250 OPTICS LETTERS / Vol. 4, No. 8 / August 1979

Injection mode locking of a TEA CO2 laser on P and Rtransitions in the 9- and 10-gim bands

P. E. Dyer and I. K. Perera

Department of Applied Physics, University of Hull, Hull HI-U6 7RX, U.K.

Received April 18, 1979

An analysis and experimental study of an injection mode-locked TEA CO2 laser operating on various transitions inthe 9- and 10 -;tm bands are presented. Locking on 30 transitions has been obtained with peak powers of -1 GWin the output pulse train.

Injection mode locking1 provides a relatively simplemeapls2 of producing high-power pulse trains from un-stable resonator TE C02 lasers. Although this tech-nique has been used on a variety of systems1-7 withapertures up to -20 cm,6 all investigations to date ap-pear to have been concerned with locking on thestrongest emission line of the TE C02 laser, i.e., P(20)in the 10.4-Am band. 1-6 In this Letter we analyze anddemonstrate experimentally injection mode locking(IML) of a nondispersive C0 2-laser resonator on a largenumber of transitions in the 9.4- and 10.4-gum bands. Inall, 30 transitions have been observed to lock in thegain-switched spike, with peak output powers of -1GW, as a result of injecting a -2-nsec, 300-W pulse intothe resonator.

To evaluate the range of wavelengths over which IMLcan be expected, we consider the buildup of intensityin a laser cavity assuming that, over the period of in-terest, the gain coefficient cij varies linearly with timeaccording to

aj = cEaJtlr (t < r),where ceoj is the peak gain-coefficient of a specifictransition and r the gain risetime. This case of a lineargain growth gives a reasonably good description of thegain-switched C02 laser.

It can be shown from Eq. (1) that, in the small-signal,single-mode approximation, the appearance time, Tj,of the gain-switched pulse is given by8 :

Tj = T ± 12r ln(Os/IT)] /2coaj

(Tj < T), (2)

where As is the photon density that produces significantsaturation of the transition of interest, (hT is the photondensity in the cavity mode at threshold that is due tospontaneous emission or injected radiation, and c is thevelocity of light. T is the time taken to reach threshold,which, for an unstable resonator of magnification M, isgiven by

T = r In MltajL (t < T).

In Eqs. (2) and (3), EZj is the peak small-signal gain av-eraged over the cavity length, L, such that aJ =ajLDIL, where LD is the length of gain medium.8

For the TEA C02 laser the highest gain transition is

normally P(20) in the 10.4-gm band,9 and, with a non-frequency-selective resonator, this will grow from noisethe most rapidly, producing gain depletion and sup-pression of other lower-gain transitions. If an injectedpulse on a transition other than P(20) is to dominateoscillation, it is necessary to ensure that its growth time,Tj, is shorter than that for P(20), i.e., Tj < T20. Thisrequires the injection of a sufficiently high photondensity, Hi, at threshold such that, from Eq. (2),r In M+ [2r ln(Os/q 1)]1/2 <r In MajL CtiJ J a 20L

2 ln(<AS/(h2o1 1/2+ c(i 20 1 (4)

where (020 is the photon density in the cavity mode atthreshold that is due to spontaneous emission on P(20).The appearance in Eq. (4) of 0i as a logarithmic termindicates that relatively strong signals are required tocapture oscillation on weak (low-gain) transitions. Incontrast, for the natural frequency [P(20)], IML can beachieved using very weak signals such that 0i >> (h20 -10-10 W; this has been demonstrated experimentally byAlcock et al. 2 and can be deduced from Eq. (4) with ofJ- a 20 o

In Fig. 1 the left-hand side of Eq. (4) is shown as afunction of gain (aCXj A 2.5% cm-1 ) for an oscillator withthe parameters T = 2 gsec, L = 2.6 m, LD = 1 m, M = 2,and 0i = 2.6 X 1010 cm- 3 and 1.4 X 104 cm-

3. The

upper time limit imposed by the growth of P(20) fromthe noise is shown as a broken line in Fig. 1 and assumesthat a2o = 2.5% cm t1 and 020 = 1 cm-

3. For both cal-

culations Os = 2.101k cm-3 is used, representative of the

TEA CO2 laser. It can be seen from Fig. I that, with Xi= 2.6 X 10's cm-3, the injected signal is predicted todominate for aoj > 1.8% cm-'; note that the range ofgain available for locking reduces as the injected signalis decreased (e.g., (h = 1.4 X 104 cm- 3 , Fig. 1). It shouldbe pointed out that for each value within the IML rangeit will normally be desirable to reduce the injected signalat threshold to a minimum (consistent with reliableoperation) in order to maintain a high peak power in thegain-switched spike. Operation with the maximumavailable injection signal is only necessary to obtaindominance at the limiting gain values, i.e., those forwhich Tj T20.

