Appl. Phys. B 43, 105-111 (1987) Applied P.o.- physics Physics B and Laser Chemistry

�9 Springer-Verlag 1987

Comparative Performances of Stable- and Unstable-Resonator TEA C O 2 Lasers with cw Injection* E. Akmansoy and J. M. Lourtioz

Institut d'Electronique Fondamentale, U.A. du CNRS No. 22, Bat. 220, Universit6 Paris XI, F-91405 Orsay, France

P. Cassard

Laboratoire d'Optique Appliqu6e, Ecole Polytechnique-ENSTA, F-91120 Palaiseau, France

Received 27 October 1986/Accepted 14 January 1987

Abstract. The performances of stable- and unstable-resonator TEA CO2 lasers with cw injection are experimentally compared. Two types of measurements are reported. First, locking band-widths are measured for a wide range of cw injected powers. It is shown that 5-gs 1-J single longitudinal mode pulses can be obtained with unstable resonator lasers for injected powers as low as 200 nW. Second, heterodyne measurements of the intrapulse TEA laser frequency are presented. The use of unstable resonators is experimentally proven to be the most efficient way to achieve reproducible high-power chirpless single-mode pulses at 10 gm.

PACS: 42.55. Ek, 42.60.Da

CW injection locking of TEA C O 2 lasers is now recognized to be one of the most efficient technique to produce intense single longitudinal mode (SLM) pulses at 10 gm. To date, the most accurate analyses of locking performances have been reported in the case of stable resonators [1-33. However, stable resonators present small transverse-mode volume, implying limited pulse energy and strong intrapulse chirping effects [2]. In contrast, unstable resonator TEA CO2 lasers are potentially better candidates for high-power applications such as LIDAR detection or optical pumping in FIR/MIR molecular gases.

Previous studies of cw injection locking in unstable resonator TEA CO/ lasers have been essentially re- stricted to the case of short-duration pulses (less than 1 gs). Even in that case, SLM operation over the entire

* This work has been supported by Direction des Recherches et Etudes Techniques

pulse duration and shot-to-shot reproducibility often seemed to be of difficult achievement [4, 5]. The feasability of 5 gs long chirpless SLM pulses was only indicated in a recent experiment [6].

In this paper, the performances of stable- and unstable-resonator TEA CO2 lasers with cw injection are compared in details. First, the conditions required for SLM operation over 5 ~ts are carefully examined. Second, heterodyne measurements of the intrapulse laser frequency are presented. Performances of un- stable resonators with different magnifications are also investigated. We undoubtly prove that the use of unstable resonator TEA lasers is the only efficient way to obtain high-energy chirpless SLM pulses at 10 gm.

1. Experimental Set-Up

The experimental set-up is shown in Fig. 1. Basically, it is comprised of a TEA CO2 laser and two cw CO2 lasers.

106 E. Akmansoy et al.

PZT

B

'EA I 'As~ \ / = A

/ \

J.

�9

CW WAVE GUIDE CO2 LASER

~pZT

~2 ~ D2 = 02

" I] ,'--'--~, ,.~Pz'r CW LOW PRESSURE

CO2 LASER

Fig. 1. Experimental arrangement. Legends: 1) Beam splitters; 2) Matching optics; 3) CaFe2 attenuators; A, B, output coupler devices of the TEA laser resonator. D1 and O1 (D2 and 02) are acronyms for detectors and oscilloscopes, respectively

The TEA laser had an active volume of 300 cc which was defined by Chang profile electrodes [7] of length 60 cm, spaced 2.3 cm apart. 14 auxiliary spark gaps (7 on each side of the main discharge) were used for uv preionization. The TEA discharge module was terminated by two KC1 Brewster windows and was operated in sealed-offconditions. A gaseous mixture of He : N2: CO2 = 7 : 1 : 1 at 0.54 atm was currently used, which provided both long pulse duration (more than 5 gs) and high shot-to-shot reproducibility. The exci- tation energy was typically of 50 J/1.

