Beam quality of a high-power CO2 laser MOPA system

Optics & Laser Technology 30 (1998) 491±496

Beam quality of a high-power CO2 laser MOPA system W. Riede*, W. Mayerhofer DLR Stuttgart, Institut fuer Technische Physik, Pfa€enwaldring 38±40, 70569 Stuttgart, Germany Received 29 May 1998; received in revised form 6 November 1998; accepted 11 December 1998

Abstract In this paper, the e€ects of ampli®cation of di€raction-limited pulsed CO2 laser radiation over several meters of ampli®cation length on beam quality and pointing stability are documented. Millijoule pulses are ampli®ed up to 3 J. Generation and ampli®cation of the 10 mm wavelength pulses were performed in the discharge volume of an e-beam sustained CO2 laser. Beam quality is measured according to the ISO/DIS 11146 standard in terms of the beam quality factor M 2. Fluence distributions were recorded with a beam analysing system of 100 mm spatial resolution. M 2 parameter values ranged up to 1.55 for ampli®ed pulse energies of 3 J. The necessity of beam-quality restoring techniques is inferred for the multijoule pulse energy regime. # 1999 Elsevier Science Ltd. All rights reserved. Keywords: beam quality; MOPA system; M 2 parameter

1. Introduction Laser applications in which the laser light must propagate freely a very long distance become more and more important. In laser based communication links, satellite imaging and reconnaissance, the beam quality is an essential feature for ecient system performance. In addition, for all laser applications where it is important to focus the beam to a small spot diameter to achieve high intensity, the beam quality is the decisive ®gure of merit. The beam quality, as proposed in the ISO standard ISO/DIS 11146 [1], has to be measured in terms of M 2, which is a dimensionless quantity of the inverse beam quality with M 2=1 being a perfect Gaussian beam, and higher values indicating lower quality. Scaling of the focal intensity with M 2 can be analysed using [2] v " #2 u u 2 M lz …1† W…z† ˆ W0 t1 ‡ pW 20 where W(z ) is the radius of the beam under consider-

ation along the propagation axis z, W0 is the radius at the beam waist and l the wavelength. In case of free propagation after the waist, the upper relation clearly indicates that the average intensity across the beam dimension scales as 1/M 4 after propagation of a distance z>>(1/M 2) (pW 20 )/l, i.e., propagation to the far®eld. In case of a caustic where a lens of focal length f is placed a distance z=f apart from the waist, W( f ) becomes the radius of the beam at the lens, and the upper relation Eq. (1) can be rewritten as v " #2 u u M2 lf t …2† W… f † ˆ W0 1 ‡ pW 20 For tight focusing, i.e. W( f )>>W0, hence W0= (M 2 lf )/pW 2( f ). Consequently, the focal intensity scales as 1/M 4. For weak focusing, i.e., W( f )>W0 and W( f ) 3 W0, the square root in Eq. (2) can be expanded to give v " #2 u u M2 lf t W… f † ˆ W0 1 ‡ pW 20 2

* Corresponding author. Tel.: +49-711-6862-515; Fax: +49-7116862-715. E-mail address: [email protected] (W. Riede) 0030-3992/98/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 3 0 - 3 9 9 2 ( 9 8 ) 0 0 0 8 2 - 6

!2 3 1 M lf 5 ˆ W 0 41 ‡ 2 pW 20 2

…3†

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W. Riede, W. Mayerhofer / Optics & Laser Technology 30 (1998) 491±496

Fig. 1. Small-signal gain distribution in the discharge unit. The electrons are coupled to the gas discharge through the e-beam window on the left. The position of the master oscillator (MO) is indicated by the circle on the lower left.

Solving Eq. (3) for W0, a nonlinear equation results  2 1 M2 lf 3 2 ˆ 0: …4† W 0 ÿ W 0W ‡ 2 p

The real solution in Eq. (4) has a leading term which scales as M 4/3, therefore the intensity scales as 1/M 8/3 in case of weak focusing. Consequently, for free propagation of a distance

Fig. 2. Set-up used for beam quality measurements (view from the top).

