Abstract

We present theoretical and experimental results for an rf-excited z-fold CO2 waveguide laser. We describe how the output power, output rotational line(s) and transverse mode(s) vary as functions of elbow mirror tilt and obtain good agreement with predictions from a multimode matrix resonator model. Observations of multilining and/or multifrequency operation are partly explained by the near equality of gain/loss ratios for two or more resonator modes.

© 1990 Optical Society of America

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References

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  1. J. J. Degnan, “The Waveguide Laser: A Review,” Appl. Phys. 11, 1–33 (1976).
    [CrossRef]
  2. R. L. Abrams, “Waveguide Gas Lasers,” in Laser Handbook, Vol. 3 (North-Holland, Amsterdam, 1979).
  3. D. R. Hall, C. A. Hill, “Rf-Discharge-Excited CO2 Lasers,” in Handbook of Molecular Lasers, P. K. Cheo, Ed. (Marcel Dekker, New York, 1987).
  4. R. L. Abrams, “Gigahertz Tunable Waveguide CO2 Laser,” Appl. Phys. Lett. 25, 304–306 (1974).
    [CrossRef]
  5. L. A. Newman, R. A. Hart, “Recent R&D Advances in Sealed-Off CO2 Lasers,” Laser Focus/Electroopt.80–96 (1987).
  6. P. E. Jackson, H. J. Baker, D. R. Hall, “CO2 Large-Area Discharge Laser Using an Unstable-Waveguide Hybrid Resonator,” Appl. Phys. Lett. 54, 1950–1952 (1989).
    [CrossRef]
  7. P. W. Smith, “A Waveguide Gas Laser,” Appl. Phys. Lett. 19, 132–134 (1971).
    [CrossRef]
  8. R. L. Abrams, W. B. Bridges, “Characteristics of Sealed-Off Waveguide CO2 Lasers,” IEEE J. Quantum Electron. QE-9, 940–946 (1973).
    [CrossRef]
  9. J. J. Degnan, D. R. Hall, “Finite-Aperture Waveguide-Laser Resonators,” IEEE J. Quantum Electron. QE-9, 901–910 (1973).
    [CrossRef]
  10. P. E. Jackson, D. R. Hall, C. A. Hill, “Comparisons of Waveguide Folding Geometries in a CO2 z-Fold Laser,” Appl. Opt. 28, 935–941 (1989).
    [CrossRef] [PubMed]
  11. C. A. Hill, “Transverse Modes of Waveguide Laser Resonators,” IEEE J. Quantum Electron. QE-24, 1936–1946 (1988).
    [CrossRef]
  12. C. A. Hill, A. D. Colley, “Misalignment Effects in a CO2 Waveguide Laser,” IEEE J. Quantum Electron.QE-26, submitted for publication.
  13. R. Gerlach, D. Wei, N. M. Amer, “Coupling Efficiency of Waveguide Laser Resonators Formed by Flat Mirrors: Analysis and Experiment,” IEEE J. Quantum Electron. QE-20, 948–963 (1984).
    [CrossRef]
  14. P. J. Gorton, R. M. Jenkins, to be published.
  15. C. A. Hill, J. R. Redding, A. D. Colley, “Multimode Treatment of Misaligned CO2 Waveguide Lasers,” presented at 9th National Quantum Electronics Conference, Oxford, September 1989; submitted for publication in J. Modern Optics.

1989

P. E. Jackson, H. J. Baker, D. R. Hall, “CO2 Large-Area Discharge Laser Using an Unstable-Waveguide Hybrid Resonator,” Appl. Phys. Lett. 54, 1950–1952 (1989).
[CrossRef]

P. E. Jackson, D. R. Hall, C. A. Hill, “Comparisons of Waveguide Folding Geometries in a CO2 z-Fold Laser,” Appl. Opt. 28, 935–941 (1989).
[CrossRef] [PubMed]

1988

C. A. Hill, “Transverse Modes of Waveguide Laser Resonators,” IEEE J. Quantum Electron. QE-24, 1936–1946 (1988).
[CrossRef]

1987

L. A. Newman, R. A. Hart, “Recent R&D Advances in Sealed-Off CO2 Lasers,” Laser Focus/Electroopt.80–96 (1987).

1984

R. Gerlach, D. Wei, N. M. Amer, “Coupling Efficiency of Waveguide Laser Resonators Formed by Flat Mirrors: Analysis and Experiment,” IEEE J. Quantum Electron. QE-20, 948–963 (1984).
[CrossRef]

1976

J. J. Degnan, “The Waveguide Laser: A Review,” Appl. Phys. 11, 1–33 (1976).
[CrossRef]

1974

R. L. Abrams, “Gigahertz Tunable Waveguide CO2 Laser,” Appl. Phys. Lett. 25, 304–306 (1974).
[CrossRef]

1973

R. L. Abrams, W. B. Bridges, “Characteristics of Sealed-Off Waveguide CO2 Lasers,” IEEE J. Quantum Electron. QE-9, 940–946 (1973).
[CrossRef]

J. J. Degnan, D. R. Hall, “Finite-Aperture Waveguide-Laser Resonators,” IEEE J. Quantum Electron. QE-9, 901–910 (1973).
[CrossRef]

1971

P. W. Smith, “A Waveguide Gas Laser,” Appl. Phys. Lett. 19, 132–134 (1971).
[CrossRef]

Abrams, R. L.