The mechanical construction of the resonator was of Invar to minimize thermal drifts. The resonator length was currently 1.15 m, but could be varied up to ,-~3.6 m. The resonator consisted of two optics. A 150 grooves/ram plane grating was used at one end for line tunability and was mounted on a piezo-ceramic for fine tuning of the resonator length. Two types of output coupler were used at the other end, depending on the resonator configuration. For the stable configuration, the output coupler consisted of a 70 %-reflectivity 20-m radius ZnSe mirror and a 6-mm aperture diaphragm placed nearby to ensure single transverse mode oper- ation. For the unstable configuration, the coupling device consisted of a stainless-steel convex mirror mounted on a 10 mm thick Ge plate with antireflecting coatings on both faces. Three distinct convex mirrors were available to perform the experiments with optical magnifications of 1.5, 1.75, 1.9, and equivalent Fresnel numbers of 0.7, 0.68, 0.66, respectively. Changing the coupling device could be done in a quick operation. The injection-locked laser performances could thus be easily compared for different resonator configurations while the operating TEA discharge conditions were maintained.

As shown in Fig. 1, the low-pressure laser served as the injection laser while the waveguide laser was used as the local oscillator. The latter was tunable over +200 MHz, which allowed us to measure the evo-

lution of the TEA laser frequency over different time scales. The long-term stability of the cw lasers was measured to be + 0.5 MHz in free-running conditions. Injection in the TEA laser cavity was achieved by using the zero-order diffraction of the TEA laser grating. About 10-3 of the incident cw power was injected into the resonator. Optical isolation between the two lasers (cw and pulsed) was accomplished by means of CaF 2 attenuators. The polarization of the two laser fields was ensured to be parallel. In most of the experiments, the injection beam was focused at the TEA laser output mirror with a ~2.5 mm spot size, which closely approached the mode-matching condition for the stable resonator configuration.

The detection set-up was comprised of two SAT 400-MHz HgCdTe detectors and two fast 7834 Tek- tronix oscilloscopes. The TEA laser output was di- vided into two beams. One fell on detector D1 and was mixed with the local oscillator beam. Beat signals were recorded on oscilloscope O 1. The other beam fell on detector D2, which allowed us to simultaneously record the TEA laser pulse shape on oscilloscope 02. The pulse energy was separately measured with a calibrated Gentec joulemeter.

2. Results

Experiments have been carried out on the 10P20 line. Two types of measurements were performed. First, the injection locking band-width was measured versus the cw injected power. Second, the intrapulse chirping effects were analyzed for different operating con- ditions. The results for stable and unstable resonator were systematically compared.

2.1. Locking Band Width Measurements

For pulsed lasers with low dynamic gain like TEA CO2 lasers, cw injection-locking is equivalent to single longitudinal mode operation 1. In our experiments, SLM operation was said to be completed when no multimode beatings were seen in the TEA laser pulse trace for the entire pulse duration. Under this con- dition, the ratio of the oscilloscope trace thickness to the pulse amplitude at maximum was measured to be

0.02, which corresponds to a rejection ratio for two modes of ,-~ 104. Figure 2 gives an example of 5.5-~ts 1.2-J SLM pulse obtained for the unstable resonator laser with M = 1.5 geometrical magnification. Evalu- ation of the rejection ratio as defined before was made from 500 ns time base recordings.

1 Different behaviours may occur in lasers with high dynamic gains. In such cases, two-mode locked pulses are predicted over a certain range of cw injection frequencies and intensities I-8]

Comparative Performances of Stable- and Unstable-Resonator 107

Fig. 2. Typical SLM laser pulse signal from the HgCdTe detector. The output energy is 1.2 J. 92 % of pulse energy is emitted during the first 5 ps

