Toric unstable CO(2) laser resonator: an experimental study

Toric unstable CO2 laser resonator: an experimental study E. F. Yelden,

H. J. J. Seguin,

C. E. Capjack,

S. K. Nikumb,

and H. Reshef

The output characteristics of a toric unstable resonator fitted to a multichannel stripline excitation system are presented. The resonator is shown to possess the usual advantages of a conventional unstable resonator plus the ability to modify the profile of the output beam by a simple change in the coupling aperture. Laser output parameters have been studied as a function of coupling fraction, magnification, and internal loss factors. Variations in the focal spot size as a function of the coupling aperture as well as resonator alignment sensitivity and polarization properties have been investigated. Key words: Unstable resonators, C02 lasers.

Introduction

Recent international materials processing activity has generated an increasing demand for compact, efficient, and reliable high-power CO, lasers. To meet these requirements several investigators have proposed a number of unique laser structures. A particularly successful version of these new designs appears to be the diffusion-cooled extended-area electrode concept.'" While the primary focus of most studies has been on excitation geometries, comparatively little effort has been expended on improved optical extraction schemes for these novel structures. Recent efforts to scale the large-area discharge concept into planar or radial arrays4'5 have generated a need for such studies. This paper is presented in an effort to help address this issue. Unstable Resonators

Because of their unique modal characteristics unstable resonators have long been a topic of special emphasis with regard to high-powered lasers. First reported by Siegman nearly a quarter of a century ago,6 numerous theoretical and experimental studies of this special class of optical cavity have periodically appeared in the scientific literature."' As a result salient features and the advantages offered by unstable resonators have gradually become better understood. These include" large-mode volumes, good trans-

The authors are with the Department of Electrical Engineering, University of Alberta, Edmonton T6G 2G7, Canada. Received 22 February

1991.

0003-6935/92/121965-10$05.00/0. o 1992 Optical Society of America.

verse-mode discrimination, controllable diffractive output coupling, efficient power extraction, and highquality far-field beam profiles. The ability to utilize a single-ended system with all-metallic water-cooled mirrors has also been an important feature that prompts the incorporation of unstable resonators in high-powered devices.

Design procedures for the fabrication of an unstable resonator system have been widely documented for specific cases. These include collimating confocal resonators", 4 in which the resonator mirrors have a coincident focus, symmetric double-ended resonators, as well as asymmetric single-ended systems.'3 In some cases the analysis has been quite elementary by requiring only a knowledge of the resonator length and mirror curvatures. Conversely, elaborate investigations such as Chernin's confocal study'4 require detailed knowledge of the gain and loss mechanisms within the active media. A resonator is defined to be either stable or unstable by an analysis of its g parameters, which are defined as" gi = 1 -LRi,

(1)

where L is the mirror separation and Ri is the mirror radii of curvature. If the condition that 0

< gg 2 < 1

(2)

is satisfied, the resonator is classified as stable. A value of gig, outside this range corresponds to an unstable optical resonator in which optical energy from the resonator is extracted primarily by diffraction over the edge of a smaller secondary mirror. The 20 April 1992 / Vol. 31, No. 12 / APPLIED OPTICS

1965

output from such a resonator is characteristically annular in shape with a typical full beam diameter of the order of several centimeters.' 5 In most applications this beam is coupled out of the laser vessel through a relatively large and concomitantly expensive ZnSe window. If desired, the beam may first be compacted with an additional optical element, such as an axicon, before exiting the laser structure. As an alternative to the conventional unstable resonator design that is described above, Reilly6 and more recently Townsend and Reilly7 have proposed a toric or unobscured unstable resonator geometry. A modified version of this design is the subject of the investigation that is presented here. A toric unstable resonator possesses the basic advantages of a conventional unstable optical cavity but in addition provides the desirable feature of output beam extraction from the secondary mirror, which is near the laser's center line. As a consequence of this fact the toric optical system lends itself to the symmetry of a radial multichannel laser excitation geometry. Such a structure is being investigated here in an effort to scale the extended-area diffusion-cooleddischarge concept into the multikilowatt regime.' The present work documents the general properties and experimental findings that have been thus far obtained with a toric unstable laser resonator fitted to a multichannel stripline excitation system. Device Description

