Abstract

We present an approximate analysis of the nonlinear operation of the hollow-waveguide laser, including gain saturation and longitudinal- as well as transverse-field distribution of the laser mode. The model presented is general and can be applied to the study of an arbitrary configuration of the waveguide laser. The laser characteristics obtained reveal that the optimal position of the output mirror (which provides maximal power efficiency of the laser system with the other parameters constant) depends on the output-power level and the mirror-reflectivity coefficient. Moreover, it has been shown that when an addition device is introduced into the cavity, the power efficiency also depends on which end of the laser the light power is extracted from.

© 1995 Optical Society of America

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  1. P. W. Smith, “A waveguide gas laser,” Appl. Phys. Lett. 19, 132–134 (1971).
    [CrossRef]
  2. H. Steffen, F. K. Kneubuhl, “Dielectric tube resonators for infrared and submillimeter wave lasers,” Phys. Lett. A 27, 612–613 (1968).
    [CrossRef]
  3. J. J. Degan, “The waveguide laser: a review,” Appl. Phys. 11, 1–33 (1976).
    [CrossRef]
  4. R. L. Abrams, “Waveguide gas lasers,” in Laser Handbook, M. L. Stitch, ed. (North-Holland, Amsterdam, 1979), pp. 41–88.
  5. P. W. Smith, O. R. Wood, P. J. Maloney, C. R. Adams, “Transversly excited waveguide gas lasers,” IEEE J. Quantum Electron. QE-17, 1166–1181 (1981).
    [CrossRef]
  6. K. D. Laakmann, W. H. Steier, “Waveguides: characteristics modes of hollow rectangular dielectric waveguides,” Appl. Opt. 15, 1334–1340 (1976).
    [CrossRef] [PubMed]
  7. D. M. Henderson, “Waveguide lasers with intracavity electric modulators: misalignment loss,” Appl. Opt. 15, 1066–1070 (1976).
    [CrossRef] [PubMed]
  8. C. A. Hill, D. R. Hall, “Waveguide laser resonator with a titled mirror,” IEEE J. Quantum Electron. QE-22, 1078–1087 (1987).
  9. M. Arnz, H.-E. Ponath, “Electric field generation in hollow dielectric waveguide lasers. I: General theory of unperturbed symmetric waveguide configuration,” J. Opt. Soc. Am. B 5, 1424–1437 (1988).
    [CrossRef]
  10. C. A. Hill, “Transverse modes of plane-mirror waveguide resonators,” IEEE J. Quantum Electron. QE-24, 1936–1945 (1988).
    [CrossRef]
  11. J. Bemnerji, A. R. Devies, P. E. Jackson, R. M. Jenkins, “Transmission and coupling losses in folded waveguide,” IEEE J. Quantum Electron. QE-26, 701–709 (1990).
  12. B. Schroder, “Transverse modes of active hollow waveguide resonators,” IEEE J. Quantum Electron. QE-27, 158–166 (1991).
    [CrossRef]
  13. D. G. Youmans, “Phase locking of adjacent channel leaky waveguide CO2 lasers,” Appl. Phys. Lett. 44, 365–367 (1984).
    [CrossRef]
  14. C. A. Hill, P. E. Jackson, “Hooting modes in a CO2 waveguide laser,” IEEE J. Quantum Electron. QE-24, 1976–1980 (1984).
  15. D. He, D. R. Hall, “Frequency dependence in REF discharge excited waveguide CO2 lasers,” IEEE J. Quantum Electron. QE-20, 509–514 (1984).
    [CrossRef]
  16. L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Cantor, A. J. DeMaria, “High power coupled CO2 waveguide laser array,” Appl. Phys. Lett. 48, 1701–1703 (1986).
    [CrossRef]
  17. C. A. Hill, “Tunable RF-excited CO2 waveguide laser with variable guide width,” IEEE J. Quantum Electron. QE-23, 1968–1973 (1987).
    [CrossRef]
  18. K. H. Abramski, A. D. Colley, H. J. Baker, D. R. Hall, “Offset frequency stabilization of RF excited waveguide CO2 laser arrays,” IEEE J. Quantum Electron. 27, 711–717 (1990).
    [CrossRef]
  19. A. D. Colley, K. H. Abramski, H. J. Baker, D. R. Hall, “Discharge-induced frequency modulation of RF excited CO2 waveguide lasers,” IEEE J. Quantum Electron. 27, 1939–1945 (1990).
    [CrossRef]
  20. D. R. Hall, P. E. Jackson, The Physics and Technology of Laser Resonators (Hiller, Bristol, New York, 1989), Chap. 3.
  21. W. W. Rigrod, “Saturation effects in high-gain lasers,” J. Appl. Phys. 36, 2487–2490 (1965).
    [CrossRef]
  22. W. W. Rigrod, “Homogeneously broadened cw lasers with uniform distributed loss,” IEEE J. Quantum Electron. QE-14, 377–381 (1978).
    [CrossRef]
  23. G. Shindler, “Optimum output efficiency of homogenously broadened lasers with constant loss,” IEEE J. Quantum Electron. QE-15, 546–549 (1980).
    [CrossRef]
  24. D. Eimerl, “Optical extraction characteristics of homogeneously broadened cw lasers with nonsaturable loss,” J. Appl. Phys. 51, 3008–3016 (1980).
    [CrossRef]
  25. A. Kujawski, P. Szczepański, “Influence of the position of the gain medium on laser output power,” Opt. Commun. 106, 231–236 (1994).
    [CrossRef]
  26. T. R. Ferguson, “Lasers with saturable gain and distributed loss,” Appl. Opt. 26, 2522–2527 (1987).
    [CrossRef] [PubMed]
  27. R. Ferguson, W. P. Latham, “Efficiency and equivalence of homogeneous broadened lossy lasers,” Appl. Opt. 31, 4113–4121 (1992).
    [CrossRef] [PubMed]
  28. D. L. Caroll, L. H. Sentman, “Maximizing output power of a low-gain laser system,” Appl. Opt. 32, 3930–3941 (1993).
  29. D. L. Carroll, “Effects of a nonhomogeneous gain saturation law on predicted performance of a high-gain and a low-gain laser systems,” Appl. Opt. 33, 1673–1681 (1994).
    [CrossRef] [PubMed]
  30. A. Kujawski, P. Szczepański, “Simple model of gain saturation in homogeneously CW lasers with distributed losses,” J. Mod. Opt. 38, 1901–1909 (1991).
    [CrossRef]
  31. A. Kujawski, P. Szczepański, “Model of gain saturation in a two-mirror laser: single mode operation,” J. Mod. Opt. 39, 2519–2529 (1992).
    [CrossRef]
  32. K. Janulewicz, P. Szczepański, “Approximate analytical method of gain saturation analysis of hollow waveguide lasers,” Appl. Opt. 30, 3818–3820 (1991).
    [CrossRef] [PubMed]
  33. A. Kujawski, P. Szczepański, “Optimization of output power in lasers,” Opt. Eng. 31, 440–446 (1992).
    [CrossRef]
  34. P. Szczepański, M. Skłodowska, W. Woliński, “Gain saturation in fiber distributed feedback lasers,” J. Lightwave Technol. 9, 329–334 (1991).
    [CrossRef]
  35. F. T. Arecchi, E. O. Schultz, Laser Handbook (North-Holland, Amsterdam, 1972), Vol. 1, Chap. 4.

