Abstract

The results of a numerical study of both the passive and the active mode-structure properties and far-field behavior of a linear, positive-branch, confocal unstable resonator with a large equivalent Fresnel number in the ideal unaberrated, intracavity phase-aberrated, and intracavity phase-corrected states are presented. A simple, saturable, gain-medium model of a homogeneously broadened CO<sub>2</sub>–electron-beam discharge laser system is employed in the active cavity study. The active cavity results presented here show that, at least for the level of gain saturation considered, the passive cavity theory of phase-aberration sensitivity remains applicable in this more-physical situation. Furthermore, the ideal correction to phase-tilt and curvature aberrations, derived from passive cavity considerations, remains exact in the presence of saturable gain. Finally, the influence of a multidithered, zonal deformable mirror on the cavity-mode structure and far-field behavior is analyzed in order to account for recent expe imental tests of the intracavity adaptive optics concept.

© 1983 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. E. Oughstun, "Intracavity adaptive optic compensation of phase aberrations. I: Analysis," J. Opt. Soc. Am. 71, 862–872 (1981).
  2. K. E. Oughstun, "Intracavity adaptive optic compensation of phase aberrations." II: Passive cavity study for a small Neq resonator," J. Opt. Soc. Am. 71, 1180–1192 (1981).
  3. J. M. Spinhirne, D. Anafi, R. Freeman, and H. R. Garcia, "Intracavity adaptive optics. 1: Astigmatism correction performance," Appl. Opt. 20, 976–984 (1981).
  4. D. Anafi, J. M. Spinhirne, R. H. Freeman, and K. E. Oughstun, "Intracavity adaptive optics. 2: Tilt correction performance," Appl. Opt. 20,1926–1932 (1981).
  5. E. A. Sziklas and A. E. Siegman, "Mode calculations in unstable resonators with flowing saturable gain. 2: Fast Fourier transform method," Appl. Opt. 14, 1874–1889 (1975).
  6. A. E. Siegman and H. Y. Miller, "Unstable optical resonator loss calculations using the Prony method," Appl. Opt. 9, 2729–2736 (1970).
  7. Yu. A. Anan'ev, "Unstable resonators and their applications (review)," Sov. J. Quantum Electron. 1, 565–586 (1972).
  8. V. E. Sherstobitov and G. N. Vinokurov, "Properties of unstable resonators with large equivalent Fresnel numbers," Sov. J. Quantum Electron. 2, 224–229 (1972).
  9. Yu. A. Anan'ev, "Establishment of oscillations in unstable resonators," Sov. J. Quantum Electron. 5, 615–617 (1975).
  10. K. E. Oughstun, K. A. Bush, and P. A. Slaymaker, "Transverse mode structure properties in off-axis ring resonators," J. Opt. Soc. Am. 71, 1598 (A) (1981).
  11. A. Maitland and M. H. Dunn, Laser Physics (North-Holland, Amsterdam, 1969), Chap. 8.
  12. G. P. Agrawal and M. Lax, "Effects of interference on gain saturation in laser resonators," J. Opt. Soc. Am. 69, 1717–1719 (1979).
  13. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, London, 1975).
  14. K. E. Oughstun, "Theory of intracavity adaptive optic mode control," Proc. Soc. Photo-Opt. Instrum. Eng. 365 (to be published).
  15. The interior volume of an unstable cavity is indicated by the region a in Fig. 2 of A. E. Siegman, "Orthogonality properties of optical resonator eigenmodes," Opt. Commun. 31, 369–373 (1979).
  16. Yu. A. Anan'ev and V. E. Sherstobitov, "Influences of the edge effects on the properties of unstable resonators," Sov. J. Quantum Electron. 1, 263–267 (1971).
  17. K. E. Oughstun, "Intracavity compensation of quadratic phase aberrations," J. Opt. Soc. Am. 72, 1529–1537 (1982).
  18. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, S9.6, Vol. 55 of National Bureau of Standards Applied Mathematics Series (U.S. Government Printing Office, Washington, D.C., 1972).

1982

1981

1979

G. P. Agrawal and M. Lax, "Effects of interference on gain saturation in laser resonators," J. Opt. Soc. Am. 69, 1717–1719 (1979).

The interior volume of an unstable cavity is indicated by the region a in Fig. 2 of A. E. Siegman, "Orthogonality properties of optical resonator eigenmodes," Opt. Commun. 31, 369–373 (1979).

1975

E. A. Sziklas and A. E. Siegman, "Mode calculations in unstable resonators with flowing saturable gain. 2: Fast Fourier transform method," Appl. Opt. 14, 1874–1889 (1975).

