h~P! 510%, 15%, and 28% for H2, D2, and CH4, respectively!.The decrease of FWM with pressure is the most pro-nounced for CH4, followed by H2 and D2, following thewave-vector mismatch proportionality among H2, D2,and CH4 @Fig. 1~b!#. This is evidenced by, e.g., the pos-itive slope of h~S1! versus pa and the negative slope ofh~S3! at high pressure ~.10 atm!, which are inverselyproportional to the averaging effect that is due to FWM.
For f 5 75 cm, above 15 atm of CH4, the fused silicaof the entrance-window inner face is etched at theexact location of the laser spot for a few minutes to afew hours of operation. This effect is attributed tothe laser-induced dissociation of CH4, which leads toreactive radicals. No such effect was noted at a pres-sure below 15 atm, even after hours of operation.The threshold pressure of etching was inversely pro-portional to f, so that it was found to be ;5 atm for f 525 cm.
1. Laser-Induced BreakdownMultiphoton ionization is a nonlinear process thatcoexists with SRS and FWM, which leads to the gas
Fig. 7. Photon conversion efficiencies as functions of pressure forH2, D2, and CH4 obtained with a Po laser with a 75-cm focal-lengthlens.
5032 APPLIED OPTICS y Vol. 36, No. 21 y 20 July 1997
breakdown.39 Alternatively, seed electrons from im-purities with subsequent laser-induced avalancheionization contribute to the formation of plasma. Ina simple model that takes into account only the en-ergy balance of the multiphoton ionization ~Ref. 39,Subsection 9.8!, the LIB threshold Ith
LIB shows thefollowing proportionality:
IthLIB }
n2Ui
tpp, (8)
where Ui is the atom ionization potential and p is thegas pressure.
LIB has been observed in KrF-pumped Ramancells.22 In the Nd:YAG setup we detected LIB bylooking into the cell from behind the folding mirrorthat injects the pump beam in the cell: Whitesparks were visible. Alternatively, the total numberof photons @~TNP!, which is given by the denominatorof the right-hand side of Eq. ~5!# at the cell output wascalculated from the measured Stokes energy spec-trum. The TNP variation with H2 pressure is shownin Fig. 8 for several lens focal lengths. With increas-ing pressure the TNP shows a dip, a maximum, anda decrease. Figure 9 helps to explain this behavior:It shows the steady-state SRS and the LIB thresholdintensities Ith. The SRS Ith is calculated as
Fig. 8. TNP in one pulse at the cell exit ~Su laser!, normalized toits maximum value ~i.e., when the cell is filled with 1 atm of air!,as a function of the H2 pressure and the lens focal length.
Fig. 9. Steady-state SRS and LIB thresholds in H2 at 266 nm and300 K. G 5 30 has been taken as the definition of the SRSthreshold, along with a Rayleigh range of 2.8 mm. For the LIBthreshold, a 1ypa dependence is considered, where pa is the H2
pressure, and adjusted to the experimental data of Alcock et al.40
Gy~g2z0!, where G 5 25 and z0 5 2.8 mm ~diffraction-limited beam of 6-mm diameter focused by an ideal50-cm focal-length lens!. A 1yp dependence hasbeen taken for the LIB Ith, normalized to 7 3 1011
Wycm2 at zero pressure, which is extrapolated fromdoubled ruby laser ~347 nm, 10-ns pulse duration!experimental data ~Ref. 39, Fig. 9.12!. These crudethreshold estimates serve to illustrate the connectionbetween the pump photon loss by LIB and SRS: Atlow pressure the SRS Ith is high so that the LIBpressure dependence dominates ~decrease of the TNPpressure curve!, but the SRS Ith decreases at a higherrate than the LIB Ith so that the Raman conversiongradually becomes the dominant process ~increase ofthe TNP curve!, but when the SRS Ith saturates withpressure it decreases at a lower rate than the LIB Ith,hence increasing the LIB effect with pressure ~de-crease of the TNP curve!. This complex interactionbetween SRS and LIB makes the TNP focal-lengthdependence difficult to predict ~Fig. 8!: Below 5-atmpressure, the shortest cell ~ f 5 25 cm! is the most
Fig. 10. TNP in one pulse at the cell exit, normalized to its max-imum value ~i.e., when the cell is filled with 1 atm of air!, as afunction of the equivalent lens focal length at 20-atm pressure.The points are labeled with the lens focal length in centimeters, thenumber of times the pump beam has been expanded before enter-ing the cell, and the M2 of the input pump beam ~3.9 and 6.2 for thePo and the Su lasers, respectively!. The equivalent lens focallength is calculated as the focal length divided by the beam expan-sion factor and multiplied by 6.2y3.9 5 1.6 for the Su laser.
Fig. 11. TNP in one pulse at the cell exit, normalized to its max-imum value ~i.e., when the cell is filled with 1 atm of air!, as afunction of Ar pressure, for pure Ar ~squares! and a mixture of10-atm H2 ~circles! or D2 ~crosses! with Ar for the Po laser with a75-cm focal-length lens.
transparent, whereas at first approximation the re-verse would be true because of the tighter focusing.At higher pressures ~.5 atm! the f 5 25-cm cell be-comes the most opaque, but the f 5 75-cm cell is stillless transparent than the f 5 50-cm cell.