1994 (2)

A. Kujawski, P. Szczepański, “Influence of the position of the gain medium on laser output power,” Opt. Commun. 106, 231–236 (1994).
[CrossRef]

D. L. Carroll, “Effects of a nonhomogeneous gain saturation law on predicted performance of a high-gain and a low-gain laser systems,” Appl. Opt. 33, 1673–1681 (1994).
[CrossRef] [PubMed]

1993 (1)

1992 (3)

R. Ferguson, W. P. Latham, “Efficiency and equivalence of homogeneous broadened lossy lasers,” Appl. Opt. 31, 4113–4121 (1992).
[CrossRef] [PubMed]

A. Kujawski, P. Szczepański, “Model of gain saturation in a two-mirror laser: single mode operation,” J. Mod. Opt. 39, 2519–2529 (1992).
[CrossRef]

A. Kujawski, P. Szczepański, “Optimization of output power in lasers,” Opt. Eng. 31, 440–446 (1992).
[CrossRef]

1991 (4)

P. Szczepański, M. Skłodowska, W. Woliński, “Gain saturation in fiber distributed feedback lasers,” J. Lightwave Technol. 9, 329–334 (1991).
[CrossRef]

A. Kujawski, P. Szczepański, “Simple model of gain saturation in homogeneously CW lasers with distributed losses,” J. Mod. Opt. 38, 1901–1909 (1991).
[CrossRef]

K. Janulewicz, P. Szczepański, “Approximate analytical method of gain saturation analysis of hollow waveguide lasers,” Appl. Opt. 30, 3818–3820 (1991).
[CrossRef] [PubMed]

B. Schroder, “Transverse modes of active hollow waveguide resonators,” IEEE J. Quantum Electron. QE-27, 158–166 (1991).
[CrossRef]

1990 (3)

J. Bemnerji, A. R. Devies, P. E. Jackson, R. M. Jenkins, “Transmission and coupling losses in folded waveguide,” IEEE J. Quantum Electron. QE-26, 701–709 (1990).

K. H. Abramski, A. D. Colley, H. J. Baker, D. R. Hall, “Offset frequency stabilization of RF excited waveguide CO2 laser arrays,” IEEE J. Quantum Electron. 27, 711–717 (1990).
[CrossRef]

A. D. Colley, K. H. Abramski, H. J. Baker, D. R. Hall, “Discharge-induced frequency modulation of RF excited CO2 waveguide lasers,” IEEE J. Quantum Electron. 27, 1939–1945 (1990).
[CrossRef]

1988 (2)

1987 (3)

T. R. Ferguson, “Lasers with saturable gain and distributed loss,” Appl. Opt. 26, 2522–2527 (1987).
[CrossRef] [PubMed]

C. A. Hill, D. R. Hall, “Waveguide laser resonator with a titled mirror,” IEEE J. Quantum Electron. QE-22, 1078–1087 (1987).