Locking band-widths were measured as follows. The TEA resonator length was varied while the injection laser tuning was fixed. Then, SLM operation over the entire pulse duration was controlled on oscilloscope O2 and the TEA laser frequency was measured over the first 500 ns of the pulse on oscillo- scope O 1. It has been previously demonstrated that the injection-locked laser frequency measured at pulse onset is always close to the passive resonator frequency [-9]. The experimental procedure is thus equivalent to that described in [-3] where the injection laser was tuned instead of the TEA laser. The cw power P incident on the TEA laser output mirror was measured with a calibrated Moll thermopile. It was varied by means of several calibrated CaF2 attenuators having

different thicknesses. The cw injection intensity which is the physical parameter of interest may be defined as P/(V/L) where L is the TEA resonator length and V the transverse mode volume. The definition assumes that a single transverse mode component of the laser field is injected. Actually, S*= V/L is the intensity-averaged cross-section of the laser beam. For unstable re- sonator, Vwas calculated according to the geometrical approximation.

Results of our measurements are reported in Fig. 3. The variations of the locking band-width with the injection intensity are shown in Fig. 3 for both types of resonators. The TEA discharge conditions are those given in Sect. 2. In Fig. 3b, the resonator magnifi- cations are M = 1.5 and M = 1.9, respectively. Measure- ment uncertainty (+_1.5 MHz) includes frequency reading errors and long-term stability of the cw lasers.

Experimental results plotted in Fig. 3 are seen to be similar for both types of resonators. SLM operation is achieved with injection intensities as low as

2.10-7 W / c m 2, Besides, locking bands spread over a few tens of MHz for injection intensities in the mW/cm 2 range. The major difference concerns the energy of the SLM pulse. This latter was measured to be ~ 60 mJ for the stable resonator instead of 0.7-1.2 J for the unstable resonator, depending on M. A closer comparison between results of Fig. 3 reveals that the locking band-width relative to the M = 1.5 unstable resonator is smaller. On the theoretical viewpoint, it has been demonstrated that locking band-widths of low gain pulsed lasers mostly depend on four para- meters [-7, 83: 1) injection intensity, 2) gain rise time, 3)

16 3

l d 4

l~

z m-6I

I,-

~_Z 10- 7

~6 8 lb 2~0

{a}

3~0 i

10-3

10-4~

10-5

1(5 6

lo-Z

- - M = 1 . 9

1(~8~'~'-- M = 1.5 t 10

§

2~0

�9 M=1.5 �9 M = 1 . 9

[b}

3=0

Fig. 3a, b. Injection locking band- width versus cw injection intensity. (a) and (b) correspond to stable and unstable resonators, respectively. Injection intensity is scaled on vertical axes for comparison of the respective minima. Arrows point to the theoretical estimations of I~i N (see text). In (b) horizontal and vertical bars give measurement uncertainties

LOCKING BANDWIDTH ( M H Z )

108 E. Akmansoy et al.

electron-density dynamics, which results in a refractive index modulation, 4) time delay between laser thres- hold and peak of modulation. Since the TEA laser was presently operated under the same discharge con- ditions, only the fourth parameter was varied when the resonator configurations were alternated. Changes in time delay are thus likely to explain differences in the locking band-width performances. However, other effects related to diffraction may be of importance for unstable resonators.

Effects originating from cavity misalignment and optical mismatch of the injection beam were inves- tigated in complementary experiments. When one of the unstable resonator mirrors was sligthly tilted, locking performances were dramatically altered. For tilt angles larger than 50 grads, SLM operation over the entire pulse duration could not be observed with the M = 1.5 magnification resonator. Figure 4 displays a typical laser pulse from a photon-drag detector when the laser is misaligned. Though the first part of the laser trace is smooth, the presence of low frequency beatings suggests that the laser is locked on two transverse modes. After ,-~ 500 ns, a complex multimode behavior appears. For resonators with larger magnifications, similar results were obtained but at larger tilt angles. These results are in agreement with those reported by W. F. Krupke and W. R. Sooy who experimentally demonstrated that operation of unstable resonator cw CO2 lasers on the lowest-loss transverse mode was very sensitive to resonator misalignments 1-10]. In addition, for TE lasers, parasitic reflections off the discharge electrodes cannot be disregarded. Observ- ations of the far-field pattern in the course of our experiments support this remark.