0146-9592/79/080250-03$0.50/0 © 1979, Optical Society of America

I R - Branch

P - Branch

I

I - Oi * 1 37 x 1O'cm-'

2-60Xfo 0cm'-

2

Gain, (percent cm1')

3

Fig. . Lower, gain-witched pulse-goth tine or two in-jected-signal levels, (i, as a function of gain. T 20 indicatesgrowth time of P(20) transition from spontaneous emissionwith a2o = 2.5%o cm- 1 . Upper, P- and R-branch gain spec-trum with vertical broken lines to indicate limiting transitionsavailable for locking for each 0i.

To relate the gain window in Fig. 1 with P- and R-branch transitions in the 10.4-gm C02 band, the gain-wavelength dependence was calculated using equationsgiven by Weaver et a. 10 with a vibrational inversionratio of 2 and rotational temperature of 375 K. Thegain spectrum, shown in Fig. 1, was normalized to aP(20) gain of 2.27% cm- t with a 10% contribution addedto P(20) to account for hot-band transitions.9 As seenfrom Fig. 1, the Tj < T2 0 range for 4i = 1.4 x 104 pho-tons/cm3 corresponds to the P(16)-P(20) transitions,and for (h; = 2.6 X 1010 photons/cm 3 to the P(12)-P(28)and R(12)-R (22) transitions, in the 10-Mim band.

To study IML experimentally a small grating-tunedwire-triggered TEA C02 oscillator equipped with alow-pressure cw section to provide temporally smoothpulses was used as the master oscillator. The -100-mJ,250-nsec-duration pulses produced by this oscillatorwere directed into an electro-optic pulse-gating system,which reduced the pulse width to -2 nsec (FWHM).The contrast ratio of the switched pulse was >100:1.The slave oscillator was a bladed-cathode double-dis-charge TEA C02 device with a discharge volume of 5 cmX 5 cm X 100 cm and was operated with a 1:1:6 CO2 :N2:He mixture at a pump energy density of 100 J liter- 1

atm- 1 . A confocal M = 2 positive-branch unstableresonator with one intracavity Brewster window wasemployed on the slave oscillator, the cavity length being

August 1979 / Vol. 4, No. 8 / OPTICS LETTERS 251

2.6 m. Pulses from the master oscillator were injectedvia a small hole in the concave resonator mirror, theactual power entering the resonator mode being esti-mated to be -300 W. The two lasers were synchronizedusing high-voitage trigger generators and delay units toan accuracy of -±25 nsec.

NaCl beam splitters were used to sample the outputbeam from the slave oscillator, and, on each shot, thetemporal history of the pulse was recorded using aphoton drag detector, output on the P(20) or other se-lected transition viewed using a high-speed Au-dopedGe detector located at the exit slit of an infrared mo-nochromator, and the emission wavelengths monitoredusing an Optical Engineering spectrum analyzer. Thedetector outputs were displayed on a Tektronix 7844 or7904 oscilloscope.

With this arrangement IML was investigated bytuning the master oscillator to a given transition andthen monitoring the slave oscillator output as the firingdelay between the two lasers was varied. By suitablechoice of the delay it was possible to optimize both thereliability and peak power (by injecting off thresholdfor high-gain transitions) of the output-pulse train.The transitions for which reproducible locking wasachieved are summarized in Table 1. A comparison ofthe results for the 10.4-gm band with the predictedlocking regime shown in Fig. 1, which, with (i = 2.6 XI 01 /cm3 and x23) = 2.5%o car', was chosen to model thepresent experiment, shows that goad agreement isachieved. Maximum output energy in the train was-20 4 for the P(20) transition, falling to -18 J for theweaker transitions, with corresponding peak powers inthe range 0.8-.0 GW. It should be noted that for

Table 1. Injection Mode-Locked C02-LaserTransitions

Injection Mode-LockedTransition Other Transitions

10-gm BandP(14)-P(22)P(12), P(24), P(26) Weak P(20) in tail of

pulseP(10), P(28) Weak P(20) in tail of

pulseR (18)R(12)-R(16), R(20) Weak P(20) in tail of

pulseR(22)a Weak P(20) in tail of

pulse

9-gm Band

P(16)-P(20) P(20) in tail of pulseP(14),a P(22)a P(20) in tail of pulseP(1 6 ),b P(1 8),b P(22) -

P(12),6 P(14) 6 P(20),6 P(24) 6 Weak 9-gm P or R linein tail

P(10),-' 5 P(26,Ib Weak 9-pm P or R linein tail

R(16)bR(12),R(14),b R(18),bR(22)6 Weak 9-gm P orB line

in tailR(10),a. b R(24)a,b Several transitions in tail

a Poor reliability-jitter limited.b With SF6 in cavity.