C. A. Hill, “Tunable RF-excited CO2 waveguide laser with variable guide width,” IEEE J. Quantum Electron. QE-23, 1968–1973 (1987).
[CrossRef]

1986 (1)

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Cantor, A. J. DeMaria, “High power coupled CO2 waveguide laser array,” Appl. Phys. Lett. 48, 1701–1703 (1986).
[CrossRef]

1984 (3)

D. G. Youmans, “Phase locking of adjacent channel leaky waveguide CO2 lasers,” Appl. Phys. Lett. 44, 365–367 (1984).
[CrossRef]

C. A. Hill, P. E. Jackson, “Hooting modes in a CO2 waveguide laser,” IEEE J. Quantum Electron. QE-24, 1976–1980 (1984).

D. He, D. R. Hall, “Frequency dependence in REF discharge excited waveguide CO2 lasers,” IEEE J. Quantum Electron. QE-20, 509–514 (1984).
[CrossRef]

1981 (1)

P. W. Smith, O. R. Wood, P. J. Maloney, C. R. Adams, “Transversly excited waveguide gas lasers,” IEEE J. Quantum Electron. QE-17, 1166–1181 (1981).
[CrossRef]

1980 (2)

G. Shindler, “Optimum output efficiency of homogenously broadened lasers with constant loss,” IEEE J. Quantum Electron. QE-15, 546–549 (1980).
[CrossRef]

D. Eimerl, “Optical extraction characteristics of homogeneously broadened cw lasers with nonsaturable loss,” J. Appl. Phys. 51, 3008–3016 (1980).
[CrossRef]

1978 (1)

W. W. Rigrod, “Homogeneously broadened cw lasers with uniform distributed loss,” IEEE J. Quantum Electron. QE-14, 377–381 (1978).
[CrossRef]

1976 (3)

1971 (1)

P. W. Smith, “A waveguide gas laser,” Appl. Phys. Lett. 19, 132–134 (1971).
[CrossRef]

1968 (1)

H. Steffen, F. K. Kneubuhl, “Dielectric tube resonators for infrared and submillimeter wave lasers,” Phys. Lett. A 27, 612–613 (1968).
[CrossRef]

1965 (1)

W. W. Rigrod, “Saturation effects in high-gain lasers,” J. Appl. Phys. 36, 2487–2490 (1965).
[CrossRef]

Abrams, R. L.

R. L. Abrams, “Waveguide gas lasers,” in Laser Handbook, M. L. Stitch, ed. (North-Holland, Amsterdam, 1979), pp. 41–88.

Abramski, K. H.

K. H. Abramski, A. D. Colley, H. J. Baker, D. R. Hall, “Offset frequency stabilization of RF excited waveguide CO2 laser arrays,” IEEE J. Quantum Electron. 27, 711–717 (1990).
[CrossRef]

A. D. Colley, K. H. Abramski, H. J. Baker, D. R. Hall, “Discharge-induced frequency modulation of RF excited CO2 waveguide lasers,” IEEE J. Quantum Electron. 27, 1939–1945 (1990).
[CrossRef]

Adams, C. R.

P. W. Smith, O. R. Wood, P. J. Maloney, C. R. Adams, “Transversly excited waveguide gas lasers,” IEEE J. Quantum Electron. QE-17, 1166–1181 (1981).
[CrossRef]

Arecchi, F. T.

F. T. Arecchi, E. O. Schultz, Laser Handbook (North-Holland, Amsterdam, 1972), Vol. 1, Chap. 4.

Arnz, M.

Baker, H. J.

A. D. Colley, K. H. Abramski, H. J. Baker, D. R. Hall, “Discharge-induced frequency modulation of RF excited CO2 waveguide lasers,” IEEE J. Quantum Electron. 27, 1939–1945 (1990).
[CrossRef]

K. H. Abramski, A. D. Colley, H. J. Baker, D. R. Hall, “Offset frequency stabilization of RF excited waveguide CO2 laser arrays,” IEEE J. Quantum Electron. 27, 711–717 (1990).
[CrossRef]

Bemnerji, J.

J. Bemnerji, A. R. Devies, P. E. Jackson, R. M. Jenkins, “Transmission and coupling losses in folded waveguide,” IEEE J. Quantum Electron. QE-26, 701–709 (1990).

Cantor, A. J.

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Cantor, A. J. DeMaria, “High power coupled CO2 waveguide laser array,” Appl. Phys. Lett. 48, 1701–1703 (1986).
[CrossRef]

Caroll, D. L.

Carroll, D. L.

Colley, A. D.

