Abstract

The effects of the forward- and backward-wave interference in a standing-wave resonator on laser output intensity are considered. In the paraxial- and plane-wave approximation and with boundary conditions appropriate for a Fabry—Perot resonator, the intensity equations are analytically solved. The variation of the output intensity with various parameters, such as the mirror reflection and absorption coefficients, small-signal gain, and atomic detuning, is considered, and the results are compared with those obtained when the interference effects are neglected. Considerable departure from the latter case is found. Our results should find application in choosing optimum parameters in the design of a laser resonator.

© 1981 Optical Society of America

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  1. A. E. Siegman and E. A. Sziklas, "Mode calculations in unstable resonators with flowing saturable gain: 1. hermite Gaussian expansions," Appl. Opt. 13, 2775–2792 (1974).
  2. 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 (1974).
  3. Yu. N. Karamzin and Yu. B. Konev, "Numerical investigation of the operation of unstable telescopic resonators allowing for diffraction and saturation in the active medium," Sov. J. Quantum Electron. 5, 144–148 (1975).
  4. V. S. Rogov and M. M. Rikenglaz, "Numerical investigation of the influence of optical inhomogeneties of the active medium on the operation of an unstable telescopic resonator," Sov. J. Quantum Electron. 7, 18–21 (1977).
  5. G. T. Moore and R. J. McCarthy, "Lasers with unstable resonators in the geometrical optics limit," J. Opt. Soc. Am. 67, 221–227 (1977); "Theory of modes in a loaded strip confocal resonator," J. Opt. Soc. Am. 67, 228–241 (1977).
  6. W. H. Louisell et al., "Simultaneous forward and backward integration for standing waves in a resonator," Appl. Opt. 18, 2730–2731 (1979).
  7. M. Lax, G. P. Agrawal, and W. H. Louisell, "Continuous Fourier- transform spline solution of unstable resonator-field distribution," Opt. Lett. 4, 303–305 (1979).
  8. G. P. Agrawal and M. Lax, "Effects of interference on gain saturation in laser resonators," J. Opt. Soc. Am. 69, 1717–1719 (1979).
  9. W. W. Rigrod, "Saturation effects in high gain lasers," J. Appl. Phys. 36, 2487–2490 (1965).
  10. M. Sargent III, M. O. Scully, and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, Reading, Mass., 1974), Chap. 8.
  11. M. Lax, W. H. Louisell, and W. B. McKnight, "From Maxwell to paraxial wave optics," Phys. Rev. A 11, 1365–1370 (1975).
  12. M. Lax et al., "Electromagnetic field distribution in a loaded unstable resonator," to be published.
  13. Equations equivalent to Eqs. (2.9) and (2.10) have been published by M. Sargent III, "Laser saturating grading phenomena," Appl. Phys. 9, 127 (1976).
  14. Equations (2.9) and (2.10) also appear in the context of optical bistability. However, the imposed boundary conditions are different as there is an externally applied field. See the article by H. J. Carmichael and J. A. Hermann, "Analytic description of optical bistability including spatial effects," Z. Phys. B 138, 365–380 (1980).
  15. For a review of the properties of unstable resonators, see the article by A. E. Siegman, "Unstable optical resonators," Appl. Opt. 13, 353–367 (1974).

1980 (1)

Equations (2.9) and (2.10) also appear in the context of optical bistability. However, the imposed boundary conditions are different as there is an externally applied field. See the article by H. J. Carmichael and J. A. Hermann, "Analytic description of optical bistability including spatial effects," Z. Phys. B 138, 365–380 (1980).

1979 (3)

1977 (2)

V. S. Rogov and M. M. Rikenglaz, "Numerical investigation of the influence of optical inhomogeneties of the active medium on the operation of an unstable telescopic resonator," Sov. J. Quantum Electron. 7, 18–21 (1977).

G. T. Moore and R. J. McCarthy, "Lasers with unstable resonators in the geometrical optics limit," J. Opt. Soc. Am. 67, 221–227 (1977); "Theory of modes in a loaded strip confocal resonator," J. Opt. Soc. Am. 67, 228–241 (1977).

1976 (1)

Equations equivalent to Eqs. (2.9) and (2.10) have been published by M. Sargent III, "Laser saturating grading phenomena," Appl. Phys. 9, 127 (1976).

1975 (2)

Yu. N. Karamzin and Yu. B. Konev, "Numerical investigation of the operation of unstable telescopic resonators allowing for diffraction and saturation in the active medium," Sov. J. Quantum Electron. 5, 144–148 (1975).

M. Lax, W. H. Louisell, and W. B. McKnight, "From Maxwell to paraxial wave optics," Phys. Rev. A 11, 1365–1370 (1975).

1974 (3)

1965 (1)

W. W. Rigrod, "Saturation effects in high gain lasers," J. Appl. Phys. 36, 2487–2490 (1965).

Agrawal, G. P.

