Abstract

Effects of small misalignments in positive- and negative-branch strip confocal unstable resonators have been compared at the same absolute values of collimated Fresnel numbers and at the same Fresnel numbers. We show that positions of beam modes in negative-branch unstable resonators are far less sensitive to misalignment because of both geometric features and diffraction effects of beam flipping in the resonators.

© 2001 Optical Society of America

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References

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  1. W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2 laser system,” IEEE J. Quantum Electron. QE-5, 575–586 (1969).
    [CrossRef]
  2. A. N. Chester, “Mode selectivity and mirror misalignment effects in unstable resonators,” Appl. Opt. 11, 2584–2590 (1972).
    [CrossRef] [PubMed]
  3. A. N. Chester, “Beam steering in confocal unstable resonators,” IEEE J. Quantum Electron. QE-9, 209–212 (1973).
    [CrossRef]
  4. P. Horwitz, “Modes in misaligned unstable resonators,” Appl. Opt. 15, 167–178 (1976).
    [CrossRef] [PubMed]
  5. J. F. Perkins, C. Cason, “Effects of small misalignments in empty unstable resonators,” Appl. Phys. Lett. 31, 198–200 (1977).
    [CrossRef]
  6. C. Santana, L. B. Felsen, “Unstable strip resonators with misaligned circular mirrors,” Appl. Opt. 17, 2352–2357 (1978).
    [CrossRef] [PubMed]
  7. C. Santana, L. B. Felsen, “Eigenvalues for unstable resonators with slightly misaligned strip mirrors,” Appl. Opt. 19, 3189–3191 (1980).
    [CrossRef] [PubMed]
  8. J. F. Perkins, R. W. Jones, “Effects of unstable resonator misalignment in the coupling domain,” Appl. Opt. 23, 358–360 (1984).
    [CrossRef]
  9. N. McCarthy, P. Lavigne, “Optical resonators with Gaussian reflectivity mirrors: misalignment sensitivity,” Appl. Opt. 22, 2704–2708 (1983).
    [CrossRef] [PubMed]
  10. T. F. Ewanizky, J. M. Craig, “Negative-branch unstable resonator Nd:YAG laser,” Appl. Opt. 15, 1465–1469 (1976).
    [CrossRef] [PubMed]
  11. K. Yasui, M. Tanaka, S. Yagi, “Negative-branch unstable resonator with a phase unifying coupler for high power Nd:YAG lasers,” Appl. Opt. 29, 1277–1280 (1990).
    [CrossRef] [PubMed]
  12. K. Kuba, T. Yamamoto, S. Yagi, “Improvement of slab-laser beam divergence by using an off-axis unstable–stable resonator,” Opt. Lett. 15, 121–123 (1990).
    [CrossRef]
  13. S. K. Dixit, B. Singh, S. V. Nakhe, J. K. Mittal, R. Bhatnagar, “Negative-branch unstable-resonator copper-vapor laser,” Opt. Lett. 15, 428–430 (1990).
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  14. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 806.
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    [CrossRef] [PubMed]
  16. K. Yasui, M. Tanaka, S. Yagi, “An unstable resonator with a phase-unifying output coupler to extract a large uniphase beam of a filled-in circular pattern,” J. Appl. Phys. 65, 17–21 (1989).
    [CrossRef]

1990 (3)

1989 (1)

K. Yasui, M. Tanaka, S. Yagi, “An unstable resonator with a phase-unifying output coupler to extract a large uniphase beam of a filled-in circular pattern,” J. Appl. Phys. 65, 17–21 (1989).
[CrossRef]

1986 (1)

1984 (1)

1983 (1)

1980 (1)

1978 (1)

1977 (1)

J. F. Perkins, C. Cason, “Effects of small misalignments in empty unstable resonators,” Appl. Phys. Lett. 31, 198–200 (1977).
[CrossRef]

1976 (2)

1973 (1)

A. N. Chester, “Beam steering in confocal unstable resonators,” IEEE J. Quantum Electron. QE-9, 209–212 (1973).
[CrossRef]

1972 (1)

1969 (1)

W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2 laser system,” IEEE J. Quantum Electron. QE-5, 575–586 (1969).
[CrossRef]

Bhatnagar, R.

Cason, C.

J. F. Perkins, C. Cason, “Effects of small misalignments in empty unstable resonators,” Appl. Phys. Lett. 31, 198–200 (1977).
[CrossRef]

Chester, A. N.

A. N. Chester, “Beam steering in confocal unstable resonators,” IEEE J. Quantum Electron. QE-9, 209–212 (1973).
[CrossRef]

A. N. Chester, “Mode selectivity and mirror misalignment effects in unstable resonators,” Appl. Opt. 11, 2584–2590 (1972).
[CrossRef] [PubMed]

Craig, J. M.