W. Riede, W. Mayerhofer / Optics & Laser Technology 30 (1998) 491±496

493

Fig. 3. Comparison of the caustics of master oscillator (MO, solid line) and power ampli®er (PA, dashed line) with one or two round trips (PA, dotted line) in the discharge unit.

z>>(1/M 2) (pW 20 )/l after the beam waist or weak/tight focusing of laser beams, a low M 2 parameter is essential. This important fact may be illustrated by an example. A laser system with M 2=1 and an average power of 100 W has the same average intensity in the far-®eld as a 900 W average power laser with M 2=3. 2. Laser system Our laser system [3] is based on an e-beam sustained CO2 laser of rectangular cross-section (10  10 cm2) and 1.2 m ampli®cation length, operating at a wavelength of 10.6 mm. The laser pulse length can be varied from 2±10 ms by changing the discharge parameters, but is ®xed to 10 ms in these experiments. Repetition rates of up to 60 pps are possible. Fig. 1 shows the measured small-signal gain distribution at an energy loading of 112.5 J/(l bar) in the discharge unit. The ebeam window is situated on the left and the cathode on the right, having a separation of 10 cm. The height of the cathode is 10 cm as well. Details of the corresponding measurement can be found in [4]. The smallsignal gain distribution was found to be symmetrical with respect to a horizontal plane at vertical position [0 cm] with the lowest values of 1.9%/cm nearby the ebeam window and the highest values near the centre of the cathode of 2.7%/cm. The circle in the lower left area shows the position of the master oscillator (MO) which was also embedded into the discharge volume. The MO was placed in the low-gain area near the ebeam window for two reasons: ®rst, the high-gain area near the cathode was available for ecient ampli®cation of the MO radiation; second, shock waves which

will disturb the MO beam quality emanate mainly from the cathode. 3. M 2 parameter measurements The set-up for beam quality evaluation is depicted in Fig. 2. The stable MO cavity of a length of 2.64 m consists of an HR cavity mirror 1 (40 plano copper mirror) and an output coupler 6 (R=58%, curved mirror, r=30 m). The MO is forced to operate in the fundamental mode with a circular aperture of 14.5 mm diameter. For ampli®cation measurements (not shown in Fig. 2) the MO radiation is redirected back into the discharge volume to achieve an ampli®cation length of 2.4 or 4.8 m. In passing a focusing lens ( f=3 m), the radiation is directed onto a pyroelectric array 11 using four HR bending mirrors 8 and two ZnSe wedges 10. Two of the HR mirrors 8 on a movable bench are setting up an optical delay line 9. By using this delay line, the ¯uence distribution E(x,y,z ) can be monitored with the pyroelectric camera 11 at di€erent locations z before and after the beam waist. The pyroelectric camera (Spiricon Pyrocam I) consists of an array of 128128 pixels with 100 mm pixel spacing. To prevent electrical interference it is placed into an all-metal shielding box 12. The procedure of measurement and calculation of the M 2 parameter is given in the ISO standard 11146 [1]. In our case, restriction is made to noncircular beams, as the laser discharge in horizontal direction breaks the rotational symmetry of the laser modes. Consequently, separate expressions must be used for horizontal (x ) and vertical ( y ) directions. According

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Table 1 M 2 parameter values for di€erent numbers of round trips in the power ampli®er (PA) No. round trips in PA Energy loading J/(l bar) M2x M2y

0 112.5

1 112.5

2 61.7

2 112.5

1.05 1.1

1.15 1.11

1.38 1.35

1.5 1.55

to [1], the second moment sx (z ), sy (z ) has to be derived from the ¯uence distribution with … …x ÿ x †2 E…x,y,z†dxdy 2 … ; sx …z† ˆ E…x,y,z†dxdy … s2y …z†

…5† 2

 E…x,y,z†dxdy … y ÿ y† … ˆ E…x,y,z†dxdy

where x and y are the centre-of-mass coordinates … … xE…x,y,z†dxdy yE…x,y,z†dxdy ; y ˆ … x ˆ … E…x,y,z†dxdy E…x,y,z†dxdy

…6†

to obtain the radius Wx(z )=2sx (z ); Wy(z )=2sy (z ). Crucial for the calculation of beam widths was the precise background nulling of the thermal noise of the pyroelectric array. A hyperbolic ®t through the calculated beam radii at di€erent positions along the caustic gives the M 2 values in x and y direction.

loading also has a deleterious e€ect on beam quality. This is obvious when comparing column 3 and 4 in Table 1. An increase in loading from 61.7 J/(l bar) to 112.5 J/(l bar) is accompanied by a degradation in beam quality (M2x =1.38, M2y =1.35 4 M2x =1.5, M2y =1.55). Two possible causes for degradation of beam quality in our single shot experiments can be considered: shock waves and discharge inhomogeneity. Dischargeinduced shock waves, starting from the cathode surface, may interfere with the laser beam. HeNe de¯ection measurements have shown that the shock wave propagates at a speed of 500 m/s. The shock wave interferes with the ampli®ed laser beam (separation from cathode: 20 mm) 40 ms after the rising edge of the laser pulse, i.e., shock waves which emanate directly from the cathode do not disturb the laser beam. Plasma ®laments can be observed during the discharge growing towards the anode (c.f. Fig. 4) with velocities on the order of several 103 m/s [5]. The length and the frequency of the ®laments was found to increase with energy loading. Additionally, cylindrical shock waves may be triggered by these ®laments. Therefore, ®lamentation is thought to be the major cause of degradation of beam quality.