The injection beam may be characterized by four parameters: 1) field polarization, 2) waist diameter, 3) relative position of the waist, 4) tilt angle off the TEA laser resonator axis. Among these parameters, the last one was found to be the less sensitive. The injection beam could be tilted with a ,,~ 2 mrds angle without any measurable degradation of the locking perfor- mances. In contrast, any polarization mismatch be- tween injection and the TEA laser resonator increased the minimum intensity for locking. This result is in some disagreement with previous results found in literature [11]. The waist-diameter and location were also involved in the locking performances. Different matching optics (Fig. 1) were used to vary these parameters. For example, the minimum injection intensity was ~ 10 times higher when the waist diame- ter was varied from 2.5 to 4 mm.

Correspondingly, the locking band-width was nar- rowed by a factor of 30% for an injected power of 400 gW. In contrast, no significant improvement was obtained when the waist diameter was decreased below

Fig. 4. Typical laser pulse signal from a ~ 1 ns risetime photon- drag in the case of the M--- 1.5 unstable resonator with a slight misalignment. The injection intensity is 1 mW/cm z

Fig. 5a, b. Beat signal between local oscillator and TEA laser. Photograph (a) stable resonator (60 mJ). Photograph (b) M = 1.9 unstable resonator (0.7 J)

2.5 mm. Finally, the best performances were attained when the beam waist was located near the convex mirror.

2.2. Intrapulse Frequency Measurements

Figure 5 displays two examples of heterodyned SLM laser pulse. Unlike experiments reported in Sect. 2.1, the local oscillator frequency was adjusted to provide low-frequency beat signals. Thus, frequency measure- ments over time scales in excess of 5 gs could be easily performed.

Comparative Performances of Stable- and Unstable-Resonator 109

3 0 �84

25 �84 - r

v 20 >- U Z

0 15i

u_

�9

lO

o A

5- �9

0 0 A �9 �9

o ~d, 9 ~ A " , t 2 a i s

TIME ( Ns )

Fig. 6a, b. Temporal evolution of the instantaneous TEA laser frequency. Curve (a) stable resonator (60 rnJ). Curve (b) M = 1.5 unstable resonator (1 J). The vertical axis origin is arbitrary

Figure 6 reports typical time dependences of the instantaneous beat-frequency for the stable resonator (curve a) and the unstable resonator (curve b), respec- tively. The unstable resonator magnification was M=1.5. Here again, the discharge conditions were those of Sect. 1. As shown in Fig. 6, the TEA laser frequency first decreases, then increases later in the pulse tail. This behavior is in general agreement with previous studies [1, 2]. However, a linear increase is clearly seen in Fig. 6 for times late in the pulse tail, which has not been reported yet.

The comparison between curves (a) and (b) in Fig. 6 shows that the chirp amplitude is twice smaller in the unstable resonator case, whereas the output energy is 16 times larger. This result clearly emphasizes the benefits of using pulsed lasers with large transverse- mode volume. Chirping was found to be independent of the injection-detuning and intensity. In contrast, the small downchirp amplitude observed during the first

700 ns was dependent on the injection parameters, which is in agreement with previous measurements [9, 12]. Actually, when the injection parameters are varied, the SLM laser pulse is delayed (or advanced) [1, 13], thereby changing the overlap between the discharge current and optical pulses.

Frequency measurements were also performed for various discharge conditions. As the major result, the chirp amplitude was found to increase linearly with pulse energy and that for both resonator cases. For example, the chirp evolution did not significantly change with the total pressure of the gas mixture, provided that the supply voltage of the TEA discharge was simultaneously adjusted to give a constant TEA

laser output energy. Though the marked dependence of chirp amplitude with output energy has been already pointed out by Willetts and Harris [2], the weak influence of gas pressure merits to be noted.