R. L. Abrams, “Gigahertz Tunable Waveguide CO2 Laser,” Appl. Phys. Lett. 25, 304–306 (1974).
[CrossRef]

R. L. Abrams, W. B. Bridges, “Characteristics of Sealed-Off Waveguide CO2 Lasers,” IEEE J. Quantum Electron. QE-9, 940–946 (1973).
[CrossRef]

R. L. Abrams, “Waveguide Gas Lasers,” in Laser Handbook, Vol. 3 (North-Holland, Amsterdam, 1979).

Amer, N. M.

R. Gerlach, D. Wei, N. M. Amer, “Coupling Efficiency of Waveguide Laser Resonators Formed by Flat Mirrors: Analysis and Experiment,” IEEE J. Quantum Electron. QE-20, 948–963 (1984).
[CrossRef]

Baker, H. J.

P. E. Jackson, H. J. Baker, D. R. Hall, “CO2 Large-Area Discharge Laser Using an Unstable-Waveguide Hybrid Resonator,” Appl. Phys. Lett. 54, 1950–1952 (1989).
[CrossRef]

Bridges, W. B.

R. L. Abrams, W. B. Bridges, “Characteristics of Sealed-Off Waveguide CO2 Lasers,” IEEE J. Quantum Electron. QE-9, 940–946 (1973).
[CrossRef]

Colley, A. D.

C. A. Hill, A. D. Colley, “Misalignment Effects in a CO2 Waveguide Laser,” IEEE J. Quantum Electron.QE-26, submitted for publication.

C. A. Hill, J. R. Redding, A. D. Colley, “Multimode Treatment of Misaligned CO2 Waveguide Lasers,” presented at 9th National Quantum Electronics Conference, Oxford, September 1989; submitted for publication in J. Modern Optics.

Degnan, J. J.

J. J. Degnan, “The Waveguide Laser: A Review,” Appl. Phys. 11, 1–33 (1976).
[CrossRef]

J. J. Degnan, D. R. Hall, “Finite-Aperture Waveguide-Laser Resonators,” IEEE J. Quantum Electron. QE-9, 901–910 (1973).
[CrossRef]

Gerlach, R.

R. Gerlach, D. Wei, N. M. Amer, “Coupling Efficiency of Waveguide Laser Resonators Formed by Flat Mirrors: Analysis and Experiment,” IEEE J. Quantum Electron. QE-20, 948–963 (1984).
[CrossRef]

Gorton, P. J.

P. J. Gorton, R. M. Jenkins, to be published.

Hall, D. R.

P. E. Jackson, D. R. Hall, C. A. Hill, “Comparisons of Waveguide Folding Geometries in a CO2 z-Fold Laser,” Appl. Opt. 28, 935–941 (1989).
[CrossRef] [PubMed]

P. E. Jackson, H. J. Baker, D. R. Hall, “CO2 Large-Area Discharge Laser Using an Unstable-Waveguide Hybrid Resonator,” Appl. Phys. Lett. 54, 1950–1952 (1989).
[CrossRef]

J. J. Degnan, D. R. Hall, “Finite-Aperture Waveguide-Laser Resonators,” IEEE J. Quantum Electron. QE-9, 901–910 (1973).
[CrossRef]

D. R. Hall, C. A. Hill, “Rf-Discharge-Excited CO2 Lasers,” in Handbook of Molecular Lasers, P. K. Cheo, Ed. (Marcel Dekker, New York, 1987).

Hart, R. A.

L. A. Newman, R. A. Hart, “Recent R&D Advances in Sealed-Off CO2 Lasers,” Laser Focus/Electroopt.80–96 (1987).

Hill, C. A.

P. E. Jackson, D. R. Hall, C. A. Hill, “Comparisons of Waveguide Folding Geometries in a CO2 z-Fold Laser,” Appl. Opt. 28, 935–941 (1989).
[CrossRef] [PubMed]

C. A. Hill, “Transverse Modes of Waveguide Laser Resonators,” IEEE J. Quantum Electron. QE-24, 1936–1946 (1988).
[CrossRef]

D. R. Hall, C. A. Hill, “Rf-Discharge-Excited CO2 Lasers,” in Handbook of Molecular Lasers, P. K. Cheo, Ed. (Marcel Dekker, New York, 1987).