The discharge apparatus in question has been described previously.4 It is shown in Fig. 1 only for reference. The structure consists of eight triangularshaped, metal electrodes that are mounted in a circular geometry. Half of the electrodes are fitted into opposing end plates, which are then mounted together in an interdigital manner. In this way eight individual narrow-gap regions are formed between the electrodes. Each side of the system is electrically isolated from the other, thereby forming a multielement stripline structure. On application of rf power to the device, independent discharge volumes are excited between each pair of electrodes. Each electrode is 50 cm in length, 4 cm in height, and separated

from adjacent elements by 5 mm. Electrodes are fabricated from nickel-coated aluminum. Electrode elements also contain water channels to enhance diffusion cooling for the individual gain regions. The entire assembly is placed inside an aluminum vacuum chamber, which also serves as the return line and shield for rf radiation. Excitation is supplied by a multikilowatt rf generator that operates at 40.68 MHz. A tunable I network is used to match the 50-H generator output to the discharge impedance. Matching is typically better than 2%. A set of resonating inductors was also placed across the electrodes to minimize the voltage variations along the device, which are caused by the additional shunting capacitance of the metallic vacuum enclosure. 8 As indicated previously the optical system that is employed is an unstable toric resonator, which is shown schematically in Fig. 2. It should be emphasized that the toric resonator that is used here was initially designed as if it were a conventional unstable resonator. The distinguishing aspect of the system only occurred during the actual physical fabrication of the mirrors. At this particular stage the center of the radius of curvature of a conventional unstable resonator was taken to be at the outer edge of the toric mirror. Thus the optical axis is actually a cylinder of radius a = 5.8 cm for the particular mirrors that are used here. The mirror surface extends slightly beyond the electrode, and hence the discharge cavity is extended by 5 mm. This feature permits optical feedback experiments to be performed with this device. However, the region beyond the discharge cavity is not made into a flat surface, or a region of stability, as suggested by Townsend and Reilly. 7 Therefore some energy may be lost from the resonator by diffraction past the optic cylinder. The resonator so formed consists of two spherical mirrors, M, and M,, that are separated by a distance of 61 cm. Unless otherwise noted, the radius of curvature R, of mirror Ml is kept constant at 25.0698 m. One interesting feature of the toric design is that the optical radiation walks from the outer edge of the mirrors radially toward the middle, thereby produc-

\ \ 7

1

2

5

4

\

\ 3

I/ 6

0

2 1

4

I I I I. I CM

Fig. 1. Multichannel slot discharge structure: 1, electrode mounting end plate; 2, optical extraction slot; 3, water-cooledtriangular-shaped electrode; 4, interelectrode discharge volume; 5, vacuum enclosure; 6, concave mirror; 7, convex mirror. 1966

APPLIED OPTICS / Vol. 31, No. 12 / 20 April 1992

4

3

(a)

2 1 Fig. 2. Cross-sectional view of the toric unstable resonator: 1, concave mirrorM 1 ; 2, convex mirror, M2; 3, ZnSe output window; 4, discharge volume.

ing an output beam that emerges from the center of convex mirror M,. For this reason the concave mirror completely covered the discharge gain cross section, whereas the convex mirror had a central aperture to allow for extraction of the optical radiation. It was found that the choice of this aperture had a profound influence on the characteristics of the output beam. Finally the output beam was coupled out of the laser chamber through an antireflection-coated ZnSe win-

(b) (a) Near-field beam pattern for the 3.18-cm aperture.

dow.

Fig. 3.

Mirrors were fabricated from an extruded AlCuTi alloy and diamond machined on a microsurface lathe. To save time and minimize cost these aluminum mirrors were left uncoated. As such they exhibited an optical absorption of 2%. Consequently the units were water cooled to minimize thermally induced surface figure distortion and misalignment. In all 53 mirrors were used to perform the experiments that are described here. One set, with gold surface coatings, was used to investigate the effects of reduced optical absorption on the output parameters. A static gas mixture that consisted of 1:1:3 = CO,:N,:He at 15 Torr, which was combined with 2 kW of rf excitation, was used throughout the tests. No attempt was made to optimize either the gas mixture, the gas pressure, or the rf input power.