Figure 10 shows the LIB that occurs in the cellwhen it is filled only with buffer gas. The measure-ments have been taken with various input pump
Fig. 12. TNP in one pulse at the cell exit, normalized to its max-imum value ~i.e., when the cell is filled with 1 atm of air!, as afunction of pressure for H2, D2 and CH4 for the Po laser with a75-cm focal-length lens.
Fig. 13. Peak conversion efficiency ~upper panel!, pressure atwhich the latter occurs ~ pa, middle panel!, and threshold pressure~bottom panel! in H2 with the ~a! Ex laser, ~b! Su laser, ~c! Po laser.Pressures were not measured below 1 atm, so that when pt or pa
occurs below this limit they are marked by an asterisk and aredisplayed in the figure as equal to 1 atm; correspondingly the peakconversion efficiency displayed is the value at 1 atm and is alsomarked by an asterisk.
20 July 1997 y Vol. 36, No. 21 y APPLIED OPTICS 5033
beam sizes vL, obtained with different beam expand-ers. At first approximation the waist size is in-versely proportional to vL, whereas it is proportionalto f. Therefore different beam-expansion configura-tions are compared by the definition of an equivalentlens focal length feq calculated as f divided by thebeam-expansion factor. The waist size is propor-tional to M2, and similarly f was divided by M2~Su!yM2~Po! 5 6.2y3.9 5 1.6 for the Su laser in order toyield a comparable focusing capability with the Polaser. For the three gases investigated, the LIB de-creases with feq, as expected from the 1yf eq
2 propor-tionality of the intensity at the waist. Theionization energies of He, Ne, and Ar are 23.6, 21.6,and 15.8 eV, respectively,40 and accordingly thetransmittance is the highest for He, followed by Neand Ar.
Figure 11 shows the effect on the photon transmit-tance of adding Ar to 10 atm of H2 or D2. At thispressure of Raman-active gas ~pa! and a lens focallength of 75 cm, the TNP is decreasing with the patrend that occurs at high pressure ~Fig. 8!. The ad-dition of a buffer gas reduces the Raman gain. Ittherefore has a similar effect, rather than reducingthe active gas pressure and hence increasing the TNPin this pressure regime. But because Ar is highlyabsorptive because of LIB ~30% reduction in TNP at20-atm pure Ar in this configuration!, increasing itspressure eventually leads to a decrease in the photontransmittance.
Murray et al.41 showed that, in gases, the ratio of
Fig. 14. Same as Fig. 13, but in D2 with ~a! the Su laser, ~b! thePo laser.
5034 APPLIED OPTICS y Vol. 36, No. 21 y 20 July 1997
the stimulated Brillouin scattering ~SBS! gain gSBS tothe SRS gain gSRS is given by
gSBS
gSRS5 C
pn1
s , (9)
where C is a constant that is dependent on the type ofRaman-active gas but is independent of the pressureand the Stokes frequency. For CH4 ~see Fig. 12!, Eq.~9! yields gSBSygSRS 5 py40,41 where p is in atmo-spheres and the 266-nm pumping wavelength hasbeen considered. Therefore SBS will have an effectcomparable with that of SRS for the CH4 pressuresconsidered in this study. Note that the backwardSBS gain exceeds the forward SBS gain. SBS isnegligible in H2 and D2 for the pressures consideredin this study.
2. Focusing GeometryFigures 13–15 show that for the three lasers andgases investigated, the threshold pressure ~pt! de-creases with increasing f for all the Stokes thresh-olds. It is also the case for pa concerning the higherStokes beams ~S3, S4!, and to a lesser extent for S1,S2, and AS1. Increasing f reduces the FWM; how-ever, the S1 threshold is independent of the FWM.Its inverse proportionality with increasing f is bestevidenced in our experimental configuration with theEx laser ~see also Figs. 16 and 17!. At first approx-imation the product of the intensity at the waistwithin the Rayleigh range ~depth of focus! is indepen-dent of f. The pt dependence on f may be explained
Fig. 15. Same as Fig. 13, but in CH4 with ~a! the Su laser, ~b! thePo laser.
by transient effects21: The gain reduction factor ~R!decreases with increasing pump intensity @through Gin Eq. ~2!#, which in turn decreases with increasing f.The pt and pa decrease of AS1, S3, and S4 with in-creasing f shows that the transient effects ~or anothereffect that explains the observed dependence! arestronger than the FWM since the latter would yieldthe reverse dependence.
