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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 13, Iss. 1 — Jan. 1, 1996
  • pp: 90–96

Generalized beam matrices. II. Mode selection in lasers and periodic misaligned complex optical systems

Anthony A. Tovar and Lee W. Casperson  »View Author Affiliations

JOSA A, Vol. 13, Issue 1, pp. 90-96 (1996)

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A generalized beam matrix method is used to investigate the mode structure of astigmatic misaligned optical systems with loss or gain. In these optical systems the usual real-argument polynomial-Gaussian beams are not eigenfunctions, and off-axis complex-argument polynomial beams must be used. New beam transformations for these complex-argument modes are reported. Stability criteria are developed, and mode selection in laser resonators that contain tilted, displaced, or curved complex optical elements is discussed.

© 1996 Optical Society of America

Original Manuscript: April 19, 1995
Revised Manuscript: August 1, 1995
Manuscript Accepted: August 1, 1995
Published: January 1, 1996

Anthony A. Tovar and Lee W. Casperson, "Generalized beam matrices. II. Mode selection in lasers and periodic misaligned complex optical systems," J. Opt. Soc. Am. A 13, 90-96 (1996)

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  1. N. G. Vakhimov, “Open resonators with mirrors having variable reflection coefficients,” Radio Eng. Electron. Phys. (USSR) 10, 1439–1446 (1965).
  2. H. Zucker, “Optical resonators with variable reflectivity mirrors,” Bell Syst. Tech. J. 49, 2349–2376 (1970).
  3. J. A. Arnaud, “Optical resonators in the approximation of Gauss,” Proc. IEEE 62, 1561–1570 (1974). [CrossRef]
  4. L. W. Casperson, S. D. Lunnam, “Gaussian modes in high loss laser resonators,” Appl. Opt. 14, 1193–1199 (1975). [CrossRef] [PubMed]
  5. A. Yariv, P. Yeh, “Confinement and stability in optical resonators employing mirrors with Gaussian reflectivity tapers,” Opt. Commun. 13, 370–374 (1975). [CrossRef]
  6. U. Ganiel, A. Hardy, Y. Silberberg, “Stability of optical laser resonators with mirrors of Gaussian reflectivity profiles, which contain an active medium,” Opt. Commun. 14, 290–293 (1975). [CrossRef]
  7. A. A. Tovar, L. W. Casperson, “Generalized beam matrices: Gaussian beam propagation in misaligned complex optical systems,” J. Opt. Soc. Am. A 12, 1522–1533 (1995). [CrossRef]
  8. A. A. Tovar, L. W. Casperson, “Gaussian beam optical systems with high gain or high loss media,” IEEE Trans. Microwave Theory Tech. 43, 1857–1862 (1995). [CrossRef]
  9. L. W. Casperson, S. J. Sheldrake, “Beam deflection and isolation in laser amplifiers,” Opt. Commun. 12, 349–353 (1974). [CrossRef]
  10. H. Kogelnik, “On the propagation of Gaussian beams of light through lenslike media including those with a loss or gain variation,” Appl. Opt. 4, 1562–1569 (1965). [CrossRef]
  11. L. W. Casperson, A. Yariv, “The Gaussian mode in optical resonators with a radial gain profile,” Appl. Phys. Lett. 12, 355–357 (1968). [CrossRef]
  12. L. W. Casperson, “Gaussian light beams in inhomogeneous media,” Appl. Opt. 12, 2434–2441 (1973). [CrossRef] [PubMed]
  13. N. McCarthy, P. Lavigne, “Large-size Gaussian mode in unstable resonators using Gaussian mirrors,” Opt. Lett. 10, 553–555 (1985). [CrossRef] [PubMed]
  14. P. Lavigne, A. Parent, D. Pascale, N. McCarthy, “A compact wide-aperature single-mode TE-CO2laser with a low chirp rate,” IEEE J. Quantum Electron. QE-22, 2200–2203 (1986). [CrossRef]
  15. D. V. Willetts, M. R. Harris, “Output characteristics of a compact 1 J carbon dioxide laser with a Gaussian reflectivity mirror,” IEEE J. Quantum Electron. 24, 849–855 (1988). [CrossRef]