A. D. Colley, K. H. Abramski, H. J. Baker, D. R. Hall, “Discharge-induced frequency modulation of RF excited CO2 waveguide lasers,” IEEE J. Quantum Electron. 27, 1939–1945 (1990).
[CrossRef]

K. H. Abramski, A. D. Colley, H. J. Baker, D. R. Hall, “Offset frequency stabilization of RF excited waveguide CO2 laser arrays,” IEEE J. Quantum Electron. 27, 711–717 (1990).
[CrossRef]

Degan, J. J.

J. J. Degan, “The waveguide laser: a review,” Appl. Phys. 11, 1–33 (1976).
[CrossRef]

DeMaria, A. J.

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Cantor, A. J. DeMaria, “High power coupled CO2 waveguide laser array,” Appl. Phys. Lett. 48, 1701–1703 (1986).
[CrossRef]

Devies, A. R.

J. Bemnerji, A. R. Devies, P. E. Jackson, R. M. Jenkins, “Transmission and coupling losses in folded waveguide,” IEEE J. Quantum Electron. QE-26, 701–709 (1990).

Eimerl, D.

D. Eimerl, “Optical extraction characteristics of homogeneously broadened cw lasers with nonsaturable loss,” J. Appl. Phys. 51, 3008–3016 (1980).
[CrossRef]

Ferguson, R.

Ferguson, T. R.

Hall, D. R.

A. D. Colley, K. H. Abramski, H. J. Baker, D. R. Hall, “Discharge-induced frequency modulation of RF excited CO2 waveguide lasers,” IEEE J. Quantum Electron. 27, 1939–1945 (1990).
[CrossRef]

K. H. Abramski, A. D. Colley, H. J. Baker, D. R. Hall, “Offset frequency stabilization of RF excited waveguide CO2 laser arrays,” IEEE J. Quantum Electron. 27, 711–717 (1990).
[CrossRef]

C. A. Hill, D. R. Hall, “Waveguide laser resonator with a titled mirror,” IEEE J. Quantum Electron. QE-22, 1078–1087 (1987).

D. He, D. R. Hall, “Frequency dependence in REF discharge excited waveguide CO2 lasers,” IEEE J. Quantum Electron. QE-20, 509–514 (1984).
[CrossRef]

D. R. Hall, P. E. Jackson, The Physics and Technology of Laser Resonators (Hiller, Bristol, New York, 1989), Chap. 3.

Hart, R. A.

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Cantor, A. J. DeMaria, “High power coupled CO2 waveguide laser array,” Appl. Phys. Lett. 48, 1701–1703 (1986).
[CrossRef]

He, D.

D. He, D. R. Hall, “Frequency dependence in REF discharge excited waveguide CO2 lasers,” IEEE J. Quantum Electron. QE-20, 509–514 (1984).
[CrossRef]

Henderson, D. M.

Hill, C. A.

C. A. Hill, “Transverse modes of plane-mirror waveguide resonators,” IEEE J. Quantum Electron. QE-24, 1936–1945 (1988).
[CrossRef]

C. A. Hill, D. R. Hall, “Waveguide laser resonator with a titled mirror,” IEEE J. Quantum Electron. QE-22, 1078–1087 (1987).

C. A. Hill, “Tunable RF-excited CO2 waveguide laser with variable guide width,” IEEE J. Quantum Electron. QE-23, 1968–1973 (1987).
[CrossRef]

C. A. Hill, P. E. Jackson, “Hooting modes in a CO2 waveguide laser,” IEEE J. Quantum Electron. QE-24, 1976–1980 (1984).

Jackson, P. E.

J. Bemnerji, A. R. Devies, P. E. Jackson, R. M. Jenkins, “Transmission and coupling losses in folded waveguide,” IEEE J. Quantum Electron. QE-26, 701–709 (1990).

C. A. Hill, P. E. Jackson, “Hooting modes in a CO2 waveguide laser,” IEEE J. Quantum Electron. QE-24, 1976–1980 (1984).

D. R. Hall, P. E. Jackson, The Physics and Technology of Laser Resonators (Hiller, Bristol, New York, 1989), Chap. 3.

Janulewicz, K.

Jenkins, R. M.

J. Bemnerji, A. R. Devies, P. E. Jackson, R. M. Jenkins, “Transmission and coupling losses in folded waveguide,” IEEE J. Quantum Electron. QE-26, 701–709 (1990).

Kennedy, J. T.

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Cantor, A. J. DeMaria, “High power coupled CO2 waveguide laser array,” Appl. Phys. Lett. 48, 1701–1703 (1986).
[CrossRef]

Kneubuhl, F. K.

H. Steffen, F. K. Kneubuhl, “Dielectric tube resonators for infrared and submillimeter wave lasers,” Phys. Lett. A 27, 612–613 (1968).
[CrossRef]

Kujawski, A.

A. Kujawski, P. Szczepański, “Influence of the position of the gain medium on laser output power,” Opt. Commun. 106, 231–236 (1994).
[CrossRef]

A. Kujawski, P. Szczepański, “Model of gain saturation in a two-mirror laser: single mode operation,” J. Mod. Opt. 39, 2519–2529 (1992).
[CrossRef]

A. Kujawski, P. Szczepański, “Optimization of output power in lasers,” Opt. Eng. 31, 440–446 (1992).
[CrossRef]

A. Kujawski, P. Szczepański, “Simple model of gain saturation in homogeneously CW lasers with distributed losses,” J. Mod. Opt. 38, 1901–1909 (1991).
[CrossRef]

Laakmann, K. D.