For most of the cases investigated, similar trendsfor pa are observed between H2, D2, and CH4 for theNd:YAG pumping: S2 takes its maximum at highpressure ~because of the downconversion of thehigher Stokes beam at high pressure!, and pa~S2! .pa~S3! . pa~S4! shows that the higher the Stokesindex, the more it is produced by FWM ~and hence ismore reduced when the pressure is increased!. De-viations from these trends are noted for D2 and CH4at f 5 25 cm and are attributed to the higher cascad-ing at this lens focal length ~S5 and S6 not shown inFigs. 13–15!. For H2 and D2, pa~S1! and pa~AS1! areseen to be roughly equal @which suggests that AS1 isproduced mainly by the ~ep!2e1
s* FWM process#, but itis not the case for CH4 ~which is attributed to thehigher wave-vector mismatch!.
The lower Stokes peak conversion efficiency ~h! ~ex-cimer: S1; Nd:YAG: S1, S2! increases whereas thehigher Stokes peak conversion efficiency ~excimer:S2, S3; Nd:YAG: S3, S4! and the anti-Stokes peakconversion efficiency decrease with increasing f.The lower gain of the excimer configuration, whichlimits the Stokes cascade, explains the differencewith the Nd:YAG lasers. For the Su laser, AS1 isseen to increase with increasing f because of the oc-
Fig. 16. S1 photon conversion efficiency in H2 with the Ex laser.
Fig. 17. S1 photon conversion efficiency in D2 with the Su laser.
currence of anti-Stokes cascading ~h of AS2 decreaseswith increasing f; this is not displayed in Figs. 13–15!. The reduced FWM with increasing f explainsthe dependence of h on increasing f, and this is mostclearly evidenced with the Ex laser ~Figs. 13 and 16!.h~S1! with the Ex laser increases regularly with in-creasing f ~Fig. 16!, whereas there is no clear depen-dence for the Nd:YAG lasers for S1 ~Fig. 17!. It isattributed to the reduced FWM ~see below! and LIBwith this excimer. Figure 18 illustrates the de-crease of pa~S3! and h~S3! with increasing f that oc-curs for the higher Stokes beams, as well as thedecrease of pt, with increasing f noted for all thebeams.
For a given input pump beam size, the Rayleighrange and the waist size are proportional to the M2
parameter, whereas they are proportional to f2 and f,respectively. It is therefore expected that increasingthe M2 yields effects that are similar to those of in-creasing the lens focal length. When two lasers arecompared, the pump beam size at the input lens andthe pump pulse duration t must be taken into accountsince both determine the intensity at the waist.From the beam-size measurements of Section 3 andwith the formulas ~7!, the waist size of the Po, Su, andEx lasers has an approximate ratio of 1 3 1:1.5 31.5:15 3 4, and the Rayleigh range has a ratio of 1 31:1.5 3 1.5:4 3 2.5 ~along the axis from the bigger tothe smaller dimensions of the Ex laser rectangularbeam!. The pulse duration of the Su, Po, and Exlasers has a ratio of 1:1.5:3, so the pulse energy wasadjusted accordingly in order to yield a similar inputpower: 55 and 80 mJ for the comparison of the Sulaser with the Po laser, respectively ~Fig. 19! and 40and 80 mJ for the comparison of the Po laser with theEx laser, respectively. Figure 19 shows that S3 andS4 are systematically lower for the Su laser than forthe Po laser. The same trend is exhibited by AS1between the two Nd:YAG lasers, except for the case ofCH4, whereas S1 and S2 do not show any clear trend.The conversion behavior differs much more betweenthe Po laser and the Ex laser than between the twoNd:YAG lasers, which is attributed to the bigger dif-ference in M2 ~Fig. 20!. h’s of S2, S3, and S4 haveratios of 20:11:1 for the Po laser and 450:55:1 for theEx laser. h~S1! occurs below 1 atm for the Po laser,and thus only a lower bound ~determined at 1 atm!
Fig. 18. S3 photon conversion efficiency in H2 with the Su laser.
20 July 1997 y Vol. 36, No. 21 y APPLIED OPTICS 5035
was measured, but even if h~S1! 5 100%, S1 and S2would have a ratio of 1.5:1 for the Po laser whereasthey have a ratio of 2.9:1 for the Ex laser. Thiscomparison between the two pairs of lasers suggeststhat the higher the M2 of the pump beam, the less theFWM, and therefore there is proportionally more con-version in the two first Stokes beams. A similarreduction in FWM was noted when the lens focallength was increased.
With Ar as a buffer gas, the S1 peak photon con-version efficiency is found to be 71% for the Su laser
Fig. 19. Peak photon conversion efficiency in H2 with a 75-cmfocal-length lens. Input pulse energies of 55 and 80 mJ for the Suand the Po lasers, respectively, are used, which yield an approxi-mately equal input power ~13 MW! for both lasers.
Fig. 20. Peak photon conversion efficiency in H2 with a 75-cmfocal-length lens. Input pulse energies of 40 and 80 mJ for the Poand the Ex lasers, respectively, are used, which yield an approxi-mately equal input power ~6.7 MW! for both lasers.