IR 116)J

I 0

P (20)I

P (40) I

t~~~~~~~~~~~~~~~~~~~~~~~~~~~~~2 0 ~~~~~~~~~~~~~~~~~~~~~~~~1

GrowthTime iI(,UIs)

is -

I 0

0 -51`

0I

T2

I

252 OPTICS LETTERS / Vol. 4, No. 8 / August 1979

i I (a) (b)

200 nsec

Fig. 2. (a) Nonspectrally resolved output waveform for in-jection on the Pio(26) transition (upper) and simultaneousoutput from monochromator set to the P 10 (20) transition(lower). (b) As in (a), but with P 10 (10) injected signal.

transitions in the wings of the IML range [e.g., Rl 0(22),P9(14), P9(22)], the shot-to-shot reliability was poorprincipally, it is thought, because of the narrow tem-poral injection window7 for these lines and limitationsimposed by the firing jitter of the two lasers.

For the transitions given in Table 1, clean modelocking was obtained in the gain-switched spike, but,with the exception of the strongest emission lines, theoutput was duovhromatic because of the growth of theP(20) transition in the pulse tail. This is illustrated inFig. 2(a), which shows the output waveform for injectionon the P(26), 10.4-gm transition together with theoutput on the P(20) transition as viewed simultaneouslyusing the monochromator. The late growth of theP(20) transition can be understood by noting that, asthe envelope of the gain-switched pulse train passesthrough a maximum, the gain on the injected transition,caj, is forced below threshold, whereas the P(20) gain,although reduced because of saturation, remains abovethreshold since a2O > acrj. This gain difference is fur-ther accentuated with short-duration injected pulsesbecause of incomplete rotational relaxation, i.e., a 2odoes not remain in equilibrium with aj at a commonrotational temperature. Hence the P(20) transition cancontinue to grow in the pulse tail and may capture orshare oscillation with the injected signal. Experi-mentally, a reduction in the P(20) component was ob-tained by reducing the N2 content of the slave oscillatorgas mixture, hence limiting gain replenishment in thetail of the pulse that is due to vibrational transfer fromN2 to C02.

It is interesting that, as a consequence of the couplingbetween the injected transition and the parasitic P(20)component, the latter exhibits a fairly high degree ofmodulation at the round-trip cavity frequency, as il-lustrated in Figs. 2(a) and 2(b). This forced lockingbehavior is thought to be due to the slightly higheramplification experienced by P(20) radiation compo-

nents within the cavity, which travel in synchronism.with the injected pulse under conditions when signifi-cant gain saturation occurs. In effect, traveling-wavegain depletion during the ten or so saturating passesmade by the injected signal provides sufficient dis-crimination to produce weak locking of the P(20)emission, which is growing (but not saturated) duringthis period.

To extend the IML range to more transitions in the9.4-Murm band, SF6 gas was allowed to flow in the intra-cavity airspace, resulting in suppression of the dominantP(20), 10.4-gm transition and a shift in the naturalemission frequency to the R(16) 10.4-gm line. Withthis net-gain reduction on the P, 10-Am band, IML wasobtained on 17 transitions in the 9.4-gm band; againclean locking of the spike accompanied by the growthof one other line in the tail of the pulse was observed.The results are summarized in Table 1. In this case theoutput energy on the various transitions was -16 J, andthe intracavity intensity was sufficiently high to causedamage to the metal unstable resonator mirrors.

It is finally noted that the technique described pro-vides a simple means of controlling the emission wave-length of high-power TE C02 lasers without recourseto damage-sensitive intracavity tuning elements. Withwavelength control, injection mode-locked CO2 laserswill undoubtably find applications in areas such as op-tical pumping and infrared-laser photochemistry.

The authors are indebted to B. Tait for his skillfultechnical assistance and thank S. A. Ramsden for hiscontinued support.

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