Abstract

A He–Ne laser with an annular gain zone is studied theoretically. It is demonstrated that the He–Ne medium in the annular discharge zone possesses enough gain to maintain laser oscillation. A multipass ring resonator, which is composed of two annular spherical mirrors, is described, and it is shown that the resonator is suitable for extracting optical energy from the He–Ne medium in the annular gain zone. Considering the availability of population inversion in the traveling-wave cavity and the influence of the crossover of the folded light beam in the resonator on the output power, a calculation formula for the output power of the laser with the multipass ring resonator is given. Calculating results prove that a 1 W output of the He–Ne laser can be obtained by a 1  m length annular discharge zone.

© 2007 Optical Society of America

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References

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  1. M. Morin and P.-A. Belanger, "Diffractive analysis of annular resonators," Appl. Opt. 31, 1942-1947 (1992).
    [CrossRef] [PubMed]
  2. R. K. Garnsworthy, L. E. S. Mathias, and C. H. H. Carmichael, "Atmospheric-pressure pulsed CO2 laser utilizing preionization by high-energy electrons," Appl. Phys. Lett. 19, 506-508 (1971).
    [CrossRef]
  3. L. W. Casperson and M. Shabbir Shekhani, "Mode properties of annular gain lasers," Appl. Opt. 14, 2653-2661 (1975).
    [CrossRef] [PubMed]
  4. G. R. Osche and H. E. Sonntag, "A compact cylindrical CO2 TEA laser," IEEE J. Quantum Electron. , QE-12, 752-756 (1976).
    [CrossRef]
  5. K. T. K. Cheng and L. W. Casperson, "Properties of a coaxial cw CO2 laser," Appl. Opt. 18, 2130-2135 (1979).
    [CrossRef] [PubMed]
  6. J. G. Xin and D. R. Hall, "Compact, multipass, single transverse mode CO2 laser," Appl. Phys. Lett. 51, 469-471 (1987).
    [CrossRef]
  7. T. Tamida and J.-i. Nishimae, "Annular resonator with a Cassegrain configuration," Appl. Opt. 36, 5844-5848 (1997).
    [CrossRef] [PubMed]
  8. P. Burlamacchi and R. Pratesi, "High-efficiency coaxial waveguide dye laser with internal excitation," Appl. Phys. Lett. 23, 475-476 (1973).
    [CrossRef]
  9. U. Wittrock, H. Weber, and B. Eppich, "Inside-pumped Nd:YAG tube laser," Opt. Lett. 16, 1092-1094 (1991).
    [CrossRef] [PubMed]
  10. D. Milam and H. Schlossberg, "Emission characteristics of a tube-shaped laser oscillator," J. Appl. Phys. 44, 2297-2299 (1973).
    [CrossRef]
  11. U. Wittrock and H. Weber, "Inside-pumped Nd:YAG tube laser with 7.5% efficiency," in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, 1991), pp. 370-371.
  12. U. Wittrock, B. Eppich, and H. Weber, "Beam quality of the 1-kw inside-pumped Nd:YAG tube laser," in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, 1992), pp. 94-95.
  13. Y. Takada, H. Saito, and T. Fujioka, "Eigenmode of an annular stable resonator," IEEE J. Quantum Electron. 24, 11-12 (1988).
    [CrossRef]
  14. D. Ehrlichmann, U. Habich, H.-D. Plum, P. Loosen, and G. Herziger, "Azimuthally unstable resonators for high-power CO2 lasers with annular gain media," IEEE J. Quantum Electron. 30, 1441-1447 (1994).
    [CrossRef]
  15. R. A. Chodzko, S. B. Mason, and E. F. Cross, "Annular converging wave cavity," Appl. Opt. 15, 2137-2144 (1976).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  19. D. Ehrlichmann, U. Habich, and H.-D. Plum, "Ring resonator for lasers with annular gain media," Appl. Opt. 33, 6919-6924 (1994).
    [CrossRef] [PubMed]
  20. O. Svelto and D. C. Hanna, Principles of Lasers (Plenum, 1982), pp. 207-210.
  21. Y. Ling, M. Qian, and P. Lu, "Study of a high-powered He-Ne laser having rectangular discharge cross section," Rev. Sci. Instrum. 66, 4055-4058 (1995).
    [CrossRef]
  22. Z. Jing, S. Hongmin, and Z. Huiguo, "Photodynamic therapy of malignancy of skin with a He-Ne laser," Chin. J. Lasers A27, 95-96 (2000) (in Chinese).
  23. J. D. Cobine, Gaseous Conductors (McGraw-Hill, 1958), pp. 151, 236-239.
  24. Chengdu Institute of Radio Engineering, Beijing Institute of Technology, Laser (Press of Science and Technology, 1983), pp. 30-31, 65 (in Chinese).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  27. L. Zhiguo, L. Jianghong, D. A. Andrews, and T. A. King. "Investigation of a microwave discharge He-Ne laser," Chin. J. Lasers A21, 705-708 (1994) (in Chinese).
  28. g0 ≈ 1.34 × 10-3 to 2 × 10-3 cm-1 has been obtained by rf excitation when R1 = 20 mm, R2 = 23 mm, d = 3 mm, He:Ne = 9:1, and the mixture pressure is 0.8 × 133.3 Pa. A report on the experimental procedures and data will be given in another paper.
  29. Y. Jinji, Discharge through Gas, 1st ed. (Science, 1983, p. 22 (in Chinese).