Latham, W. P.

Maloney, P. J.

P. W. Smith, O. R. Wood, P. J. Maloney, C. R. Adams, “Transversly excited waveguide gas lasers,” IEEE J. Quantum Electron. QE-17, 1166–1181 (1981).
[CrossRef]

Newman, L. A.

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Cantor, A. J. DeMaria, “High power coupled CO2 waveguide laser array,” Appl. Phys. Lett. 48, 1701–1703 (1986).
[CrossRef]

Ponath, H.-E.

Rigrod, W. W.

W. W. Rigrod, “Homogeneously broadened cw lasers with uniform distributed loss,” IEEE J. Quantum Electron. QE-14, 377–381 (1978).
[CrossRef]

W. W. Rigrod, “Saturation effects in high-gain lasers,” J. Appl. Phys. 36, 2487–2490 (1965).
[CrossRef]

Schroder, B.

B. Schroder, “Transverse modes of active hollow waveguide resonators,” IEEE J. Quantum Electron. QE-27, 158–166 (1991).
[CrossRef]

Schultz, E. O.

F. T. Arecchi, E. O. Schultz, Laser Handbook (North-Holland, Amsterdam, 1972), Vol. 1, Chap. 4.

Sentman, L. H.

Shindler, G.

G. Shindler, “Optimum output efficiency of homogenously broadened lasers with constant loss,” IEEE J. Quantum Electron. QE-15, 546–549 (1980).
[CrossRef]

Sklodowska, M.

P. Szczepański, M. Skłodowska, W. Woliński, “Gain saturation in fiber distributed feedback lasers,” J. Lightwave Technol. 9, 329–334 (1991).
[CrossRef]

Smith, P. W.

P. W. Smith, O. R. Wood, P. J. Maloney, C. R. Adams, “Transversly excited waveguide gas lasers,” IEEE J. Quantum Electron. QE-17, 1166–1181 (1981).
[CrossRef]

P. W. Smith, “A waveguide gas laser,” Appl. Phys. Lett. 19, 132–134 (1971).
[CrossRef]

Steffen, H.

H. Steffen, F. K. Kneubuhl, “Dielectric tube resonators for infrared and submillimeter wave lasers,” Phys. Lett. A 27, 612–613 (1968).
[CrossRef]

Steier, W. H.

Szczepanski, P.

A. Kujawski, P. Szczepański, “Influence of the position of the gain medium on laser output power,” Opt. Commun. 106, 231–236 (1994).
[CrossRef]

A. Kujawski, P. Szczepański, “Optimization of output power in lasers,” Opt. Eng. 31, 440–446 (1992).
[CrossRef]

A. Kujawski, P. Szczepański, “Model of gain saturation in a two-mirror laser: single mode operation,” J. Mod. Opt. 39, 2519–2529 (1992).
[CrossRef]

P. Szczepański, M. Skłodowska, W. Woliński, “Gain saturation in fiber distributed feedback lasers,” J. Lightwave Technol. 9, 329–334 (1991).
[CrossRef]

A. Kujawski, P. Szczepański, “Simple model of gain saturation in homogeneously CW lasers with distributed losses,” J. Mod. Opt. 38, 1901–1909 (1991).
[CrossRef]

K. Janulewicz, P. Szczepański, “Approximate analytical method of gain saturation analysis of hollow waveguide lasers,” Appl. Opt. 30, 3818–3820 (1991).
[CrossRef] [PubMed]

Wolinski, W.

P. Szczepański, M. Skłodowska, W. Woliński, “Gain saturation in fiber distributed feedback lasers,” J. Lightwave Technol. 9, 329–334 (1991).
[CrossRef]

Wood, O. R.

P. W. Smith, O. R. Wood, P. J. Maloney, C. R. Adams, “Transversly excited waveguide gas lasers,” IEEE J. Quantum Electron. QE-17, 1166–1181 (1981).
[CrossRef]

Youmans, D. G.

D. G. Youmans, “Phase locking of adjacent channel leaky waveguide CO2 lasers,” Appl. Phys. Lett. 44, 365–367 (1984).
[CrossRef]

Appl. Opt. (7)

Appl. Phys. (1)

J. J. Degan, “The waveguide laser: a review,” Appl. Phys. 11, 1–33 (1976).
[CrossRef]

Appl. Phys. Lett. (3)

P. W. Smith, “A waveguide gas laser,” Appl. Phys. Lett. 19, 132–134 (1971).
[CrossRef]

D. G. Youmans, “Phase locking of adjacent channel leaky waveguide CO2 lasers,” Appl. Phys. Lett. 44, 365–367 (1984).
[CrossRef]