Near-field beam pattern for the 1.27-cm aperture. The magnifica-

Resonator Output Characteristics

One of the most interesting aspects of this resonator is how the character of the output beam may be varied by a change in the output aperture of the convex mirror M2. Figure 3 shows a typical near-field output pattern obtained under identical conditions, except for two different aperture sizes. Both patterns are for a convex mirror radius R

= -16.1550

m,

which corresponds to a geometrical magnification of M = 1.25. Figure 3(a) is for a 3.18-cm aperture, whereas Fig. 3(b) is for a 1.27-cm aperture. Both of

these near-field patterns were observed 40 cm from the ZnSe output window by imaging the output beam with a ceramic board. The transition from the individ-

(b)

tion is 1.25 in both cases.

ual beams that are present in Fig. 3(a) to a single beam in Fig. 3(b) is immediately evident. The eight beamlets, one from each of the interelectrode regions, have overlapped completely to produce a single output beam. Figure 4 shows the corresponding near-field intensity profile that is obtained with each of the apertures discussed above. These profiles were derived by using a computer-based image analysis device, which was developed recently.5" 9 With this approach the output beam is imaged onto a thermally sensitive screen that fluoresces when it is illuminated with UV light. When heated by a laser beam the fluorescence of that portion of the screen is quenched in direct proportion to the intensity of heating. In this manner an image of the beam's intensity profile is formed on the screen. This image is then recorded with a standard color video camera, digitized by a Live 2000 frame grabber, and finally analyzed by an Amiga 2000 computer. As is clear from Fig. 4(a) each of the individual beamlets that are obtained from the larger 3.18-cm aperture has a similar structure and amplitude. This fact is documented further in Fig. 5(a), which is a cross-sectional view through the xz plane of the intensity profile given in Fig. 4(a). In contrast Figs. 20 April 1992 / Vol. 31, No. 12 / APPLIED OPTICS

1967

a)

7

7-,

.cI, a)

do

-J-J

7

(b) Fig. 4. (a) Near-field intensity profile for the 3.18-cm aperture. (b) Near-field intensity profile for the 1.27-cmaperture. The magnification is 1.25 in both cases.

4(b) and 5(b) are the corresponding near-field intensity profiles obtained with the 1.27-cm aperture. It is evident that the profile of the beam from the 1.27-cm aperture has coalesced to fill in the available aperture area completely. This resulting single beam is approximately twice as broad but occupies a smaller area than the corresponding multiple beamlets from the 3.18-cm aperture do.

In an effort to characterize the output parameters in more detail, the 1le' focal spot sizes, obtained from a 25-cm focal length lens, for various aperture sizes 1968

APPLIED OPTICS / Vol. 31, No. 12 / 20 April 1992

were measured. Data were collected at a constant magnification of M = 1.25. A BeamScan Model LBA 1/A laser beam analyzer was employed to facilitate the analysis. Results of this investigation are presented in Figs. 6 and 7. Figure 6 shows a typical far-field beam pattern obtained with a 3.18-cm aperture. This picture was obtained by placing a Perspex rod at the focal point of a 25-cm ZnSe lens and then by permitting the beam to penetrate the material for a brief period. As may be seen the focused beam is clean and exhibits a strong central peak with little or no

1.1 1.0

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

0.0

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-1.2

-0.8

-0.4

0.0

0.4

0.8

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1.6

Distance from beam center (cm)

(a) 1.1

Fig. 6. Typical far-field beam pattern for an M = 1.25 resonator. 1.0

0.9

tures between 2.92 and 3.56 cm [all points to the right of line (b)], features the condition of eight distinct output beams. This portion is characterized by a considerably flatter slope. It should also be noted that in the two extreme conditions the focal spot size varies inversely with the aperture, as is expected from standard diffraction theory.20 To the left of line (a) the

0.8 0.7 cts

0.6

.6

A

0.5

:c)1 Z, V

0.4 0.3 0.2

2.0

-

1.9

_

1.8

_

I

I

I

I

0 *

(a)

1.7 0.1

0.0 L -0.8

1.6 -0.6

-0.4

-0.2

0.0

0.2

0.4

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Distance from beam center (cm) (b)

1.5

single

E

1.4

beam

I

I

P

1.3

region

* I

i

Fig. 5. (a) Cross-sectional intensity profile for the 3.18-cm aperture. (b) Cross-sectional intensity profile for the 1.27-cm aperture. The magnification is 1.25 in both cases.