5036 APPLIED OPTICS y Vol. 36, No. 21 y 20 July 1997
~10-atm H2, 35-atm Ar! and 54% for the Po laser~8-atm H2, 30-atm Ar!. This effect is also similar tothat of increasing f ~see Subsection 4.A.4 below!.There must nevertheless be an optimal focusing ge-ometry ~determined by M2 or f ! because the focusingof looser and looser h eventually decreases, as is thecase for the Ex laser for which h of S1 is two to threetimes smaller than that for the Nd:YAG lasers.Nevertheless KrF lasers are capable of producingpulse energies that are several times those of thequadrupled Nd:YAG laser and can thus possibly yieldS1 and S2 pulse energies higher than with the Nd:YAG laser, even though the conversion efficiency islower. The dependence of h on the pump energy hasnot been investigated. An alternative way of tightlyfocusing yet limiting the FWM and LIB is to usecylindrical lenses.42
3. Buffer GasesThe active-gas and buffer-gas pressures ~pa and pb,respectively! were varied in order to determine thosethat maximize the first Stokes conversion efficiency~h! ~ pa and pb, respectively!, as shown in Table 4.
The three buffer gases were tested at a fixed lensfocal length ~ f 5 75 cm; Po laser!. pa is seen toincrease with the buffer-gas molecular mass ~Mb! forboth active gases ~Table 4!, which follows from thedependence of the Raman gain with Mb ~Fig. 3!. pbfor Ar ~.30 atm! is much bigger than that for He andNe ~,10 atm!. For the former, the optimum is foundwhen the Raman gain dependence with pb is in theasymptotic regime and hence it is the wave-vectormismatch that is predominant, whereas for the latterit is mainly the gain reduction that controls the op-timum.
The level of h reached with the addition of a buffergas depends on the gain reduction, the FWM wave-vector mismatch, and the LIB, which eventuallyworsens with increasing pb. In Fig. 11, the net effectof adding Ar to high-pressure H2 or D2 ~.5 atm, say!is to increase the power of the lower Stokes photon
Table 4. Mixture of Active and Buffer Gases that Maximize the First Stokes Photon Conversion Efficiency ~h!
Laser
Lens FocalLength
~cm!ActiveGas
Active-GasPressure
~atm!BufferGas
Buffer-GasPressure
~atm!h
~%!
Su 25 H2 5 Ar 20 31D2 10 20 35
50 H2 10 Ar 55 56D2 10 30 47
75 H2 10 Ar 40 64D2 10 40 47
Po 50 H2 10 Ar 25 41D2 12 15 30
75 H2 1.5 He 10 353.0 Ne 8.0 32
10 Ar 33 61D2 2.0 He 2.5 39
3.0 Ne 6.0 3710 Ar 35 33
CH4 10 Ar 45 52
conversion efficiencies ~S1, S2! by reducing the LIBand the FWM, but it eventually leads to a powerdecrease that is due to the increasing LIB in thebuffer gas and the Raman gain reduction. The FWMand the LIB depend on the focusing geometry ~ f andthe input pump M2!. The highest h in H2 is obtainedby the addition of Ar, which is also found for the Sulaser ~not shown in Table 4! and in a previous exper-iment that used another type of Nd:YAG laser.9 hfor D2 is similar for the three buffer gases, whereasfor the Su laser, h is 20% higher with Ar than with Heand Ne ~not shown in Table 4!, as seen in Figs. 21 and22. h~S2! in H2 attains similar levels as those for S1,and in D2 the addition of buffer gas is profitable forh~S2! only with Ar ~with the Po laser!. In both activegases, S3 and S4 show no optimum when a buffer gasis added.
The lens focal length was varied for the Ar buffercase ~Su laser; Table 4!. As for the pure active gases~see Subsection 4.A.2!, the peak conversion efficiencyincreases with f, the effect being the strongest in H2.Figures 23 and 24 show that this dependence of hwith f is due to the reduction in FWM, as evidencedby the reduced energy sharing among the Stokes con-version efficiencies when f increases. Moreover, LIBis a limiting factor when focusing tightly ~ f 5 25 cm!since less than 50% photon transmission ~TNP! wasmeasured for an Ar pressure above 20 atm in eitherH2 or D2.
The peak conversion efficiency in CH4:Ar could be
Fig. 21. Photon conversion efficiency in H2 when He is added to1.5-atm H2, Ne is added to 3-atm H2, and Ar is added to 10-atm H2.The Po laser, with 75-cm focal-length lens, is used.
Fig. 22. Photon conversion efficiency in D2 when He is added to2-atm D2, Ne is added to 3-atm D2, and Ar is added to 10-atm D2.The Po laser, with 75-cm focal-length lens, is used.
optimized to be ;50% higher than that in the D2:Ar~with the Po laser!. This effect is attributed to thehigher gain ~Figs. 1 and 2! and FWM wave-vectormismatch ~Fig. 1! with respect to D2. Figure 25shows that in CH4, Ar acts efficiently since the S1conversion efficiency more than doubles between 0and 40 atm of Ar, whereas S2, S3, and S4 all decreasewith Ar pressure. No etching of the optics was notedat the 10-atm CH4 pressure and these Ar pressures,even after hours of operation.