  16. P. Lavigne, N. McCarthy, A. Parent, K. J. Snell, “Laser mode control with variable reflectivity mirrors,” Can. J. Phys. 66, 888–895 (1988). [CrossRef]
  17. S. De Silvestri, P. Laporta, V. Magni, O. Svelto, “Unstable laser resonators with super-Gaussian mirrors,” Opt. Lett. 13, 201–203 (1988). [CrossRef] [PubMed]
  18. K. J. Snell, N. McCarthy, M. Piche, P. Lavigne, “Single transverse mode oscillation from an unstable resonator Nd:YAG laser using a variable reflectivity mirror,” Opt. Commun. 65, 377–382 (1988). [CrossRef]
  19. S. De Silvestri, P. Laporta, V. Magni, G. Valentini, G. Cerullo, “Comparative analysis of Nd:YAG unstable resonators with super-Gaussian variable reflectance mirrors,” Opt. Commun. 77, 179–184 (1990). [CrossRef]
  20. S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990). [CrossRef]
  21. J. J. Kasinski, W. Hughes, D. DiBiase, P. Bournes, R. Burnham, “One joule output from a diode-array-pumped Nd:YAG laser with side-pumped rod geometry,” IEEE J. Quantum Electron. 28, 977–985 (1992). [CrossRef]
  22. D. M. Tratt, “Optimizing coherent lidar performance with graded-reflectance laser resonator optics,” Appl. Opt. 31, 4233–4239 (1992). [CrossRef] [PubMed]
  23. K. L. Webster, C. C. Sung, “Mode-medium instability and its correction with a Gaussian-reflectivity mirror,” Appl. Opt. 31, 319–328 (1992). [CrossRef] [PubMed]
  24. See, for example, P. Lavigne, N. McCarthy, J.-G. Demers, “Design and characterization of complementary Gaussian reflectivity mirrors,” Appl. Opt. 24, 2581–2586 (1985). [CrossRef] [PubMed]
  25. W. R. Bennett, “Inversion mechanisms in gas lasers,” Appl. Opt. Suppl. 2, Chemical Lasers, pp. 3–33 (1965).
  26. B. N. Perry, P. Rabinowitz, M. Newstein, “Wave propagation in media with focused gain,” Phys. Rev. A 27, 1989–2002 (1983). [CrossRef]
  27. See the introduction of S. Zaidi, D. L. MacFarlane, “Mode evolution of optical resonators with a radial gain profile,” Phys. Rev. A 47, 588–596 (1993), and references therein. [CrossRef] [PubMed]
  28. F. R. Nash, “Mode guidance parallel to the junction plane of double-heterostructure GaAs lasers,” J. Appl. Phys. 44, 4696–4707 (1973). [CrossRef]
  29. N. McCarthy, P. Lavigne, “Optical resonators with Gaussian reflectivity mirrors: misalignment sensitivity,” Appl. Opt. 22, 2704–2708 (1983). [CrossRef] [PubMed]
  30. N. McCarthy, P. Lavigne, “Optical resonators with Gaussian reflectivity mirrors: output beam characteristics,” Appl. Opt. 23, 3845–3850 (1984). [CrossRef] [PubMed]
  31. N. McCarthy, M. Morin, “High-order transverse modes of misaligned laser resonators with Gaussian reflectivity mirrors,” Appl. Opt. 28, 2189–2191 (1989). [CrossRef] [PubMed]
  32. H. Kogelnik, “Imaging of optical modes—resonators with internal lenses,” Bell Syst. Tech. J. 44, 455–494 (1965).
  33. M. Nazarathy, A. Hardy, J. Shamir, “Generalized mode propagation in first-order optical systems with loss or gain,” J. Opt. Soc. Am. 72, 1409–1420 (1982). [CrossRef]
  34. L. W. Casperson, “Beam modes in complex lenslike media and resonators,” J. Opt. Soc. Am. 66, 1373–1379 (1976). [CrossRef]
  35. A. A. Tovar, L. W. Casperson, “Off-axis complex-argument polynomial-Gaussian beams in optical systems,” J. Opt. Soc. Am. A 8, 60–68 (1991). [CrossRef]
  36. L. W. Casperson, “Mode stability of lasers and periodic optical systems,” IEEE J. Quantum Electron. QE-10, 629–634 (1974). [CrossRef]
  37. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 837.
  38. Ref. 37, pp. 798–801.

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