(b)

1.2

I

1.1

I

|

*

individual beamlet

region

* 0

0

1.0 I

0.9 I.I

energy contained in the sidelobes, which is usually referred to as TEMOO in nature. Figure 7 illustrates the dependence of the focal spot size on the coupling aperture size. It is interesting to note that there appears to be three different regimes of operation as the aperture is increased. The first regime is for apertures that are between 0.95 and 1.78 cm [points to the left of line (a)]. They are characterized by a steep slope. This is the regime in which the output emerges as a single beam. The second part of the graph, for aperture sizes of 2.162.54 cm [between lines (a) and (b)], is characterized by a transition region where the inner portions of the beamlets overlap but their outer edges are still distinctly separate. Finally, the third regime, for aper-

0.8 0.7

A

0.6 0 .0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

I

aperture size (cm)

Fig. 7. The 1/e' focal spot size versus the aperture size in the convex mirror M2 for a constant magnification of 1.25. A 25-cm focal length ZnSe lens was used during the tests. Line (a) is the largest aperture to produce a single output beam, and line (b) is the smallest aperture to produce eight individual beams. The two apertures shown between lines (a) and (b) neither fill the aperture entirely nor have completely distinct beamlets. The triangles correspond to the calculated theoretical diffraction-limited spot size for the representative single beam and individual beamlet cases. 20 April 1992 / Vol. 31, No. 12 / APPLIED OPTICS

1969

140

steep slope is indicative of the limiting size of the aperture. To the right of line (b) the essentially flat slope indicates a constant effective aperture where

120 _

the beams do not interact at all. Furthermore the focal spot size of one single channel was found to be similar to that of all eight channels acting simultaneously, irrespective of the aperture size. Had the individual beamlets been coherently phase-locked together, a much sharper peak in the intensity profile or a correspondingly smaller focal spot size, which is in direct proportion to N', where N is the number of individual sources in the array, should have been exhibited." The triangles in Fig. 7 correspond to the calculated theoretical diffraction-limited spot size for the representative single beam and individual beamlet cases.'0 It is encouraging to see from Fig. 7 that even in the absence of phase locking the beamlets combine to give a near-diffraction-limited focused spot size. Output Power Considerations

A series of experiments has been performed to determine the effect of the convex mirror aperture on the output power achievable from the device. The magnification of the resonator was also varied to determine its influence on system behavior. Figures 8-10 show the results of this study for three representative magnifications over a broad range of aperture sizes. These apertures correspond to coupling fractions 8* ranging from 9% for the smallest aperture to 34% for the largest. This range spans the regime in which near ideal geometrical output coupling should be experienced. In this context and because of the geometry of the discharge structure, the resonator may be treated as a superposition of eight individual strip resonators. As such the condition corresponds to an ideal geometrical output coupling factor of 8 = 1 1IM.'I3 It should be emphasized that the above

i

.

100 _

80

(b)

_

(a) S.

60 _

40

20 L 0.15

2.0

2.5

I 3.5

I 3.0

4.0

aperture size (cm)

Fig. 9. Laser output power versus the aperture size for a magnification of M = 1.25. Curve (a) is for uncoated aluminum alloy mirrors; curve (b) is for gold-coated mirrors.

values of 8 * are the actual values of output coupling calculated as the ratio of the aperture radius in the secondary mirror to the total radius of the primary mirror, which is a value that is independent of the resonator magnification. In contrast is the ideal geometric coupling factor, which should depend solely on the magnification. The radii of curvature of the convex mirrorM, for magnifications of 1.15, 1.25, and 1.35 were -20.3601, -16.1550, and -12.6560 m, respectively. These measurements correspond to ideal values of 8 of 13, 20, and 26%. It is clear that all the curves follow the same general trend; that is, each shows a peak in the output power for apertures in the 2.54-2.92-cm range. These

120

120

100 _

100 _

*

0

0

V

0

80 -

t-

80 _ 0.