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Cantor, A. J. DeMaria, “High power coupled CO2 waveguide laser array,” Appl. Phys. Lett. 48, 1701–1703 (1986).
[CrossRef]

IEEE J. Quantum Electron. (12)

C. A. Hill, “Tunable RF-excited CO2 waveguide laser with variable guide width,” IEEE J. Quantum Electron. QE-23, 1968–1973 (1987).
[CrossRef]

K. H. Abramski, A. D. Colley, H. J. Baker, D. R. Hall, “Offset frequency stabilization of RF excited waveguide CO2 laser arrays,” IEEE J. Quantum Electron. 27, 711–717 (1990).
[CrossRef]

A. D. Colley, K. H. Abramski, H. J. Baker, D. R. Hall, “Discharge-induced frequency modulation of RF excited CO2 waveguide lasers,” IEEE J. Quantum Electron. 27, 1939–1945 (1990).
[CrossRef]

C. A. Hill, P. E. Jackson, “Hooting modes in a CO2 waveguide laser,” IEEE J. Quantum Electron. QE-24, 1976–1980 (1984).

D. He, D. R. Hall, “Frequency dependence in REF discharge excited waveguide CO2 lasers,” IEEE J. Quantum Electron. QE-20, 509–514 (1984).
[CrossRef]

C. A. Hill, “Transverse modes of plane-mirror waveguide resonators,” IEEE J. Quantum Electron. QE-24, 1936–1945 (1988).
[CrossRef]

J. Bemnerji, A. R. Devies, P. E. Jackson, R. M. Jenkins, “Transmission and coupling losses in folded waveguide,” IEEE J. Quantum Electron. QE-26, 701–709 (1990).

B. Schroder, “Transverse modes of active hollow waveguide resonators,” IEEE J. Quantum Electron. QE-27, 158–166 (1991).
[CrossRef]

W. W. Rigrod, “Homogeneously broadened cw lasers with uniform distributed loss,” IEEE J. Quantum Electron. QE-14, 377–381 (1978).
[CrossRef]

G. Shindler, “Optimum output efficiency of homogenously broadened lasers with constant loss,” IEEE J. Quantum Electron. QE-15, 546–549 (1980).
[CrossRef]

P. W. Smith, O. R. Wood, P. J. Maloney, C. R. Adams, “Transversly excited waveguide gas lasers,” IEEE J. Quantum Electron. QE-17, 1166–1181 (1981).
[CrossRef]

C. A. Hill, D. R. Hall, “Waveguide laser resonator with a titled mirror,” IEEE J. Quantum Electron. QE-22, 1078–1087 (1987).

J. Appl. Phys. (2)

W. W. Rigrod, “Saturation effects in high-gain lasers,” J. Appl. Phys. 36, 2487–2490 (1965).
[CrossRef]

D. Eimerl, “Optical extraction characteristics of homogeneously broadened cw lasers with nonsaturable loss,” J. Appl. Phys. 51, 3008–3016 (1980).
[CrossRef]

J. Lightwave Technol. (1)

P. Szczepański, M. Skłodowska, W. Woliński, “Gain saturation in fiber distributed feedback lasers,” J. Lightwave Technol. 9, 329–334 (1991).
[CrossRef]

J. Mod. Opt. (2)

A. Kujawski, P. Szczepański, “Simple model of gain saturation in homogeneously CW lasers with distributed losses,” J. Mod. Opt. 38, 1901–1909 (1991).
[CrossRef]

A. Kujawski, P. Szczepański, “Model of gain saturation in a two-mirror laser: single mode operation,” J. Mod. Opt. 39, 2519–2529 (1992).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

A. Kujawski, P. Szczepański, “Influence of the position of the gain medium on laser output power,” Opt. Commun. 106, 231–236 (1994).
[CrossRef]

Opt. Eng. (1)

A. Kujawski, P. Szczepański, “Optimization of output power in lasers,” Opt. Eng. 31, 440–446 (1992).
[CrossRef]

Phys. Lett. A (1)

H. Steffen, F. K. Kneubuhl, “Dielectric tube resonators for infrared and submillimeter wave lasers,” Phys. Lett. A 27, 612–613 (1968).
[CrossRef]

Other (3)

R. L. Abrams, “Waveguide gas lasers,” in Laser Handbook, M. L. Stitch, ed. (North-Holland, Amsterdam, 1979), pp. 41–88.

D. R. Hall, P. E. Jackson, The Physics and Technology of Laser Resonators (Hiller, Bristol, New York, 1989), Chap. 3.

F. T. Arecchi, E. O. Schultz, Laser Handbook (North-Holland, Amsterdam, 1972), Vol. 1, Chap. 4.

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Figures (10)

Fig. 1
Fig. 1

Waveguide laser configuration considered in this paper.

Fig. 2
Fig. 2

Small-signal gain g0 as a function of the output-mirror reflectivity coefficient r2 for several cross sections of the waveguide. The distance between the end mirrors and the waveguide is z1 = z2 = 1 mm. The losses between the end mirrors and the waveguides are neglected.