Dixit, S. K.

Ewanizky, T. F.

Felsen, L. B.

Horwitz, P.

Jones, R. W.

Krupke, W. F.

W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2 laser system,” IEEE J. Quantum Electron. QE-5, 575–586 (1969).
[CrossRef]

Kuba, K.

Lavigne, P.

McCarthy, N.

Mittal, J. K.

Nakhe, S. V.

Paxton, A. H.

Perkins, J. F.

J. F. Perkins, R. W. Jones, “Effects of unstable resonator misalignment in the coupling domain,” Appl. Opt. 23, 358–360 (1984).
[CrossRef]

J. F. Perkins, C. Cason, “Effects of small misalignments in empty unstable resonators,” Appl. Phys. Lett. 31, 198–200 (1977).
[CrossRef]

Santana, C.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 806.

Singh, B.

Sooy, W. R.

W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2 laser system,” IEEE J. Quantum Electron. QE-5, 575–586 (1969).
[CrossRef]

Tanaka, M.

K. Yasui, M. Tanaka, S. Yagi, “Negative-branch unstable resonator with a phase unifying coupler for high power Nd:YAG lasers,” Appl. Opt. 29, 1277–1280 (1990).
[CrossRef] [PubMed]

K. Yasui, M. Tanaka, S. Yagi, “An unstable resonator with a phase-unifying output coupler to extract a large uniphase beam of a filled-in circular pattern,” J. Appl. Phys. 65, 17–21 (1989).
[CrossRef]

Yagi, S.

Yamamoto, T.

Yasui, K.

K. Yasui, M. Tanaka, S. Yagi, “Negative-branch unstable resonator with a phase unifying coupler for high power Nd:YAG lasers,” Appl. Opt. 29, 1277–1280 (1990).
[CrossRef] [PubMed]

K. Yasui, M. Tanaka, S. Yagi, “An unstable resonator with a phase-unifying output coupler to extract a large uniphase beam of a filled-in circular pattern,” J. Appl. Phys. 65, 17–21 (1989).
[CrossRef]

Appl. Opt. (8)

Appl. Phys. Lett. (1)

J. F. Perkins, C. Cason, “Effects of small misalignments in empty unstable resonators,” Appl. Phys. Lett. 31, 198–200 (1977).
[CrossRef]

IEEE J. Quantum Electron. (2)

A. N. Chester, “Beam steering in confocal unstable resonators,” IEEE J. Quantum Electron. QE-9, 209–212 (1973).
[CrossRef]

W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2 laser system,” IEEE J. Quantum Electron. QE-5, 575–586 (1969).
[CrossRef]

J. Appl. Phys. (1)

K. Yasui, M. Tanaka, S. Yagi, “An unstable resonator with a phase-unifying output coupler to extract a large uniphase beam of a filled-in circular pattern,” J. Appl. Phys. 65, 17–21 (1989).
[CrossRef]

Opt. Lett. (3)

Other (1)

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 806.

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Figures (6)

Fig. 1
Fig. 1

Resonator model.

Fig. 2
Fig. 2

Beam modes for a PB unstable resonator with a collimated Fresnel number of 5.4. The horizontal axes are in arbitrary units so that the dotted lines represent the front mirror.

Fig. 3
Fig. 3

Beam modes for a NB unstable resonator with a collimated Fresnel number of -5.4. The horizontal axes are in arbitrary units so that the dotted lines represent the front mirror.

Fig. 4
Fig. 4

Equivalent lens guides for (a) PB and (b) NB unstable resonators.

Fig. 5
Fig. 5

Beam modes for a NB unstable resonator with a collimated Fresnel number of 13.5. The horizontal axes are in arbitrary units so that the dotted lines represent the front mirror.

Fig. 6
Fig. 6

Comparison of beam mode characteristics and power losses of resonators with the same absolute value: (a) and (b) collimated Fresnel number of 5.4 and (a) and (c) equivalent Fresnel number of 13.5.

Equations (9)

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v2x2=jNC-11 v1x1exp-jπNCx1-x22dx1,
NC=Ma2Bλ,
B=M+1M L,
r1r2=M+1M-1-2M-12MM-1-M+1M-1R1θ1R2θ2,
ε=r1=M+1-2LM-12 θ1+M-4LM-12 θ2=a1θ1+a2θ2,
|ε|NB=|a1|NB|θ1|+|a2|NB|θ2|=χ2|a1|PB|θ1|+χ|a2|PB|θ2|,
|ε|PB=|a1|PB|θ1|+|a2|PB|θ2|,
χ=|M|-1|M|+1.
|ε|NB=|a1|NB|θ1|+|a2|NB|θ2|=χ3|a1|PB|θ1|+χ2|a2|PB|θ2|,

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