B. Stokes Beam Quality
The quality of the output pump beam when the cell isfilled with air at atmospheric pressure was measuredand compared with the beam quality at input: TheM2 is unchanged ~within 5%! for the Ex laser and ismultiplied by a factor of 2.0 for the two Nd:YAGlasers ~yielding M2 of 7.8 and 12.4 for the Po and theSu lasers, respectively!. At 80-mJ pulse energy, thebeam profiles of the two latter lasers show a numberof hot spots ~at 266 nm! that induced stress on theantireflection coatings and the fused-silica sub-strates, hence degrading the beam quality. Suchproblems were not encountered with the Ex laser.
The output pump beam quality of the excimerwhen the cell is filled with 25-atm Ar was measuredto be unchanged ~M2 within 5%! compared with whenit is filled with air at atmospheric pressure, whereasfor the Po and the Su lasers it is multiplied by factors
Fig. 23. Photon conversion efficiency with the Su laser in H2 whenAr is added, as a function of the lens focal length ~ f !. The H2
pressure is 5, 10, and 10 atm for f 5 25, 50, and 75 cm, respectively.
Fig. 24. Photon conversion efficiency with the Su laser in D2 whenAr is added, as a function of the lens focal length ~ f !. The D2
pressure is 10 atm for all the cases of f displayed.
20 July 1997 y Vol. 36, No. 21 y APPLIED OPTICS 5037
Table 5. Beam Quality Measured at the Output of the Raman Cella
LaserActiveGas
Active-GasPressure
~atm!BufferGas
Buffer-GasPressure
~atm!xyy
~Ex Laser! BeamM2
Parameter
Ex H2 8.5 — x P 1.0 6 0.1S1 0.48 6 0.04S2 0.51 6 0.1
y P 1.6 6 0.1S1 0.66 6 0.06S2 0.48 6 0.09
26 — x P 1.1 6 0.1S1 0.57 6 0.09S2 0.37 6 0.04
y P 1.6 6 0.1S1 0.94 6 0.08S2 0.57 6 0.06
15 He 7.5 x P 1.0 6 0.1S1 0.41 6 0.1S2 0.23 6 0.05
y P 1.2 6 0.1S1 0.68 6 0.08S2 0.45 6 0.07
Su H2 5 Ar 25 S1 1.2 6 0.1Po H2 2 — S1 0.73 6 0.06
10 — P 3.3 6 0.3S1 3.4 6 0.4S2 12.5 6 1.5
10 Ar 25 P 1.2 6 0.1S1 1.1 6 0.2
10 He 10 S1 1.4 6 0.2D2 2.5 — P 1.1 6 0.1
S1 0.52 6 0.04
aThe cell-lens focal length is 50 cm ~Su and Ex lasers! and 75 cm ~Po laser!. For the Ex laser, the knife-edge measurement was performedalong the biggest ~x! and the lowest ~y! dimensions of the rectangular beam, whereas for the Nd:YAG lasers the M2 parameters along twoperpendicular axes were measured to be within 10% of each other and are presented as an average in the table. The M2 parameter isnormalized with the M2 of the output pump beam when the cell is filled with 25 atm of Ar, namely, 273 ~x! and 27.6 ~y! for the Ex laser, 16.1for the Su laser, and 14.0 for the Po laser. The normalized M2 is denoted as M2. The uncertainties of M2 are calculated from the dispersionof the measurement points around the model curve, Eqs. ~6!. P in the Beam column refers to the residual output pump.
of 1.8 ~to M2 5 14.0! and 1.3 ~to M2 5 16.1!, respec-tively. In these measurements f 5 50 cm for the Exand the Su lasers and f 5 75 cm for the Po laser. Forthe Ex laser, the TNP at the exit of the cell wasmeasured to vary less than 3% when Ar was added~up to 30 atm!, indicating at most a weak LIB. TheTNP’s at 25-atm Ar for the Po and the Su lasers weremeasured to be 46% and 29% lower, respectively,than when the cell was filled with air at atmosphericpressure ~see also Fig. 11!. Therefore the beam deg-radation of the Nd:YAG lasers when Ar is added isattributed to LIB.
In Table 5, the M2 parameter of the Stokes beam isnormalized with the M2 of the output pump when thecell is filled with 25 atm of Ar, namely, 273 3 27.6 forthe Ex laser, 16.1 for the Su laser, and 14.0 for the Polaser. The normalized M2 is denoted as M2. TheM2 parameter defined in this way avoids only to someextent the effect of the LIB on the beam quality;however, it helps in interpreting the sole SRS–FWMeffects. For the Ex laser there is a clear improve-ment ~M2 , 1! between the quality of the input pumpbeam and that of S1, as well as between S1 and S2.This beam cleanup effect is weakly dependent on the
5038 APPLIED OPTICS y Vol. 36, No. 21 y 20 July 1997
Raman gain, as noted between 8.5 and 26 atm of H2~except for S1 in the y direction!. Adding a He bufferslightly improves the beam quality. Similar resultswere obtained with f 5 25-cm and f 5 75-cm lenses.Different features characterize the Nd:YAG lasers.At low amplification ~2-atm H2 or 2.5-atm D2; Polaser! the Stokes beam quality is measured to be thesame as or better than that of the input beam. Athigher amplification ~10-atm H2; Po laser! the Stokes
Fig. 25. Photon conversion efficiency when Ar is added to 10-atmCH4. The Po laser, with a 75-cm focal-length lens, is used.