Fig. 3
Fig. 3

Small-signal gain g0 plotted versus output-mirror reflectivity coefficient r2 for several cross sections of the waveguide. The distance between the total reflecting mirror and the waveguide and the output mirror and the waveguide are z1 = 1 mm and z2 = 1000 mm, respectively.

Fig. 4
Fig. 4

Small-signal gain g0 as a function of the normalized distance between the waveguide and the output mirror relative to the curvature radius of the output mirror z2/R2 for the two output-mirror reflectivities. The width and the height of the waveguide are a = 2.0 mm.

Fig. 5
Fig. 5

Small-signal gain g0 as a function of the normalized distance between the waveguide and the output mirror relative to the curvature radius of the output mirror z2/R2 for two output-mirror reflectivities. The width and the height of the waveguide are a = 2.44 mm.

Fig. 6
Fig. 6

Small-signal gain g0 plotted versus the normalized distance between the waveguide and the output mirror relative to the curvature radius of the output mirror z2/R2 for two values of the output-mirror reflectivity coefficient r2. The width and the height of the waveguide are a = 2.9 mm.

Fig. 7
Fig. 7

Small-signal gain g0 plotted as a function of the normalized distance between the waveguide and the output mirror relative to the curvature radius of the output mirror, z2/R2, for several values of the output-mirror reflectivity coefficient r2.

Fig. 8
Fig. 8

Dependence of the small-signal gain g0 on the normalized distance between the waveguide and the output mirror relative to the curvature radius of the output-mirror, z2/R2, for several normalized output-power levels Pout/Ps. The output-mirror reflectivity is r2 = 0.89.

Fig. 9
Fig. 9

Small-signal gain g0 as a function of the normalized distance between the waveguide and the output mirror relative to the curvature radius of the output mirror, z2/R2, for several output-power levels. The output-mirror reflectivity is r2 = 0.2.

Fig. 10
Fig. 10

Dependence of the small-signal gain g0 on the normalized distance between the waveguide and the output mirror relative to the curvature radius of the mirror, z2/R2, for two output-mirror reflectivities. The losses between the end mirrors and the waveguide equal α1 = α2 = 0.005 cm−1.

Equations (31)