C. A. Hill, A. D. Colley, “Misalignment Effects in a CO2 Waveguide Laser,” IEEE J. Quantum Electron.QE-26, submitted for publication.

C. A. Hill, J. R. Redding, A. D. Colley, “Multimode Treatment of Misaligned CO2 Waveguide Lasers,” presented at 9th National Quantum Electronics Conference, Oxford, September 1989; submitted for publication in J. Modern Optics.

Jackson, P. E.

P. E. Jackson, H. J. Baker, D. R. Hall, “CO2 Large-Area Discharge Laser Using an Unstable-Waveguide Hybrid Resonator,” Appl. Phys. Lett. 54, 1950–1952 (1989).
[CrossRef]

P. E. Jackson, D. R. Hall, C. A. Hill, “Comparisons of Waveguide Folding Geometries in a CO2 z-Fold Laser,” Appl. Opt. 28, 935–941 (1989).
[CrossRef] [PubMed]

Jenkins, R. M.

P. J. Gorton, R. M. Jenkins, to be published.

Newman, L. A.

L. A. Newman, R. A. Hart, “Recent R&D Advances in Sealed-Off CO2 Lasers,” Laser Focus/Electroopt.80–96 (1987).

Redding, J. R.

C. A. Hill, J. R. Redding, A. D. Colley, “Multimode Treatment of Misaligned CO2 Waveguide Lasers,” presented at 9th National Quantum Electronics Conference, Oxford, September 1989; submitted for publication in J. Modern Optics.

Smith, P. W.

P. W. Smith, “A Waveguide Gas Laser,” Appl. Phys. Lett. 19, 132–134 (1971).
[CrossRef]

Wei, D.

R. Gerlach, D. Wei, N. M. Amer, “Coupling Efficiency of Waveguide Laser Resonators Formed by Flat Mirrors: Analysis and Experiment,” IEEE J. Quantum Electron. QE-20, 948–963 (1984).
[CrossRef]

Appl. Opt.

Appl. Phys.

J. J. Degnan, “The Waveguide Laser: A Review,” Appl. Phys. 11, 1–33 (1976).
[CrossRef]

Appl. Phys. Lett.

R. L. Abrams, “Gigahertz Tunable Waveguide CO2 Laser,” Appl. Phys. Lett. 25, 304–306 (1974).
[CrossRef]

P. E. Jackson, H. J. Baker, D. R. Hall, “CO2 Large-Area Discharge Laser Using an Unstable-Waveguide Hybrid Resonator,” Appl. Phys. Lett. 54, 1950–1952 (1989).
[CrossRef]

P. W. Smith, “A Waveguide Gas Laser,” Appl. Phys. Lett. 19, 132–134 (1971).
[CrossRef]

IEEE J. Quantum Electron.

R. L. Abrams, W. B. Bridges, “Characteristics of Sealed-Off Waveguide CO2 Lasers,” IEEE J. Quantum Electron. QE-9, 940–946 (1973).
[CrossRef]

J. J. Degnan, D. R. Hall, “Finite-Aperture Waveguide-Laser Resonators,” IEEE J. Quantum Electron. QE-9, 901–910 (1973).
[CrossRef]

C. A. Hill, “Transverse Modes of Waveguide Laser Resonators,” IEEE J. Quantum Electron. QE-24, 1936–1946 (1988).
[CrossRef]

R. Gerlach, D. Wei, N. M. Amer, “Coupling Efficiency of Waveguide Laser Resonators Formed by Flat Mirrors: Analysis and Experiment,” IEEE J. Quantum Electron. QE-20, 948–963 (1984).
[CrossRef]

Laser Focus/Electroopt.

L. A. Newman, R. A. Hart, “Recent R&D Advances in Sealed-Off CO2 Lasers,” Laser Focus/Electroopt.80–96 (1987).

Other

R. L. Abrams, “Waveguide Gas Lasers,” in Laser Handbook, Vol. 3 (North-Holland, Amsterdam, 1979).

D. R. Hall, C. A. Hill, “Rf-Discharge-Excited CO2 Lasers,” in Handbook of Molecular Lasers, P. K. Cheo, Ed. (Marcel Dekker, New York, 1987).

C. A. Hill, A. D. Colley, “Misalignment Effects in a CO2 Waveguide Laser,” IEEE J. Quantum Electron.QE-26, submitted for publication.

P. J. Gorton, R. M. Jenkins, to be published.

C. A. Hill, J. R. Redding, A. D. Colley, “Multimode Treatment of Misaligned CO2 Waveguide Lasers,” presented at 9th National Quantum Electronics Conference, Oxford, September 1989; submitted for publication in J. Modern Optics.