beam is very much degraded ~M2 5 3.4 and 12.5 forS1 and S2, respectively!, which can hardly be ex-plained by the sole LIB. Adding 25-atm Ar to 10-atm H2 improves the M2 of S1 by more than a factorof 3. Adding 10-atm He improves the M2 of S1 by afactor of 2.5 ~its conversion efficiency is modified by20%!. A similar S1 beam quality in the presence ofan Ar buffer is obtained with both Nd:YAG lasers.These results are consistent with previous measure-ments of the beam divergence,9,16,17 with the differ-ence that, in this work, the M2 parametermeasurement is independent of the beam diameter.
The S1 and the S2 beam profiles with the Ex laser~measured with a pinhole instead of the knife-edgescanned in the beam, Fig. 4! duplicated the beamprofile of the input pump, whereas those with theNd:YAG lasers showed an annular structure at highpressure ~attributed to FWM!, which tends to disap-pear when buffer gas is added or the pressure of theactive gas is decreased. Off-axis lobes that disap-peared when f was increased were previously notedby Cheng and Kobayashi.17
The expressions beam cleanup and beam degrada-tion are used when the M2 parameters of the outputStokes beam are lower and higher, respectively, thanthose of the M2 of the input pump. The beam-
Fig. 26. Curves yield the dependence of the partial pressures ofH2, D2, and Ar in such a way that the steady-state Raman gain ofH2 equals that of D2 in a mixture of the three gases. The circlesindicate experimental results for which the pressure of Ar could beadjusted so that the energy in the first Stokes beam of D2 equalsthe energy in the first Stokes beam of H2.
quality measurements are consistent with a numer-ical model,21 which showed that there is beamcleanup at low amplification ~i.e., before the S1 con-version efficiency becomes less than that of S2! andbeam degradation at high amplification. The beamdegradation is partly caused by the depletion at thebeam center that is due to the conversion to higherStokes beams, but mainly by the FWM, which addsoff-axis lobes to the beam profile ~corresponding to theangle of phase matching of the FWM!. This effect ofthe FWM is evidenced by the fact that adding a buffergas improves the Stokes beam quality.
5. Mixture of Two Raman-Active Gases
A. Hydrogen and Deuterium
At a given lens focal length, the optimization processdepends on four parameters: the input pump en-ergy and the partial pressures of H2, D2, and thebuffer gas ~Ar in this study!. In order to facilitatethe optimization, the dependence of the partial pres-sures of H2, D2, and Ar such that the steady-stateRaman gain in H2 equals that in D2 is plotted in Fig.26. We note that these optimum pressures are quitesensitive to the pressure of H2, as expected from itshigher gain ~5 times the gain of D2 at 266 nm and10-atm active-gas pressure!. For example, when theH2 pressure is increased from 4 to 5 atm, the D2pressure has to be increased from 12 to 16.5 atm,while the Ar pressure is kept at 5 atm, or the Arpressure has to be decreased from 7 to 3 atm whilethe D2 pressure is kept at 15 atm. In Fig. 26 are alsoshown the H2 and the D2 pressures at which equalenergy in S1~D2! and S1~H2! could be experimentallyobtained when the Ar pressure is varied up to 30 atm~these are also given in Table 6!. The agreementbetween the measurements and the theoreticalcurves is reasonable, taking into account that such acomparison is not direct, since not only the Ramangain is significant but also the FWM wave-vector mis-match. We note that, either theoretically or exper-imentally, the dependence of the D2 pressure on theH2 pressure is almost linear, so that, as a roughguide, the H2 pressure has to be multiplied by a factorbetween 2.5 and 3.5 to yield the D2 pressure in order
Table 6. Experimental Partial Pressures in a Mixture of H2, D2, and Ar that Yield Equal Pulse Energies in the first Stokes beams of D2 and H2a
aA lower bound in the Ar pressure column and correspondingly an — in the S1 energy column means that, in the indicated pressurerange, equal energy in both first Stokes beams could not be reached. A 75-cm focal-length lens was used.
20 July 1997 y Vol. 36, No. 21 y APPLIED OPTICS 5039
that equal energies in S1~D2! and S1~H2! can beachieved when the Ar pressure is varied.
A similar dependence of the Stokes efficiencies onAr pressure ~pb! is noted in all cases studied @Fig. 27~Su laser! and Fig. 28 ~Po laser!#. The sum of thesecond Stokes beams of H2 and D2 decreases with pb,which shows that these beams are not substantiallyfurther converted ~otherwise they would first in-crease and then decrease with pb!. S1~D2! increaseswith pb ~sometimes after a short decrease!, indicatingthat energy is backconverted from S2~D2! when Ar isadded. S1~H2! first increases and then decreaseswith pb, showing that it is less further converted thanS1~D2!. This effect is attributed to a higher cascad-ing in D2, as was noted with the individual activegases ~see Subsection 4.A!. The residual pumpbeam increases with pb, as is also the case with asingle active gas. Figure 29 shows that the pulseenergies of the residual pump beam and the firstStokes beam are weakly sensitive to the input pulseenergy. Even if the gas partial pressures do notyield in this case equal power in S1~D2! and S1~H2!,we note that the ratio of S1~D2! to S1~H2! pulse energyis approximately constant with respect to the inputpump beam energy.