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E m n q R ( x , y , z ) = R m n q ( z ) E m n R ( x , y , z ) ,
E m n q S ( x , y , z ) = S m n R ( z ) E m n S ( x , y , z ) ,
E m n q R ( x , y , z ) = E m n S ( x , y , z ) = E m n ( x , y , z ) .
d ( I,II R m n q ) d z + ( i δ m n q + α 1 , 2 ) ( I,II R m n q ) = 0 ,
d ( I,II S m n q ) d z + ( i δ m n q + α 1 , 2 ) ( I,II S m n q ) = 0 ,
d ( III R m n q ) d z + [ ( i δ m n q g ) + α 0 ] ( III R m n q ) = 0 ,
d ( III S m n q ) d z + [ ( i δ m n q g ) + α 0 ] ( III S m n q ) = 0 ,
g = k 0 2 β m n III E m n s g 0 f ( x , y , z ) | III E m n ( x , y , z ) | 2 1 + [ | III R m n q ( z ) | 2 + | III S m n q ( z ) | 2 ] | III E m n ( x , y , z ) | 2 P S d s ,
d d z ( | I,II R m n q | 2 | I,II S m n q | 2 ) = 2 α 1 , 2 ( | I,II R m n q | 2 + | I,II S m n q | 2 ) .
d d z ( | III R m n q | 2 | III S m n q | 2 ) = 2 α 0 ( | III R m n q | 2 + | III S m n q | 2 ) + k 0 β m n III E m n × s g 0 f ( x , y , z ) | III E m n ( x , y , z ) | 2 [ | III R m n q ( z ) | 2 + | III S m n q ( z ) | 2 ] 1 + [ | III R m n q ( z ) | 2 + | III S m n q ( z ) | 2 ] | III E m n ( x , y , z ) | 2 P S d s .
d d z ( | I R m n q | 2 | I S m n q | 2 + | II R m n q | 2 | II S m n q | 2 + | III R m n q | 2 | III S m n q | 2 ) = 2 α 1 ( | I R m n q | 2 + | I S m n q | 2 ) 2 α 2 ( | II R m n q | 2 + | II S m n q | 2 ) 2 α 0 ( | III R m n q | 2 + | III S m n q | 2 ) + k 0 β m n III E m n s g 0 f ( x , y , z ) | III E m n ( x , y , z ) | 2 [ | III R m n q ( z ) | 2 + | III S m n q ( z ) | 2 ] 1 + [ | III R m n q ( z ) | 2 + | III S m n q ( z ) | 2 ] | III E m n ( x , y , z ) | 2 P S d s .
| I R m n q ( 0 ) | 2 = r 1 2 | I S m n q ( 0 ) | 2 , [ ( 1 a 1 2 ) r 1 2 ] | I S m n q ( 0 ) | 2 s | I E m n ( x , y , 0 ) | 2 d s = P m n q S ,
| III R m n q ( L tot ) | 2 r 2 2 = | III S m n q ( L tot ) | 2 , [ ( 1 a 2 2 ) r 2 2 ] | III S m n q ( L tot ) | 2 s | III E m n ( x , y , L tot ) | 2 d s = P m n q R ,
| I R m n q ( z 1 ) | 2 η 1 = | III R m n q ( z 1 ) | 2 , | III S m n q ( z 1 ) | 2 η 1 = | I S m n q ( z 1 ) | 2 ,
| III R m n q ( z 1 + L ) | 2 η 2 = | II R m n q ( z 1 + L ) | 2 , | II S m n q ( z 1 + L ) | 2 η 2 = | III S m n q ( z 1 + L ) | 2 ,
η 1 mn,m′n′ = η 1 = { s [ I E m n ( x , y , z 1 ) ] * [ III E m n ( x , y , z 1 ) ] ds } 2 I E m n ( x , y , z 1 ) III E m n ( x , y , z 1 ) ,
η 2 mn,m′n′ = η 2 = { s [ III E m n ( x , y , z 1 + L ) ] * [ III E m n ( x , y , z 1 + L ) ] ds } 2 I E m n ( x , y , z 1 + L ) III E m n ( x , y , z 1 + L ) .
| II R m n q ( L tot ) | 2 ( 1 r 2 2 ) + | I S m n q ( 0 ) | 2 ( 1 r 1 2 ) + | I R m n q ( z 1 ) | 2 ( 1 η 1 ) + | III S m n q ( z 1 ) | 2 ( 1 η 1 ) + | III R m n q ( z 1 + L ) | 2 ( 1 η 2 ) + | II S m n q ( z 1 + L ) | 2 ( 1 η 2 ) + 0 z 1 2 α 1 [ | I R m n q ( z ) | 2 + | I S m n q ( z ) | 2 ] d z + z 1 z 1 + L 2 α 0 [ | III R m n q ( z ) | 2 + | III S m n q ( z ) | 2 ] + z 1 + L L tot 2 α 2 [ | II R m n q ( z ) | 2 + | II S m n q ( z ) | 2 ] = k 0 β m n III E m n z 1 z 1 + L d z s g 0 f ( x , y , z ) | III E m n ( x , y , z ) | 2 [ | III R m n q ( z ) | 2 + | III S m n q ( z ) | 2 ] 1 + [ | III R m n q ( z ) | 2 + | III S m n q ( z ) | 2 ] | III E m n ( x , y , z ) | 2 P s d s .
| I R m n q ( z ) | = A exp ( α 1 z ) ,
| I S m n q ( z ) | = A exp ( α 1 z ) ,
| II R m n q ( z ) | = C r 2 exp [ α 2 ( z L tot ) ] ,
| II S m n q ( z ) | = C exp [ α 2 ( z L tot ) ] ,
| II i R m n q ( z ) | = B exp [ γ ( z z 1 ) ] ,
| III S m n q ( z ) | = B r 1 η 1 exp ( 2 α 1 z 1 ) exp [ γ ( z z 1 ) ] ,
γ = 1 2 L [ 2 α 1 z 1 + 2 α 2 z 2 + ln ( 1 η 1 η 2 r 1 r 2 ) ] .
A 2 = B 2 exp ( 2 α 1 z 1 ) η 1 , C 2 = B 2 r 2 r 1 exp ( 2 α 1 z 1 ) η 1 .
B 2 = P out r 1 η 1 exp ( 2 α 1 z 1 ) [ ( 1 a 1 2 ) r 1 2 r 1 I E m n ( x , y , 0 ) + ( 1 a 2 2 ) r 2 2 r 2 II E m n ( x , y , L tot ) ] 1 .
g 0 = ( { [ exp ( 2 γ L ) 1 ] [ exp ( 2 γ L ) 1 ] exp ( 4 α 1 z 1 ) r 1 2 η 1 2 } ( 1 + α 0 γ ) ) × { k 0 β m n III E m n z 1 z 1 + L d z s f ( x , y , z ) | III E m n ( x , y , z ) | 2 [ | III R m n q ( z ) | 2 + | III S m n q ( z ) | 2 ] 1 + P out P s [ | III R m n q ( z ) | 2 + | III S m n q ( z ) | 2 ] | III E m n ( x , y , z ) | 2 N d s } 1 ,
| III R m n q ( z ) | 2 + | III S m n q ( z ) | 2 = exp [ 2 γ ( z z 1 ) ] + exp [ 2 γ ( z z 1 ) ] exp ( 4 α 1 z 1 ) r 1 2 η 1 2 ,
III E m n ( x , y , z ) = { ( m π x 2 a ) sin cos × ( n π x 2 b ) sin cos } , m , n = { even odd ,
N = exp ( 2 α 1 z 1 ) r 1 η 1 [ ( 1 a 1 2 ) r 1 2 r 1 I E m n ( x , y , 0 ) + ( 1 a 2 2 ) r 2 2 r 2 E m n ( x , y , L tot ) ] .

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