0 :1

0. 0

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I 1.0

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Z0

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40 H

40 _

200 .5

I ____ I 1.0 1.5

I 2.0

I 2.5

I 3.0

I ___ 3.5 4.0

aperture size (cm)

Fig. 8. Laser output power versus the aperture size for a magnification of M = 1.15. 1970

APPLIED OPTICS / Vol. 31, No. 12 / 20 April 1992

20 0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

aperture size (cm)

Fig. 10. Laser output power versus the aperture size for a magnification of M = 1.35.

particular apertures correspond to a 24% and a 27.7% output coupling factor 8 *, respectively. With the exception of the M = 1.15 case, the peak in the output power is consistent with predictions of the ideal geometrical theory that is mentioned above. For this particular magnification an ideal output coupling fraction of = 13% is predicted. This calculation presumes that gain media are present over the entire cross section of the secondary mirror. However, as is evident in Fig. 1, this is not the situation for the particular system in question here. Because of the geometry of the structure, there is a central zone in which no discharge is present. Any gain in this region is due solely to diffusion of the excited species into the area. Hence the region exhibits a higher absorption and a concomitant decrease in the output power than would otherwise be the case. Consequently the optimum output aperture for M = 1.15 is shifted toward a larger size, which makes better use of the available gain within the region. In addition to the data for the uncoated aluminum alloy mirrors, Fig. 9, curve (b) also shows the data that are obtained with gold-coated mirror surfaces. These experiments were performed to evaluate the impact of a reduced mirror absorption on the output power and coupling characteristics. As is evident the gold-coated mirrors show an increase in the attainable optical power of approximately 20%. This value was recorded with a 2.16-cm aperture, which translates into a coupling factor of * = 20.5%. These findings are in good agreement with the projected ideal geometrical coupling value of 20%. In an ideal situation the gain and loss mechanisms within the active medium are ignored, and it is assumed that the mirrors have perfect reflectivity. Therefore, by increas-

ing the reflectivityof the mirrors through the introduction of gold-coated surfaces, a situation that is closer to the ideal is realized. These aspects are borne out by an analysis presented by Kaufman and Oppenheim." Their analysis is based on the well-known Rigrod formulation but applied to a higher-gain system. By using previously measured small-signal gain values of 0.50 m-, a saturation intensity of 1 kW/cm' together with the 10.6-pm reflectivities that are expected from uncoated aluminum mirrors of 98% (Ref. 23) as well as that of gold-coated mirrors of =99.4%,23a shift in the optimum output coupling value of near 3.5% is predicted. In addition an increase of 23% in the overall output power is projected. These results are a consequence only of the change in mirror reflectivity, if all other factors are held constant. It is clear that these theoretical projections agree well with the experimental findings reported here. It was further observed that when the individual beamlets coalesced to fill in the near-field output profile completely, the power decreased to - 80% of its maximum value. This situation occurred with the 1.27-, 1.78-, and 2.54-cm apertures for magnifications of 1.15, 1.25, and 1.35, respectively. Considering that for the individual beamlets to overlap they must

traverse a region of the resonator that contains no discharge, these findings are not unexpected. The comparatively small 20% reduction that is observed, despite the increased number of lossy round trips that are experienced with uncoated mirrors, suggests that vibrationally excited species must diffuse into the central portion of the structure, thereby providing a measure of additional gain for the beams. A second plausible explanation for the power decrease is related to the aperture size in the convex mirror as well as the beam size in each individual channel. For any given magnification there is a corresponding beam size associated with it. Hence, if the aperture that is selected is smaller than the beam, a portion of the beam may be reflected past the central tip of the primary concave mirror and thereby lost in the opposite gain cell. This situation occurs for any aperture that is smaller than 1.37, 2.08, and 2.73 cm for magnifications of 1.15, 1.25, and 1.35, respectively. In spite of this, however, a large penalty in output power is therefore not observed despite the selection to operate with only a single beam instead of eight individual beamlets. It is observed from Figs. 8-10 that the maximum output power that is obtained is not constant but depends on the particular magnification used. To investigate this phenomenon further, a series of experiments was performed in which the maximum output power was measured as a function of the geometrical magnification. Figure 11 presents the data for a range of magnifications from M = 1.10 to 1.50. For each point on the graph a series of different aperture sizes was used to determine which provided optimum coupling. This aperture was then used to measure the output power that is shown in Fig. 11. The curve exhibits a well-defined peak for magnifications between 1.25 and 1.30. For values of M below this peak the optical radiation makes a larger number 120

100 _

0

0

80 ii,

5

60

40 k

20 _ 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 magnification

Fig. 11. Laser output power versus magnification. Each point represents the optimum aperture for any given magnification. 20 April 1992 / Vol. 31, No. 12 / APPLIED OPTICS