Table 6 summarizes the results of the search ofequal energy in S1~D2! and S1~H2!. Up to 9 and 14mJ were obtained with the Po and the Su lasers,
Fig. 27. Residual pump energy, S1 of D2, S1 of H2, S2 of D2, andS2 of H2, as functions of Ar pressure in a mixture of H2, D2, and Ar.The parameters are 50 mJ at cell input, Su laser, 7.0-atm H2,19-atm D2, and 75-cm focal-length lens.
Fig. 28. Residual pump energy, S1 of D2, S1 of H2, S2 of D2, andS2 of H2, as functions of Ar pressure in a mixture of H2, D2, and Ar.The parameters are 70 mJ at cell input, Po laser, 5.5-atm H2,15-atm D2, 75-cm focal-length lens.
5040 APPLIED OPTICS y Vol. 36, No. 21 y 20 July 1997
respectively ~the pump input power was approxi-mately equal between the two lasers!. The higherefficiency of the Su laser is attributed to the lowernumerical aperture with respect to the Po laser ~high-er M2!. This argument yields a high sensitivity tothe focusing geometry that indicates the predomi-nance of FWM, which can be explained in the case ofmixing two active gases by the bigger number of pos-sible FWM processes compared with a single active-gas configuration.
The M2 parameter is normalized with the M2 of theoutput pump beam when the cell is filled with 25-atmAr, in the same way as in Subsection 4.B. The beamquality was measured for the Su laser at 7-atm H2,19-atm D2, 33-atm Ar, f 5 75 cm, and 50-mJ inputpump pulse energy @yielding 14 mJ in S1~H2! andS1~D2!; Table 6#. The M2’s of the residual pumpbeam, S1~D2!, and S1~H2! were found to be 2.1 6 0.2,1.2 6 0.1, and 1.1 6 0.1, respectively. The beamqualities of both first Stokes beams are similar tothose measured with a singe active gas, whereas thatof the residual pump beam is approximately twotimes worse. The full-angle divergences ~at 86%power! of the recollimated beams at some fixed posi-tion of the output lens were found to be 0.50 6 0.02,0.42 6 0.02, and 0.85 6 0.03 mrad for S1~D2!, S1~H2!,and the residual pump beam, respectively. Theworse divergence of the residual pump beam is due tothe worse beam quality, which represents an intrin-sic limitation of the Raman cell rather than a matterof the optical setup after the cell.
We investigated the spectrum of the cell outputradiation by removing the prism at cell output ~Fig.4!, taking the reflection of the radiation on a fused-silica surface, dispersing it with a grating, and mea-suring the distance between the lines on a flat panellocated at 2 m on the grating. Nineteen spectralcomponents were found ~Table 7! that were identifiedto be composed of only Stokes or anti-Stokes beams ofeither single H2, single D2, or the Raman-shifted fre-quencies in D2 of the single H2 lines or the Raman-shifted frequencies in H2 of the single D2 lines. Theclosest wavelengths to S1~D2! ~289 nm! and S1~H2!~299 nm! are seen to lie 5 nm apart ~284 nm!.
Fig. 29. Residual pump energy, S1 of D2 and S1 of H2, as functionsof the input pump energy in a mixture of H2, D2, and Ar. Theparameters are Po laser, 7.5-atm H2, 18.5-atm D2, 16.5-atm Ar,75-cm focal-length lens.
B. Other Gas Fillings
A mixture of H2, CH4, and Ar was also investigated.The conversion efficiency to S1~H2! and S1~CH4! isseen to be lower than with the ~H2, D2! mixture ~moreenergy is observed to be converted to the higherStokes beams!. With 15-atm H2, 10-atm CH4, 20-atm Ar, f 5 75 cm, and 70-mJ input pump pulseenergy ~Po laser!, 6, 8, and 8 mJ were measured inthe residual pump beam, S1~CH4!, and S1~H2!, re-spectively. At this pressure of CH4 no etching of theoptics was observed.
Ethane ~C2H6! was tried in an attempt to obtaintwo wavelength-shifted beams from its two principalvibrational modes ~C™C and C™H stretching, whichyield 273 and 289 nm, respectively, from the 266-nmpumping radiation!. It proved to be unsatisfactoryfor the following reasons. First, LIB has a muchlower threshold than in H2, D2 or CH4: Intensesparks were visible at 1 bar of C2H6 with a corre-sponding cell photon transmission of ;30% ~the ion-ization energy of C2H6 equals40 11.5 eV!. Second,C2H6 becomes liquid at room temperature for pres-sures above 10 atm, which limits its applicability.Third, the Raman gain at low pressure ~,10 atm! istoo low for high-power applications: at most, 5 mJat 273 nm and 1 mJ at 289 nm were obtained at7.5-atm pressure.