Other experiments were carried out to compare the chirp evolutions in unstable resonator lasers with three different magnifications (M = 1.5, 1.75, 1.9). When the resonator magnification M was increased, the trans- verse mode volume and pulse energy were simulta- neously decreased. The chirp evolution was found to be almost independent on M.

Finally, the influence of the cavity filling factor f was investigated in one experiment. The discharge conditions were kept constant while the convex mirror was set at different positions from the TEA module. The chirp amplitude was measured to scale as ~ (f)15. The departure from the expected linear law can be readily attributed to simultaneous variations of the output energy and laser-beam cross section. The best performances were presently obtained for a 3.6-m long resonator with 2.1 optical magnification and an equivalent Fresnel number of 0.42. A total chirp of 3.5 MHz was measured for a 0.7-J 6-gs long SLM pulse, which is quite close to performances recently reported by Lawrence et al. [6].

3. Discussion

3.1. M i n i m u m In jec t ion In tens i t y

Following the analysis reported in [3], the minimum cw intensity required for locking is predicted to be

IM~ N = F . (goc/V) �9 hv o - L, (1)

where F is the intensity ratio between the injection and noise-driven fields, go the laser gain at threshold, V the transverse mode volume, Vo the laser frequency and, L the cavity length. Two main approximations are used to derive (1) [3]: i) a single transverse mode is considered, ii) the lower laser level population is negligible at threshold.

IMI N was calculated for the three cases of resonators reported in Fig. 3. According to Sect. 2.1, F was estimated to be 104 in our experiments< The mode volume was calculated to be 33 cc for the stable resonator, 180cc and 125 cc for the unstable res- onators with M = 1.5 and M = 1.9, respectively. The threshold gain was identified to - 1 / ( 2 L ) . l n ( R T ) ,

where R is the output coupler reflectivity and T, the

2 In this estimation, we implicitly assume that the injection driven mode competes with a single mode originating from spontaneous noise on line center. Separate calculations of the TEA CO2 laser mode spectrum showed that typically half of the laser power is emitted in that mode at gain switching [8]. Therefore, F may be presently underestimated by a factor of 2

110 E. Akmansoy et al.

transmission per cavity round trip including diffrac- tion losses. For the stable resonator, R and T were 0.7 and 0.5, respectively. For the unstable resonators, R and T were 1 and 1 / M 2, respectively.

The calculated values of IMIN are pointed by arrows in Fig. 3. For the stable resonator case (Fig. 3a), the experimental value oflu~N iS just ,,~ 5 dB larger than the theoretical one. The small discrepancy may be easily attributed to imperfect mode matching and underes- timation of F in (1). It is important to note that the present result is almost identical to that previously reported for a stable resonator with a quite different geometry [3]. For the unstable resonator cases (Fig. 3b), the minimum injection intensity is measured to scale from 100 to 200 nW/cm z. To our knowledge, these are the smallest values ever reported for any resonator configuration (stable or unstable) [3, 5, 13]. However, the discrepancy between the experimental and theoretical values of IMXN is slightly larger than in the stable-resonator case. Actually, diffraction plays a determinant role in unstable resonators [14, 15]. Though ideal mode matching cannot be realistically attained [16], the present result shows that efficient experimental conditions can be reprodueibly achieved even when different unstable resonators are used.

3.2. Spectral Per formances

Several effects may contribute to intrapulse frequency variations in injection-locked TEA CO2 lasers. Fre- quency pulling effects due to anomalous dispersion have been shown to induce either chirp or downchirp at gain switching when the laser is injected far off line center [17]. When the laser is injection locked near line center, this effect is quite negligible.

The downchirp observed at the beginning of TEA laser pulses is usually related to refractive index modulation induced by the discharge electron density. Several studies already support this hypothesis [9, 12, 18]. For standard operating conditions like those of Fig. 6, the downchirp was typically less than 1 MHz. For gas pressures higher than 0.7 arm, downchirp was no more detected. Since a fast decrease of the current discharge was simultaneously measured, this obser- vation may be attributed to an efficient damping of the discharge electron density.