1971

of passes through the gain media. However, the effect of these increased passes is offset by the concurrent losses that are accumulated through mirror absorption. Therefore, any power gains that are made within the active medium are more than negated by internal cavity losses.'3 Hence the observed maximum output power decreases. Of equal importance is the lack of discharge in the central region. Thus, as explained above for the M = 1.10 and 1.15 cases, the peak in the output power is shifted to a higher value of output coupling than the ideal prediction. The reduction in maximum power that is observed at lower magnifications may be due to similar reasons. Conversely, for values of M that are larger than 1.30, the photons make fewer passes in the gain media. Thus the full advantage of the energy stored is not experienced. Consequently the output power decreases for magnifications beyond = 1.30. Misalignment Sensitivity

A brief investigation of the toric resonator sensitivity was also undertaken. By definition the angular sensitivity S is a measure of how much misalignment a resonator can withstand before a significant reduction in its output parameters is observed. In practice this usually corresponds to the condition that the oscillating cavity axis coincide with the edge of the opposite mirror. An equivalent criterion is when the observed output power has been reduced by = 50%." Krupke and Sooy' presented a theoretical analysis to help quantify this important parameter. Their formulation is characterized by the S parameter, which is defined as S = (1 - g)/(1 - g,),

(3)

where the gi are given by Eq. (1). Equation (3) gives a relative measure of the alignment sensitivity. In this context larger values of S indicate a more sensitive alignment situation. For comparison the alignment sensitivities of the M = 1.10, M = 1.25, and M = 1.50 resonators were measured. Analytically these three situations correspond to S values of 14.9, 5.23, and 3.23, respectively. The criterion used in these sensitivity studies was that the output radiation drop to 50% of its optimum value. Knowing the distance of the alignment screw to the pivot point of the mirror and the tilt that is required to affect this condition allowed the angular deviation to be calculated. Following this approach a

beam began to take on a crescent shape or became lopsided as the resonator was misaligned. This is in agreement with the hypothesis of Townsend and Reilly. 7 However, their prediction of a hole forming in the output beam during misalignment could not be confirmed since the aperture size that is used during these experiments already contained eight individual beamlets. PolarizationProperties

It has been well documented in the scientific litera-

ture that the polarization state of a laser's output beam can profoundly influence a laser-material processing interaction.' 5 This is especially true for applications such as cutting, scribing, and drilling.","7This being the case the polarization properties of the toric resonator were investigated. To perform these measurements a ZnSe wire grid polarizer was inserted between the output of the laser and a power meter. Rotation of the polarizer in conjunction with power readings thereby allowed a determination of output beam polarization. Because of the unique features of the toric resonator that were outlined previously, polarization measurements were made for both the single-beam output and the eight individual beamlet configurations. Figure 12 shows the polarization state that is observed when all eight distinct beamlets are present. It is evident that each channel is linearly polarized in a direction that is parallel to its electrode faces. Although this result is typical of many rf-excited waveguide CO, lasers,'8 it was not anticipated here. In particular tests have been performed in which the electrode faces were made to be rough to determine if waveguiding effects are important. These studies indicated that the lasing performance of the system was not hampered by the roughness of the electrode faces, and therefore waveguide effects were not expected. The polarization state of the beam that emerges from the 1.27-cm aperture is less intuitive. Measurements that are performed with this aperture indicate that there is no preferential direction of polarization of the beam as a whole. In particular the electric field exiting the test polarizer exhibits an equal amplitude for all polarizer orientations. It is believed that this particular condition results from

deviation of 42 s was found for theM = 1.10 case, 83 s

for the M = 1.25 situation, and a value of 141 s for the M = 1.50 resonator. These values are in qualitative agreement with Krupke and Sooy. It should be mentioned also that the resonator became more sensitive to misalignment as the magnification decreased. In fact, for a value of M = 1.05 (S = 40.2), the resonator was so sensitive that a stable condition with all eight beams lasing simultaneously was not achievable. Also noteworthy is the appearance of the output beams during misalignment. It was evident that the 1972

APPLIED OPTICS / Vol. 31, No. 12 / 20 April 1992

Fig. 12. Schematic representation of the discharge geometry. The arrows indicate the direction of polarization within each individual discharge region.

the superposition of the individual polarizations that exist within each slot.'9 This hypothesis was confirmed by observing the polarization at a point, which, although dominated by a single beamlet, still contained contributions from the other channels. This was accomplished with a slightly larger aperture size. Although an intensity maximum in the direction corresponding to the slot geometry was measured, a uniform background intensity at all other polarization angles was also apparent. Similar patterns were also detected with the remaining seven channels as well.