2000 (1)

Z. Jing, S. Hongmin, and Z. Huiguo, "Photodynamic therapy of malignancy of skin with a He-Ne laser," Chin. J. Lasers A27, 95-96 (2000) (in Chinese).

1997 (1)

1995 (1)

Y. Ling, M. Qian, and P. Lu, "Study of a high-powered He-Ne laser having rectangular discharge cross section," Rev. Sci. Instrum. 66, 4055-4058 (1995).
[CrossRef]

1994 (3)

D. Ehrlichmann, U. Habich, H.-D. Plum, P. Loosen, and G. Herziger, "Azimuthally unstable resonators for high-power CO2 lasers with annular gain media," IEEE J. Quantum Electron. 30, 1441-1447 (1994).
[CrossRef]

L. Zhiguo, L. Jianghong, D. A. Andrews, and T. A. King. "Investigation of a microwave discharge He-Ne laser," Chin. J. Lasers A21, 705-708 (1994) (in Chinese).

D. Ehrlichmann, U. Habich, and H.-D. Plum, "Ring resonator for lasers with annular gain media," Appl. Opt. 33, 6919-6924 (1994).
[CrossRef] [PubMed]

1992 (1)

1991 (1)

1988 (1)

Y. Takada, H. Saito, and T. Fujioka, "Eigenmode of an annular stable resonator," IEEE J. Quantum Electron. 24, 11-12 (1988).
[CrossRef]

1987 (2)

H. Schülke, G. Herziger, and R. Weste, "Multipass resonators for laser systems," in High Power Laser: Sources, Laser-Material Interactions, High Excitations, and Fast Dynamics, E. W. Kreutz, A. Quenzer, and D. Schuöcker, eds., Proc. SPIE 801, 45-50 (1987).

J. G. Xin and D. R. Hall, "Compact, multipass, single transverse mode CO2 laser," Appl. Phys. Lett. 51, 469-471 (1987).
[CrossRef]

1980 (3)

1979 (1)

1977 (1)

1976 (2)

R. A. Chodzko, S. B. Mason, and E. F. Cross, "Annular converging wave cavity," Appl. Opt. 15, 2137-2144 (1976).
[CrossRef] [PubMed]

G. R. Osche and H. E. Sonntag, "A compact cylindrical CO2 TEA laser," IEEE J. Quantum Electron. , QE-12, 752-756 (1976).
[CrossRef]

1975 (1)

1973 (2)

P. Burlamacchi and R. Pratesi, "High-efficiency coaxial waveguide dye laser with internal excitation," Appl. Phys. Lett. 23, 475-476 (1973).
[CrossRef]

D. Milam and H. Schlossberg, "Emission characteristics of a tube-shaped laser oscillator," J. Appl. Phys. 44, 2297-2299 (1973).
[CrossRef]

1971 (1)

R. K. Garnsworthy, L. E. S. Mathias, and C. H. H. Carmichael, "Atmospheric-pressure pulsed CO2 laser utilizing preionization by high-energy electrons," Appl. Phys. Lett. 19, 506-508 (1971).
[CrossRef]

Andrews, D. A.

L. Zhiguo, L. Jianghong, D. A. Andrews, and T. A. King. "Investigation of a microwave discharge He-Ne laser," Chin. J. Lasers A21, 705-708 (1994) (in Chinese).