Table 7. Spectrum at Output of a Raman Cell Filled with a Mixture ofH2, D2, and Ar, as Dispersed by a Gratinga
aThe lines are identified with the following notation: For ex-ample, S1~D2, 299.0! indicates the first Stokes beam in D2 of the299.0 nm beam, which is the first Stokes beam in H2 of the266.0-nm input pump. The parameters are 70 mJ at cell input, Polaser, 5.5-atm H2, 15-atm D2, 12.5-atm Ar, and 75-cm focal-lengthlens.
6. Conclusion
In single-pass UV Raman cells there is a complexinteraction among the stimulated Raman scattering~SRS!, four-wave-mixing ~FWM!, transient effects,and the laser-induced breakdown ~LIB!. All theseeffects complicate the interpretation of conversion ef-ficiency and beam-quality measurements. One aimof this paper is to unravel some simplified guidelinesthat allow an easier interpretation of the measure-ments and hence possibly a better optimization of thecell performance. A model of SRS, FWM, and thetransient effects21 helps to explain further several ofthe features observed ~Stokes threshold, effect of theFWM, dependence on the lens focal length, Stokesbeam quality!.
There is strong evidence that LIB is a phenomenonthat has to be included in the interpretation of single-pass high-energy Raman cell measurements. Noclear focal-length dependence of the LIB was foundbecause of the interaction among LIB, SRS, andFWM. H2 and D2 show similar LIB behaviors,whereas this behavior is stronger in CH4. LIB de-grades the Stokes beam quality ~by roughly a factor of2 in our setup!.
There is some evidence that transient effects in theSRS process play a significant role, because of thehigh Stokes amplification rate that occurs withtightly focused beams in the UV. First, an estima-tion of the amplification rate for a typical high-gainsingle-pass Raman cell configuration in the UVshows that it is higher than the dephasing frequencyof the Raman medium. Second, steady-state calcu-lations of the threshold pressure are orders of mag-nitude apart from the observed values, whereas suchcalculations, when carried out with a simple modelthat takes into account transient SRS effects, are ofthe same order than the observed values. Third, inthe linear SRS regime ~i.e., at sufficiently low pres-sure or energy!, the Stokes conversion efficiency isseen to grow in the regions of pressure that are char-acterized by an almost constant steady-state Ramangain.
The addition of Ar to H2 brings higher conversionefficiencies than with He or Ne, whereas for D2 thethree types of buffer gas are equivalent. CH4 leadsto higher efficiencies than D2, but above 15 atm itetched the antireflection coatings and the fused-silicasubstrate. There is a strong dependence of the con-version efficiencies on the lens focal length ~ f !. In-creasing f reduces all the Stokes thresholds andincreases the first Stokes conversion efficiency. Theformer feature may be explained by transient effects.The input pump-beam quality ~M2 parameter! affectsthe conversion process through the focusing geome-try. Increasing the pump M2 is similar to increasingthe lens focal length. A difference in conversion ef-ficiencies of ;20%–50% ~the higher Stokes efficiencyshowing a larger difference! is found between the twoNd:YAG lasers, which are characterized by M2’s of3.9 and 6.2 ~at the fourth harmonic!. Cylindricallenses yield a higher first Stokes conversion efficiency
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than that with spherical lenses, as it would limit theLIB and the FWM.
Concerning the Stokes beam quality, two regimesare identified: low and high amplification, the limitbetween the two occurring when the second Stokesbeam has energy that is equal to that of the firstStokes beam ~onset of the intensity-averaging re-gime!. At low amplification there is beam cleanup~the M2 of the Stokes beam is lower than that of theinput pump beam!, whereas at high amplification thebeam quality degrades ~the M2 of the Stokes beam ishigher! because of the predominance of FWM. Theaddition of a buffer gas improves the Stokes M2 con-siderably by reducing the FWM. A factor of 3 im-provement in the first Stokes M2 parameter wasmeasured when 10-atm of He or Ar were added.
Between 10 and 15 mJ in the first Stokes beam ofD2 and H2 ~pumped by the Nd:YAG laser fourth har-monic! can be obtained from a single Raman cell filledwith the appropriate mixture of D2, H2, and Ar. TheStokes beam quality is comparable with that ob-tained with a single active gas, while the quality ofthe residual pump beam is approximately two timesworse. With the collimating lens positioned such asto make a compromise between the divergence of thetwo first Stokes beams and the residual pump beam,the full-angle divergence ~at 86% power! of the twoformer beams is measured to be less than 0.5 mrad,while for the latter it is approximately 0.9 mrad.These divergences make the beam appropriate, e.g.,for the measurement of ozone by a DIAL.
This work was supported by the Swiss Federal Of-fice for Education and Science, grant Eureka-BBW~94!3. The authors thank P.-A. Bielmann andD. Jeker for their technical assistance. One of thereviewers is acknowledged for his pertinent remarks.
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