The fact that the combined single beam exhibits no preferential polarization direction is a useful property in many material processing applications. In particular during cutting operations a change in direction will often be manifest as a reduction in process speed if the beam is linearly polarized.'7 In drilling applications a linearly polarized beam usually produces a slightly elliptical hole.'6 Both of these potential problems appear to be addressable by the toric resonator fitted with an appropriate aperture. Summary

The properties of a toric unstable resonator have been investigated experimentally. It was found that the toric configuration behaves similarly to a conventional unstable resonator, particularly with respect to the dependence of output power on the coupling factor and magnification. However, because of the unique geometry of the toric resonator, it has some inherent advantages for the application that is considered here. Of these the most evident is the ability to change the character of the laser's output from a number of individual beamlets to a single combined beam simply by changing the size of the coupling aperture. It was also found that this alteration reduced the maximum output power by only approximately 20%, even in the presence of extremely lossy mirrors. With low-loss optics the change in total power should be insignificant. In addition it was determined that the focal spot size varies inversely with the aperture. However, a much sharper dependence is seen when the output beams interact with each other compared with that when they act independently. The angular sensitivity to misalignment of the toric resonator was also investigated. The sensitivity was shown to increase with decreasing magnification. It was also found that stable alignment could not be achieved at low magnification. Finally the polarization properties of the resonator were studied. Data revealed that each slot is polarized in a direction that is parallel to its electrode faces. However, when a single output beam is derived from a superposition of all the individual beamlets, no preferential direction of polarization is exhibited. The accumulated results document the toric unstable resonator as a viable alternative to a conventional unstable resonator. This type of resonator structure

could prove to be particularly useful in the scaling of extended-area radial discharge arrays for high-power laser construction. Experiments are presently being conducted to achieve coherent optical phase locking of all the individual channels. When this situation is realized a toric resonator should provide an effective approach to derive a powerful and coherent output beam from an unusually compact structure. The authors gratefully acknowledge the continuing financial support of the Natural Sciences and Engineering Research Council of Canada. Also, the authors thank C. V. Sellathamby for his assistance with the intensity profile experiments. References 1. K. M. Abramski, A. D. Colley, H. J. Baker, and D. R. Hall,

"Power scaling of large-area transverse radio frequency discharge CO, lasers," Appl. Phys. Lett. 54, 1833-1835 (1989). 2. P. E. Jackson, H. J. Baker, and D. R. Hall, "CO2 large-area discharge laser using an unstable waveguidehybrid resonator," Appl. Phys. Lett. 54, 1950-1952 (1989). 3. D. R. Hall and H. J. Baker, "Area scaling boosts CO, laser performance," Laser Focus World 25, 77-80 (Oct. 1989). 4. E. F. Yelden, H. J. J. Seguin, C. E. Capjack, and S. K. Nikumb,

"Multi-channel slab discharge for CO, laser excitation," Appl. Phys. Lett. 58, 693-695 (1991). 5. E. F. Yelden, H. J. J. Seguin, C. E. Capjack, and S. K. Nikumb,

"A multi-channel slot discharge CO, laser employing a toric unstable resonator," Opt. Commun. 82, 503-508 (1991). 6. A. E. Siegman, "Unstable optical resonators for laser applications," Proc. IEEE 53, 277-287 (1965). 7. A. E. Siegman, "Unstable 353-367 (1974).

optical resonators,"

Appl. Opt. 13,

8. W. F. Krupke and W. R. Sooy, "Properties of an unstable confocal resonator CO, laser system," IEEE J. Quantum Electron. QE-5, 575-586 (1969). 9. R. J. Freiberg, P. P. Chenausky, and C. J. Buczek, "An experimental study of unstable confocal CO2 resonators," IEEE J. Quantum Electron. QE-8, 882-892 (1972). 10. S. R. Barone, "Optical resonators in the unstable region," Appl. Opt. 6, 861-863 (1967). 11. M. A. Gorriz, "Wave propagation program-a

necessary tool

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