Belanger, P.-A.

Brickman, R. O.

Burlamacchi, P.

P. Burlamacchi and R. Pratesi, "High-efficiency coaxial waveguide dye laser with internal excitation," Appl. Phys. Lett. 23, 475-476 (1973).
[CrossRef]

Byer, R. L.

Carmichael, C. H. H.

R. K. Garnsworthy, L. E. S. Mathias, and C. H. H. Carmichael, "Atmospheric-pressure pulsed CO2 laser utilizing preionization by high-energy electrons," Appl. Phys. Lett. 19, 506-508 (1971).
[CrossRef]

Casperson, L. W.

Cheng, K. T. K.

Chodzko, R. A.

Cobine, J. D.

J. D. Cobine, Gaseous Conductors (McGraw-Hill, 1958), pp. 151, 236-239.

Cross, E. F.

Ehrlichmann, D.

D. Ehrlichmann, U. Habich, and H.-D. Plum, "Ring resonator for lasers with annular gain media," Appl. Opt. 33, 6919-6924 (1994).
[CrossRef] [PubMed]

D. Ehrlichmann, U. Habich, H.-D. Plum, P. Loosen, and G. Herziger, "Azimuthally unstable resonators for high-power CO2 lasers with annular gain media," IEEE J. Quantum Electron. 30, 1441-1447 (1994).
[CrossRef]

Eppich, B.

U. Wittrock, H. Weber, and B. Eppich, "Inside-pumped Nd:YAG tube laser," Opt. Lett. 16, 1092-1094 (1991).
[CrossRef] [PubMed]

U. Wittrock, B. Eppich, and H. Weber, "Beam quality of the 1-kw inside-pumped Nd:YAG tube laser," in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, 1992), pp. 94-95.

Erkkila, J. H.

Fujioka, T.

Y. Takada, H. Saito, and T. Fujioka, "Eigenmode of an annular stable resonator," IEEE J. Quantum Electron. 24, 11-12 (1988).
[CrossRef]

Garnsworthy, R. K.

R. K. Garnsworthy, L. E. S. Mathias, and C. H. H. Carmichael, "Atmospheric-pressure pulsed CO2 laser utilizing preionization by high-energy electrons," Appl. Phys. Lett. 19, 506-508 (1971).
[CrossRef]

Habich, U.

D. Ehrlichmann, U. Habich, and H.-D. Plum, "Ring resonator for lasers with annular gain media," Appl. Opt. 33, 6919-6924 (1994).
[CrossRef] [PubMed]

D. Ehrlichmann, U. Habich, H.-D. Plum, P. Loosen, and G. Herziger, "Azimuthally unstable resonators for high-power CO2 lasers with annular gain media," IEEE J. Quantum Electron. 30, 1441-1447 (1994).
[CrossRef]

Hall, D. R.

J. G. Xin and D. R. Hall, "Compact, multipass, single transverse mode CO2 laser," Appl. Phys. Lett. 51, 469-471 (1987).
[CrossRef]

Hanna, D. C.

O. Svelto and D. C. Hanna, Principles of Lasers (Plenum, 1982), pp. 207-210.

Herziger, G.

D. Ehrlichmann, U. Habich, H.-D. Plum, P. Loosen, and G. Herziger, "Azimuthally unstable resonators for high-power CO2 lasers with annular gain media," IEEE J. Quantum Electron. 30, 1441-1447 (1994).
[CrossRef]

H. Schülke, G. Herziger, and R. Weste, "Multipass resonators for laser systems," in High Power Laser: Sources, Laser-Material Interactions, High Excitations, and Fast Dynamics, E. W. Kreutz, A. Quenzer, and D. Schuöcker, eds., Proc. SPIE 801, 45-50 (1987).

Hongmin, S.

Z. Jing, S. Hongmin, and Z. Huiguo, "Photodynamic therapy of malignancy of skin with a He-Ne laser," Chin. J. Lasers A27, 95-96 (2000) (in Chinese).

Huiguo, Z.

Z. Jing, S. Hongmin, and Z. Huiguo, "Photodynamic therapy of malignancy of skin with a He-Ne laser," Chin. J. Lasers A27, 95-96 (2000) (in Chinese).

Jianghong, L.

L. Zhiguo, L. Jianghong, D. A. Andrews, and T. A. King. "Investigation of a microwave discharge He-Ne laser," Chin. J. Lasers A21, 705-708 (1994) (in Chinese).