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Figures (11)

Fig. 1
Fig. 1

Sketch of elbow in z-fold waveguide laser, with distant tilted plane folding mirror.

Fig. 2
Fig. 2

Output power vs elbow mirror x-tilt (a) and y-tilt (b) for z-fold laser with four plane mirrors. 45 Torr 3He:1CO2:1N2 + 5% Xe, ≃350-W rf input power at 125 MHz. Shows regions of mode beating (hooting) and multiline operation.

Fig. 3
Fig. 3

Output power vs elbow mirror y-tilt, with 90 Torr and ≃550-W rf input power. These are near-optimum conditions for power output with well-aligned plane mirrors10; we can infer that the small-signal gain g0 is lower than at 45 Torr, but that the saturation intensity IS is much higher. Rough sketches of phosphor-screen beam profiles are shown.

Fig. 4
Fig. 4

Transverse beam profiles at 90 Torr for several plane-mirror y-tilt values (φy = 0–5 mrad), showing more detail than in Fig. 3. Each profile is normalized to give the same peak intensity.

Fig. 5
Fig. 5

Output power vs elbow mirror x-tilt (a) and y-tilt (b), with 90 Torr, curved folding mirrors (R ≃ 1.5 m) and ≃550-W rf input.

Fig. 6
Fig. 6

Output power vs elbow mirror x-tilt, with 90 Torr, partial waveguiding10 and ≃700-W rf input.

Fig. 7
Fig. 7

Round-trip loss at 10.59 μm predicted for first four modes of misaligned z-fold resonator with four plane mirrors. The modes are labeled 1 to 4 in order of increasing loss, so that the fundamental mode 1 is by definition the lowest-loss mode at any given tilt value.

Fig. 8
Fig. 8

Round-trip loss predicted for three important CO2 wavelengths: 10.59, 10.25, and 9.55 μm (fundamental mode only). Estimated loss factors (as in Ref. 12): Re[( − 1)−1/2] = 0.9, 1.3, and 1.8, respectively; Re[( − 1)−1/2] = 0.5, 0.8, and 1.0, respectively.

Fig. 9
Fig. 9

Comparison of measured and predicted powers for plane-mirror tilt. Solid lines: distributed-loss Rigrod predictions12 with 2α = −1/L ln|γ| (L = total guide length ≃ 115 cm, γ = round-trip eigenvalue of lowest-loss mode at 10.59 μm). Reasonable fits are obtained with g0 = 1.2% cm−1 and IS = 2.5 kW cm−2 at 45 Torr, and g0 = 0.71% cm−1 and IS = 10.7 kW cm−2 at 90 Torr. In Ref. 10 we estimated g0 = 0.68 ± 0.03% cm−1 and IS = 10.2 ± 0.8 kW cm−2 at 90 Torr.

Fig. 10
Fig. 10

Fractional losses vs φ for the fundamental resonator mode at 10.59 μm. If unit power leaves the aperture of channel 1 (or leg 1), then 1 − a1, ≡ exp(−δ1) enters channel 2 (curve a; see Fig. 1 for fold geometry). Similarly, a fraction exp(−δ2) enters channel 1 after unit power leaves channel 2 (curve b). We do not expect δ1, to equal δ2, because the laser round-trip path is not symmetrical about the folding mirror. Also shown are the fractional losses in propagating along channel 1 (curve c; nearly independent of sense of travel) and reflecting from the well-aligned Case I mirror at the end of channel 1 (curve d).

Fig. 11
Fig. 11

Fractional waveguide mode content of the fundamental resonator mode just before the output mirror. EH1n amplitudes a1n, are normalized so that ∑|a1n|2 = 1. The mode crossing point at φy ≃ 1 mrad (Fig. 7) is indicated by dotted lines. In practice, a clear but less abrupt change in output beam profile can be seen; compare this figure with the profiles of Fig. 4.

Equations (6)

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c m n , m n = p , q A p q m n ( d , φ x ) A p q m n ( 0 , 0 ) ,
A p q m n ( d , φ x ) = ( 2 / π ) 1 / 2 ( 2 p p ! 2 q q ! ) - 1 / 2 α r exp ( i φ p q ) × [ I p m ( d , φ x ) I q n ( d , 0 ) ] ,
α = [ 1 + ( 2 d / b ) 2 ] - 1 / 2 ;
φ p q = ( p + q + 1 ) tan - 1 ( 2 d / b ) ;
b = π w 0 2 / λ .
I p m = - 1 1 H p [ 2 α r ( u - Δ u ) ] exp { - [ α r ( u - Δ u ) 2 ] ( 1 + i 2 d / b ) } × exp { i k a φ x ( u - Δ u ) } { cos sin ( m π u 2 ) d u ,             m = { odd even

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