4. Results and discussion Fig. 3 shows the shape of the caustic for laser emission from the MO alone, ampli®cation in one round trip, and ampli®cation in two round trips through the discharge unit with 2.4 m and 4.8 m ampli®cation length, respectively. A separation of 3 m from the focusing lens de®nes the position z=0 cm in Fig. 3. For sake of clarity the results of the hyperbolic ®ts which yield the M 2 parameters are summarised in Table 1. Also stated in Table 1 is the number of round trips and energy loading in [J/(l bar)] applied to the discharge. The radiation from the MO (M2x =1.05, M2y =1.1) is almost di€raction limited, therefore serves well as a probe beam for beam quality measurements. The fact that M 2 rises from one round trip (M2x =1.15, M2y =1.11) to two round trips (M2x =1.5, M2y =1.55) in the ampli®er indicates the deleterious e€ect of the discharge on beam quality. An increase in the energy

Fig. 4. Picture of discharge channel showing ®laments moving from cathode (right) to anode (left). The ®laments terminate somewhere in the discharge gap (stable discharge).

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Fig. 5. Focal ¯uence distributions of radiation from the MO (left) and PA after two round trips (right).

Fig. 6. Probability distribution of horizontal far-®eld angle as an indication of pointing stability of the MO for di€erent energy loadings (61.7 J/(l bar), upper curve and 112.5 J/(l bar), lower curve).

The pulse energy ampli®cation factor was 21 for two round trips in the discharge at 112.5 J/(l bar). The shift of the position of the beam waist downstream from the z=0 cm position (c.f. Fig. 3) to z=+16 cm for MO radiation and z=+73 cm for one round trip is solely due to propagation e€ects after the concave output coupler. This was con®rmed by laser analysis software which yielded for bare cavity calculations waist positions of +21 cm and +73 cm, respectively, when adopting the experimental parameters. Focal ¯uence distributions of radiation from MO and ampli®er after two round trips are shown in Fig. 5. The ¯uence distribution emerging from the MO (Fig. 5, left) shows a high degree of roundness whereas the ampli®ed ¯uence distribution (Fig. 5, right) shows asymmetry. Pointing stability measurements of the MO for two di€erent energy loadings (61.7 J/(l bar) and 112.5 J/(l bar) were performed. We used the set-up shown in Fig. 2 with the delay line 9 positioned such that the pyroelectric array 11 was in the focal plane of lens 7. By recording the centroid positions of the ¯uence distributions from 200 shots, the probability distribution of the horizontal far-®eld angle was calculated. A distinct decrease in pointing stability was monitored when increasing the loading from 61.7 J/(l bar) (Fig. 6, upper curve) to 112.5 J/(l bar) (Fig. 6, lower curve). The solid line which shows a Gaussian ®t through the data points has a 1/e2 half width of 64 mrad at a loading of 61.7 J/(l bar), and 93 mrad at a loading of 112.5 J/(l bar). The absolute value is certainly dependent on the type of cavity used. In case of a cavity with plano

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output coupler [6] much lower pointing stability values of 20 mrad were measured. 5. Conclusion The e€ects of ampli®cation on the beam quality of pulsed CO2 laser radiation in a high-power discharge volume were investigated. Deterioration of M 2 values up to 1.55 from an originally di€raction limited laser beam was encountered at moderate energy loading of the discharge for ampli®ed pulse energies of 3 Joules. Discharge ®lamentation is the most probable cause of beam quality deterioration on ampli®cation. Therefore, beam quality restoring techniques have to be developed when CO2 laser pulse energies of several joules have to be provided with adequate beam quality.

References [1] ISO/DIS 11146. Test methods for laser beam parameters; beam widths, divergence angle and beam propagation factor. Berlin: Beuth-Verlag, 1995. [2] Sasnett MW. Propagation of multimode laser beamsÐthe M 2 factor. In: Hall DR, Jackson PE, editors. The physics and technology of laser resonators. Bristol: Adam Hilger, 1989. p. 132± 42. [3] Mayerhofer W, Zeyfang E, Design data of a repetitively pulsed 50 kW-multigas-laser and recent experimental results. Contribution to GCL/HPL '98, St. Petersburg, 1998. [4] Riede W, et al. Parametric investigation of the small-signal gain in a large aperture e-beam controlled CO2 laser. SPIE 1996;3092:215. [5] Mayerhofer W, et al. Pulsed e-beam stabilized supersonic CO laser. Oxford: GCL '84, 1984. [6] Riede W, et al. Investigation of beam quality and gain behaviour in a large aperture e-beam controlled CO2 laser. SPIE 1996;3092:182.