Jing, Z.

Z. Jing, S. Hongmin, and Z. Huiguo, "Photodynamic therapy of malignancy of skin with a He-Ne laser," Chin. J. Lasers A27, 95-96 (2000) (in Chinese).

Jinji, Y.

Y. Jinji, Discharge through Gas, 1st ed. (Science, 1983, p. 22 (in Chinese).

King, T. A.

L. Zhiguo, L. Jianghong, D. A. Andrews, and T. A. King. "Investigation of a microwave discharge He-Ne laser," Chin. J. Lasers A21, 705-708 (1994) (in Chinese).

Ling, Y.

Y. Ling, M. Qian, and P. Lu, "Study of a high-powered He-Ne laser having rectangular discharge cross section," Rev. Sci. Instrum. 66, 4055-4058 (1995).
[CrossRef]

Loosen, P.

D. Ehrlichmann, U. Habich, H.-D. Plum, P. Loosen, and G. Herziger, "Azimuthally unstable resonators for high-power CO2 lasers with annular gain media," IEEE J. Quantum Electron. 30, 1441-1447 (1994).
[CrossRef]

Lu, P.

Y. Ling, M. Qian, and P. Lu, "Study of a high-powered He-Ne laser having rectangular discharge cross section," Rev. Sci. Instrum. 66, 4055-4058 (1995).
[CrossRef]

Mason, S. B.

Mathias, L. E. S.

R. K. Garnsworthy, L. E. S. Mathias, and C. H. H. Carmichael, "Atmospheric-pressure pulsed CO2 laser utilizing preionization by high-energy electrons," Appl. Phys. Lett. 19, 506-508 (1971).
[CrossRef]

Milam, D.

D. Milam and H. Schlossberg, "Emission characteristics of a tube-shaped laser oscillator," J. Appl. Phys. 44, 2297-2299 (1973).
[CrossRef]

Morin, M.

Nishimae, J.-i.

Osche, G. R.

G. R. Osche and H. E. Sonntag, "A compact cylindrical CO2 TEA laser," IEEE J. Quantum Electron. , QE-12, 752-756 (1976).
[CrossRef]

Paxton, A. H.

Perry, B.

Plum, H.-D.

D. Ehrlichmann, U. Habich, and H.-D. Plum, "Ring resonator for lasers with annular gain media," Appl. Opt. 33, 6919-6924 (1994).
[CrossRef] [PubMed]

D. Ehrlichmann, U. Habich, H.-D. Plum, P. Loosen, and G. Herziger, "Azimuthally unstable resonators for high-power CO2 lasers with annular gain media," IEEE J. Quantum Electron. 30, 1441-1447 (1994).
[CrossRef]

Plummer, W. W.

Pratesi, R.

P. Burlamacchi and R. Pratesi, "High-efficiency coaxial waveguide dye laser with internal excitation," Appl. Phys. Lett. 23, 475-476 (1973).
[CrossRef]

Qian, M.

Y. Ling, M. Qian, and P. Lu, "Study of a high-powered He-Ne laser having rectangular discharge cross section," Rev. Sci. Instrum. 66, 4055-4058 (1995).
[CrossRef]

Rabinowitz, P.

Saito, H.

Y. Takada, H. Saito, and T. Fujioka, "Eigenmode of an annular stable resonator," IEEE J. Quantum Electron. 24, 11-12 (1988).
[CrossRef]

Schlossberg, H.

D. Milam and H. Schlossberg, "Emission characteristics of a tube-shaped laser oscillator," J. Appl. Phys. 44, 2297-2299 (1973).
[CrossRef]

Schülke, H.

H. Schülke, G. Herziger, and R. Weste, "Multipass resonators for laser systems," in High Power Laser: Sources, Laser-Material Interactions, High Excitations, and Fast Dynamics, E. W. Kreutz, A. Quenzer, and D. Schuöcker, eds., Proc. SPIE 801, 45-50 (1987).

Shekhani, M. Shabbir

Sonntag, H. E.

G. R. Osche and H. E. Sonntag, "A compact cylindrical CO2 TEA laser," IEEE J. Quantum Electron. , QE-12, 752-756 (1976).
[CrossRef]

Stein, A.

Svelto, O.

O. Svelto and D. C. Hanna, Principles of Lasers (Plenum, 1982), pp. 207-210.

Takada, Y.