Yu. A. Anan'ev, "Establishment of oscillations in unstable resonators," Sov. J. Quantum Electron. 5, 615–617 (1975).

1972

Yu. A. Anan'ev, "Unstable resonators and their applications (review)," Sov. J. Quantum Electron. 1, 565–586 (1972).

V. E. Sherstobitov and G. N. Vinokurov, "Properties of unstable resonators with large equivalent Fresnel numbers," Sov. J. Quantum Electron. 2, 224–229 (1972).

1971

Yu. A. Anan'ev and V. E. Sherstobitov, "Influences of the edge effects on the properties of unstable resonators," Sov. J. Quantum Electron. 1, 263–267 (1971).

1970

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, S9.6, Vol. 55 of National Bureau of Standards Applied Mathematics Series (U.S. Government Printing Office, Washington, D.C., 1972).

Agrawal, G. P.

Anafi, D.

Anan'ev, Yu. A.

Yu. A. Anan'ev, "Establishment of oscillations in unstable resonators," Sov. J. Quantum Electron. 5, 615–617 (1975).

Yu. A. Anan'ev, "Unstable resonators and their applications (review)," Sov. J. Quantum Electron. 1, 565–586 (1972).

Yu. A. Anan'ev and V. E. Sherstobitov, "Influences of the edge effects on the properties of unstable resonators," Sov. J. Quantum Electron. 1, 263–267 (1971).

Born, M.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, London, 1975).

Bush, K. A.

K. E. Oughstun, K. A. Bush, and P. A. Slaymaker, "Transverse mode structure properties in off-axis ring resonators," J. Opt. Soc. Am. 71, 1598 (A) (1981).

Dunn, M. H.

A. Maitland and M. H. Dunn, Laser Physics (North-Holland, Amsterdam, 1969), Chap. 8.

Freeman, R.

Freeman, R. H.

Garcia, H. R.

Lax, M.

Maitland, A.

A. Maitland and M. H. Dunn, Laser Physics (North-Holland, Amsterdam, 1969), Chap. 8.

Miller, H. Y.

Oughstun, K. E.

Sherstobitov, V. E.

V. E. Sherstobitov and G. N. Vinokurov, "Properties of unstable resonators with large equivalent Fresnel numbers," Sov. J. Quantum Electron. 2, 224–229 (1972).

Yu. A. Anan'ev and V. E. Sherstobitov, "Influences of the edge effects on the properties of unstable resonators," Sov. J. Quantum Electron. 1, 263–267 (1971).

Siegman, A. E.

Slaymaker, P. A.

K. E. Oughstun, K. A. Bush, and P. A. Slaymaker, "Transverse mode structure properties in off-axis ring resonators," J. Opt. Soc. Am. 71, 1598 (A) (1981).

Spinhirne, J. M.

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, S9.6, Vol. 55 of National Bureau of Standards Applied Mathematics Series (U.S. Government Printing Office, Washington, D.C., 1972).

Sziklas, E. A.

Vinokurov, G. N.

V. E. Sherstobitov and G. N. Vinokurov, "Properties of unstable resonators with large equivalent Fresnel numbers," Sov. J. Quantum Electron. 2, 224–229 (1972).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, London, 1975).

Appl. Opt.

J. Opt. Soc. Am.

Opt. Commun.

The interior volume of an unstable cavity is indicated by the region a in Fig. 2 of A. E. Siegman, "Orthogonality properties of optical resonator eigenmodes," Opt. Commun. 31, 369–373 (1979).

Sov. J. Quantum Electron.

Yu. A. Anan'ev and V. E. Sherstobitov, "Influences of the edge effects on the properties of unstable resonators," Sov. J. Quantum Electron. 1, 263–267 (1971).

Yu. A. Anan'ev, "Unstable resonators and their applications (review)," Sov. J. Quantum Electron. 1, 565–586 (1972).

V. E. Sherstobitov and G. N. Vinokurov, "Properties of unstable resonators with large equivalent Fresnel numbers," Sov. J. Quantum Electron. 2, 224–229 (1972).

Yu. A. Anan'ev, "Establishment of oscillations in unstable resonators," Sov. J. Quantum Electron. 5, 615–617 (1975).

Other

A. Maitland and M. H. Dunn, Laser Physics (North-Holland, Amsterdam, 1969), Chap. 8.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, London, 1975).

K. E. Oughstun, "Theory of intracavity adaptive optic mode control," Proc. Soc. Photo-Opt. Instrum. Eng. 365 (to be published).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, S9.6, Vol. 55 of National Bureau of Standards Applied Mathematics Series (U.S. Government Printing Office, Washington, D.C., 1972).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.