Finally, the refractive index perturbation originat- ing from the hydrodynamic expansion of the laser medium is recognized to be the main cause of chirp in laser pulses within the 1 to 50 gs duration range. This effect is usually called Laser Induced Medium Pertur- bation (LIMP). LIMP phenomena studies were first directed at thermal defocusing and output beam quality degradation in Nd-doped glass lasers with intracavity absorbing media [19] or in e-beam con- trolled multimode CO2 lasers [20, 21]. Direct studies

of LIMP-induced chirp were mostly reported by Willetts and Harris, and were directed at hybrid or injection-locked TEA CO2 lasers [2, 22-24]. As a major result of the latter studies, a scaling-law of the chirp amplitude, fly(t), was established according to a simplified model of laser gas hydrodynamics

fir(t) = c~. v o �9 E/ (LS*2) �9 t" (2)

where e is a global coefficient including the Gladstone- Dale constant and other molecular constants, Vo is the laser frequency, E the pulse energy, S* the average beam cross section, L the resonator length, and n an exponent which is either 2 for short pulses or 3 for long pulses.

Most of the experimental results reported in Sect. 2.2 are in qualitative agreement with predictions of (2). Proportionality of 6v to pulse energy E and the dominant influence of S* were experimentally verified. However, some discrepancies related to the time evolution and S* dependence have to be noted.

First, a detailed comparison between the chirp amplitudes obtained from various resonators revealed that 6v experimentally scaled as ~(1/S*) 1"6. In ad- dition, a separate comparison of our chirp perfor- mances to those reported by Lawrence et al. [6] approximately gave the same experimental law. The departure from the (1/S*) 2 law predicted by (2) might be attributed to an oversimplified estimation of the unstable resonator mode volume, and thus of S*, after the geometrical approximation. On the other side, (2) was established for a Gaussian-shaped laser beam. Actually, diffraction effects cannot be ignored and should be included into the hydrodynamic treatment for a quantitative analysis of chirp in unstable res- onator lasers.

Second, the experimental evolution of by could be well fitted to theory with exponent n between 2 and 3, but for times within the first 2.5 gs of the laser pulse. In contrast, the linear increase of 6v late in the pulse tail is not explained. This linear increase was repeatedly obtained with any type of resonator and for various discharges conditions. This clearly indicates that the temporal profile of chirp is not only related to the total energy of the pulse, but also to the energy deposition rate into the laser gas. Therefore, different laser pulse shapes should lead to different temporal profiles of chirp. This remark is likely to explain differences between our experimental results and those reported for rectangular-shaped pulses in [23]. In (2), t 2 or t 3 laws have been established assuming an instantaneous conversion of vibrational energy of the lower vibra- tional CO2 modes into translational energy. A correct analysis of gas heating should also account for the finite V - - T / R relaxation rates involved in laser kinetics.

Comparative Performances of Stable- and Unstable-Resonator 111

4. Conclusion

A detailed analysis of cw injection-locking in unstable- resonator TEA CO2 lasers has been presented. It has been demonstrated that 1-J single-mode pulses in excess of 5 gs can be reproducibly obtained with remarkably low injected powers. Locking perfor- mances, i.e. locking band-widths and minimum injec- tion intensities, are quite similar to those of lasers with stable resonators. The much more pronounced in- fluence of resonator misalignments is the only disad- vantage when small magnification factors are used.

In contrast, the simultaneous achievement of high output energy and weak intrapulse chirp is the key advantage of unstable resonators. It has been shown that the resonator parameters could be adjusted to provide chirp amplitudes as low as possible. Chirpless SLM pulses at 10 ~tm appear to be readily obtainable at any energy level, with only one obvious restriction by limited capabilities of power supply. Because there is no intracavity element and thus no risk of optical damages, the cw injection-locking technique is now definitely proven to be superior to that based on hybrid TEA laser configuration [25].

Acknowledgements. The authors gratefully acknowledge the expert technical assistance of D. Bouchon and J. P. Pagrs in the construction and operation of lasers.

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