Y. Takada, H. Saito, and T. Fujioka, "Eigenmode of an annular stable resonator," IEEE J. Quantum Electron. 24, 11-12 (1988).
[CrossRef]

Tamida, T.

Treacy, E. B.

Trutna, W. R.

Turner, E. B.

Weber, H.

U. Wittrock, H. Weber, and B. Eppich, "Inside-pumped Nd:YAG tube laser," Opt. Lett. 16, 1092-1094 (1991).
[CrossRef] [PubMed]

U. Wittrock and H. Weber, "Inside-pumped Nd:YAG tube laser with 7.5% efficiency," in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, 1991), pp. 370-371.

U. Wittrock, B. Eppich, and H. Weber, "Beam quality of the 1-kw inside-pumped Nd:YAG tube laser," in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, 1992), pp. 94-95.

Weste, R.

H. Schülke, G. Herziger, and R. Weste, "Multipass resonators for laser systems," in High Power Laser: Sources, Laser-Material Interactions, High Excitations, and Fast Dynamics, E. W. Kreutz, A. Quenzer, and D. Schuöcker, eds., Proc. SPIE 801, 45-50 (1987).

Wittrock, U.

U. Wittrock, H. Weber, and B. Eppich, "Inside-pumped Nd:YAG tube laser," Opt. Lett. 16, 1092-1094 (1991).
[CrossRef] [PubMed]

U. Wittrock and H. Weber, "Inside-pumped Nd:YAG tube laser with 7.5% efficiency," in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, 1991), pp. 370-371.

U. Wittrock, B. Eppich, and H. Weber, "Beam quality of the 1-kw inside-pumped Nd:YAG tube laser," in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, 1992), pp. 94-95.

Xin, J. G.

J. G. Xin and D. R. Hall, "Compact, multipass, single transverse mode CO2 laser," Appl. Phys. Lett. 51, 469-471 (1987).
[CrossRef]

Zhiguo, L.

L. Zhiguo, L. Jianghong, D. A. Andrews, and T. A. King. "Investigation of a microwave discharge He-Ne laser," Chin. J. Lasers A21, 705-708 (1994) (in Chinese).

Appl. Opt. (8)

Appl. Phys. Lett. (3)

P. Burlamacchi and R. Pratesi, "High-efficiency coaxial waveguide dye laser with internal excitation," Appl. Phys. Lett. 23, 475-476 (1973).
[CrossRef]

J. G. Xin and D. R. Hall, "Compact, multipass, single transverse mode CO2 laser," Appl. Phys. Lett. 51, 469-471 (1987).
[CrossRef]

R. K. Garnsworthy, L. E. S. Mathias, and C. H. H. Carmichael, "Atmospheric-pressure pulsed CO2 laser utilizing preionization by high-energy electrons," Appl. Phys. Lett. 19, 506-508 (1971).
[CrossRef]

Chin. J. Lasers (2)

L. Zhiguo, L. Jianghong, D. A. Andrews, and T. A. King. "Investigation of a microwave discharge He-Ne laser," Chin. J. Lasers A21, 705-708 (1994) (in Chinese).

Z. Jing, S. Hongmin, and Z. Huiguo, "Photodynamic therapy of malignancy of skin with a He-Ne laser," Chin. J. Lasers A27, 95-96 (2000) (in Chinese).

IEEE J. Quantum Electron. (3)

G. R. Osche and H. E. Sonntag, "A compact cylindrical CO2 TEA laser," IEEE J. Quantum Electron. , QE-12, 752-756 (1976).
[CrossRef]

Y. Takada, H. Saito, and T. Fujioka, "Eigenmode of an annular stable resonator," IEEE J. Quantum Electron. 24, 11-12 (1988).
[CrossRef]

D. Ehrlichmann, U. Habich, H.-D. Plum, P. Loosen, and G. Herziger, "Azimuthally unstable resonators for high-power CO2 lasers with annular gain media," IEEE J. Quantum Electron. 30, 1441-1447 (1994).
[CrossRef]

J. Appl. Phys. (1)

D. Milam and H. Schlossberg, "Emission characteristics of a tube-shaped laser oscillator," J. Appl. Phys. 44, 2297-2299 (1973).
[CrossRef]

Opt. Lett. (3)

Proc. SPIE (1)

H. Schülke, G. Herziger, and R. Weste, "Multipass resonators for laser systems," in High Power Laser: Sources, Laser-Material Interactions, High Excitations, and Fast Dynamics, E. W. Kreutz, A. Quenzer, and D. Schuöcker, eds., Proc. SPIE 801, 45-50 (1987).