Carmichael, H. J.

Equations (2.9) and (2.10) also appear in the context of optical bistability. However, the imposed boundary conditions are different as there is an externally applied field. See the article by H. J. Carmichael and J. A. Hermann, "Analytic description of optical bistability including spatial effects," Z. Phys. B 138, 365–380 (1980).

Hermann, J. A.

Equations (2.9) and (2.10) also appear in the context of optical bistability. However, the imposed boundary conditions are different as there is an externally applied field. See the article by H. J. Carmichael and J. A. Hermann, "Analytic description of optical bistability including spatial effects," Z. Phys. B 138, 365–380 (1980).

Karamzin, Yu. N.

Yu. N. Karamzin and Yu. B. Konev, "Numerical investigation of the operation of unstable telescopic resonators allowing for diffraction and saturation in the active medium," Sov. J. Quantum Electron. 5, 144–148 (1975).

Konev, Yu. B.

Yu. N. Karamzin and Yu. B. Konev, "Numerical investigation of the operation of unstable telescopic resonators allowing for diffraction and saturation in the active medium," Sov. J. Quantum Electron. 5, 144–148 (1975).

Lamb, Jr., W. E.

M. Sargent III, M. O. Scully, and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, Reading, Mass., 1974), Chap. 8.

Lax, M.

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

M. Lax, G. P. Agrawal, and W. H. Louisell, "Continuous Fourier- transform spline solution of unstable resonator-field distribution," Opt. Lett. 4, 303–305 (1979).

M. Lax, W. H. Louisell, and W. B. McKnight, "From Maxwell to paraxial wave optics," Phys. Rev. A 11, 1365–1370 (1975).

M. Lax et al., "Electromagnetic field distribution in a loaded unstable resonator," to be published.

Louisell, W. H.

McCarthy, R. J.

McKnight, W. B.

M. Lax, W. H. Louisell, and W. B. McKnight, "From Maxwell to paraxial wave optics," Phys. Rev. A 11, 1365–1370 (1975).

Moore, G. T.

Rigrod, W. W.

W. W. Rigrod, "Saturation effects in high gain lasers," J. Appl. Phys. 36, 2487–2490 (1965).

Rikenglaz, M. M.

V. S. Rogov and M. M. Rikenglaz, "Numerical investigation of the influence of optical inhomogeneties of the active medium on the operation of an unstable telescopic resonator," Sov. J. Quantum Electron. 7, 18–21 (1977).

Rogov, V. S.

V. S. Rogov and M. M. Rikenglaz, "Numerical investigation of the influence of optical inhomogeneties of the active medium on the operation of an unstable telescopic resonator," Sov. J. Quantum Electron. 7, 18–21 (1977).

Sargent III, M.

M. Sargent III, M. O. Scully, and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, Reading, Mass., 1974), Chap. 8.

Sargent III, M.

Equations equivalent to Eqs. (2.9) and (2.10) have been published by M. Sargent III, "Laser saturating grading phenomena," Appl. Phys. 9, 127 (1976).

Scully, M. O.

M. Sargent III, M. O. Scully, and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, Reading, Mass., 1974), Chap. 8.

Siegman, A. E.

Sziklas, E. A.

Appl. Opt. (4)

Appl. Phys. (1)

Equations equivalent to Eqs. (2.9) and (2.10) have been published by M. Sargent III, "Laser saturating grading phenomena," Appl. Phys. 9, 127 (1976).

J. Appl. Phys. (1)

W. W. Rigrod, "Saturation effects in high gain lasers," J. Appl. Phys. 36, 2487–2490 (1965).

J. Opt. Soc. Am. (2)

Opt. Lett. (1)

Phys. Rev. A (1)

M. Lax, W. H. Louisell, and W. B. McKnight, "From Maxwell to paraxial wave optics," Phys. Rev. A 11, 1365–1370 (1975).

Sov. J. Quantum Electron. (2)

Yu. N. Karamzin and Yu. B. Konev, "Numerical investigation of the operation of unstable telescopic resonators allowing for diffraction and saturation in the active medium," Sov. J. Quantum Electron. 5, 144–148 (1975).

V. S. Rogov and M. M. Rikenglaz, "Numerical investigation of the influence of optical inhomogeneties of the active medium on the operation of an unstable telescopic resonator," Sov. J. Quantum Electron. 7, 18–21 (1977).

Z. Phys. B (1)

Equations (2.9) and (2.10) also appear in the context of optical bistability. However, the imposed boundary conditions are different as there is an externally applied field. See the article by H. J. Carmichael and J. A. Hermann, "Analytic description of optical bistability including spatial effects," Z. Phys. B 138, 365–380 (1980).

Other (2)

M. Lax et al., "Electromagnetic field distribution in a loaded unstable resonator," to be published.

M. Sargent III, M. O. Scully, and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, Reading, Mass., 1974), Chap. 8.

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