Rev. Sci. Instrum. (1)

Y. Ling, M. Qian, and P. Lu, "Study of a high-powered He-Ne laser having rectangular discharge cross section," Rev. Sci. Instrum. 66, 4055-4058 (1995).
[CrossRef]

Other (7)

g0 ≈ 1.34 × 10-3 to 2 × 10-3 cm-1 has been obtained by rf excitation when R1 = 20 mm, R2 = 23 mm, d = 3 mm, He:Ne = 9:1, and the mixture pressure is 0.8 × 133.3 Pa. A report on the experimental procedures and data will be given in another paper.

Y. Jinji, Discharge through Gas, 1st ed. (Science, 1983, p. 22 (in Chinese).

J. D. Cobine, Gaseous Conductors (McGraw-Hill, 1958), pp. 151, 236-239.

Chengdu Institute of Radio Engineering, Beijing Institute of Technology, Laser (Press of Science and Technology, 1983), pp. 30-31, 65 (in Chinese).

O. Svelto and D. C. Hanna, Principles of Lasers (Plenum, 1982), pp. 207-210.

U. Wittrock and H. Weber, "Inside-pumped Nd:YAG tube laser with 7.5% efficiency," in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, 1991), pp. 370-371.

U. Wittrock, B. Eppich, and H. Weber, "Beam quality of the 1-kw inside-pumped Nd:YAG tube laser," in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, 1992), pp. 94-95.

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Figures (14)

Fig. 1
Fig. 1

Schematic of an annular He–Ne laser. A is the electrical glow discharge region. B is an electrical insulation region, C 1 and C 2 are preionized electrodes. D 1 and D 2 are the anode and cathode, respectively. M 1 and M 2 are annular spherical mirrors, a small part of mirror M1 is utilized for output coupling.

Fig. 2
Fig. 2

Cross section of the positive column of the annular discharge gap. Wall (1), outer surface of the inner tube; wall (2), inner surface of the outer tube; →, moving directions of electrons or ions by diffusion.

Fig. 3
Fig. 3

Electronic density (unit: n 0 ) in the section of the rectangular tube laser. Length unit: millimeters, a = 147.6   mm , b = 3   mm , n 0 = 1 .

Fig. 4
Fig. 4

Electronic density (unit: n 0 ) in the section of the annular discharging zone. Length unit: millimeters, R 0 = 23.5   mm , d = 3   mm , n 0 = 1 .

Fig. 5
Fig. 5

Sixteen-pass ring resonator.

Fig. 6
Fig. 6

Series of equally spaced thin lenses.

Fig. 7
Fig. 7

Maxima radial half-width w rad of the beam and the angle direction distance w ang between neighborhood patterns.

Fig. 8
Fig. 8

Variations of w rad and V max with μ.

Fig. 9
Fig. 9

Crossover of the light beam when μ = 1 , 3 .

Fig. 10
Fig. 10

Crossover area of the light beam.

Fig. 11
Fig. 11

Waves of ν 1 and ν 1 modes interact with Ne atoms in a standing-wave cavity.

Fig. 12
Fig. 12

Waves of ν 1 and ν 1 modes interact with Ne atoms in the ring cavity, where only the m 1 mirror is diagrammed.

Fig. 13
Fig. 13

Laser output power as a function of transmissivity.

Fig. 14
Fig. 14

Calculated values of output power for the He–Ne laser having an annular discharge cross section ( λ = 0.6328 μ m ). TEM m n : w m n : ( w m w n ) , w m = 2 m + 1 w , w n = 2 n + 1 w .

Tables (1)

Tables Icon

Table 1 N-Pass Ring Resonator Design Parameters a

Equations (56)

Equations on this page are rendered with MathJax. Learn more.

( d n d t ) r = 2 π r D a ( d n d r ) r , ( R 0 r R 2 ) .
( d n d t ) r + d r = 2 π ( r + d r ) D a ( d n d r ) r + d r , ( R 0 r R 2 ) .
( d n d t ) r + d r = 2 π ( r + d r ) D a ( d n d r ) r + d r ,
( d n d t ) r = 2 π D a ( d n d r ) r .
d v = 2 π r D a ( d n d r ) r 2 π ( r + d r ) D a ( d n d r ) r + d r d r .
d v = Z n 2 π r d r ,
d 2 n d r 2 + 1 r d n d r + z D a n = 0 , ( R 1 r R 2 ) .
r = R 0 ± x
n = n 0 R 0 r cos [ ( z D a + 1 4 R 0 2 ) ( r R 0 ) ] , ( R 1 r R 2 ) ,
z = 4 π 2 R 0 2 d 2 4 R 0 2 d 2 D a .
D a = μ + k T e / e ,
S = a ( V V i ) .
z = 600 m p a v o e 3 e π ( e V i 2 k T e ) exp ( e V i k T e ) ,
m v o e 2 / 2 = k T e .
n = n 0 J 0 ( r z D a ) .
R z D a = 2.405 ,
exp ( e V i / k T e ) e V i / k T e = 600 C 2 p 2 2 e R 2 ( 2.405 ) 2 π m ,
C = a V i / μ + p .
exp ( e V i / k T e ) e V i / k T e = 600 × 4 R 0 2 d 2 C 2 p 2 2 e π m ( 4 π 2 R 0 2 d 2 ) .
R = 4.81 R 0 d 4 π 2 R 0 2 d 2 .
q = π ( R 2 2 R 1 2 ) π R 2 = 2 ( 4 π 2 R 0 2 d 2 ) 4.81 2 R 0 d .
n = n 0   cos ( π a x ) cos ( π b y ) , a 2 x a 2 , b 2 y b 2 ,
R = 0.765 a b a 2 + b 2 .
n = n 0 R 0 r   cos ( π r R 0 d ) , ( R 1 r R 2 ) .
Z = D a π 2 ( a 2 + b 2 a 2 b 2 ) .
[ A C B D ] = [ a 11 a 21 a 12 a 22 ] N / 2 ,
[ a 11 a 21 a 12 a 22 ] = [ 1 0 L 1 1 ] [ 1 2 ρ 0 1 ] [ 1 0 L 1 1 ] [ 1 2 ρ 0 1 ] ,
( L 1 ) 2 = L 2 + 2 R 0 2 [ 1 cos ( φ 2 ) ] ,
φ = cos - 1 ( 2 g 2 1 ) ,
φ 2 = θ = cos - 1 ( 1 L ρ ) ,
g = 1 L ρ .
w = ( 2 λ B π ) 1 / 2 [ 4 ( A + D ) 2 ] 1 / 4 ,
ρ ( m 1 ) = 2 B D A ,
V ( 00 ) = N L π 2 w .
w 00 = ( λ 2 π | C | ) 1 / 2 [ 4 ( A + D ) 2 ] 1 / 4 .
N θ = μ 2 π ,
w rad = 1 2 ( O C O G ) = 1 2 ( R 2 R 1 cos ( θ / 2 ) ) .
w ang 4 π R 0 / N ,
R 0 1 2 ( R 2 + O G ) = R 2 + R 1 / cos ( θ / 2 ) 2 .
w rad = 1 2 ( R 2 R 1 cos   μ π N ) .
η V = V V in V ,
η V = 1 w n 2 L t g 1.5 ζ 0.8 ,
g 0 = 3.0 × 10 4 / D ,
g 0 = 3.0 × 10 4 2 R ,
Δ ν ring = c L ring ,
λ ¯ = 1 2 π σ 2 n 0 = k T 2 π σ 2 p ,
λ ¯ He 1.4 × 10 4   m, λ ¯ Ne 1.0 × 10 4   m,
λ τ S V Z λ τ S .
Δ n n = ( m 2 π k T ) 1 / 2 λ / 4 τ S λ / 4 τ S exp ( m V Z 2 / 2 k T ) d V Z = 2 π [ X 1 1 ! X 3 3 ! + 1 2 ! X 5 5 ! ] ,
P c = A t P in = A t I s ( 2 g 0 l 2 α + t 1 ) ,
P c = A t K I s ( 2 g 0 l α + T 2 ) = A t K I s ( 2 g 0 l 2 α + t 1 ) ,
p one   direction = V mode W m W n L * A f t I s ( g o L * η V a + t 1 ) ,
p duo   direction = V mode W m W n L * A f t I s ( 2 g o L * η V a + t 2 ) ,
t opt = ( g 0 L * a η V ) 1 / 2 a .
I s = 1.36 W / cm 2 .
P / A = 0.384615 W / cm 2 .

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