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Optics Letters

Optics Letters


  • Vol. 11, Iss. 2 — Feb. 1, 1986
  • pp: 76–78

Unstable resonators with negative equivalent Fresnel numbers

A. H. Paxton  »View Author Affiliations

Optics Letters, Vol. 11, Issue 2, pp. 76-78 (1986)

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The equivalent Fresnel numbers of two unstable resonators of current interest for application in free-electron lasers are negative. For a resonator of this class, the equivalent collimated round-trip propagation of Siegman’s canonical formulation is a time-reversed propagation, and the modes and eigenvalues are the complex conjugates of those corresponding to a resonator having a positive equivalent Fresnel number with the same magnitude.

© 1986 Optical Society of America

Original Manuscript: August 12, 1985
Manuscript Accepted: November 18, 1985
Published: February 1, 1986

A. H. Paxton, "Unstable resonators with negative equivalent Fresnel numbers," Opt. Lett. 11, 76-78 (1986)

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  1. A. E. Siegman, IEEE J. Quantum Electron. QE-12, 35 (1976). [CrossRef]
  2. A. H. Paxton, T. C. Salvi, Opt. Commun. 26, 305 (1978); T. C. Salvi, A. H. Paxton, Appl. Opt. 18, 2098 (1979). [CrossRef]
  3. M. Piche, P. Lavigne, F. Martin, P.A. Belanger, Appl. Opt. 22, 1999 (1983). [CrossRef] [PubMed]
  4. K. E. Oughstun, P. A. Slaymaker, K. A. Bush, IEEE J. Quantum Electron. QE-19, 1558 (1983). [CrossRef]
  5. P. G. Gobbi, G. C. Reali, Opt. Commun. 52, 195 (1984); P. G. Gobbi, S. Morosi, G. C. Reali, A. S. Zarkasi, Appl. Opt. 24, 26 (1985). [CrossRef] [PubMed]
  6. A. H. Paxton, L. M. Gutheinz, Electro-Opt. Syst. Design 14, 31 (1982).
  7. G. T. Moore, Proc. Soc. Photo-Opt. Instrum. Eng. 453, 255 (1983).
  8. S. A. Mani, J. H. Hammond, in Proceedings of the International Conference on Lasers 81, C. B. Collins, ed. (STS, McLean, Va., 1981), p. 586.
  9. P. R. Akkapeddi, P. Glenn, A. Fuschetto, Q. Appert, V. K. Viswanathan, presented at Southwest Conference on Optics, March 4–8, 1985, Albuquerque, N.M.
  10. A. Sarnik, P. Glenn, presented at Southwest Conference on Optics, March 4–8, 1985, Albuquerque, N.M.
  11. If, however, the resonator mode has a focus between the image location and the outcoupling aperture, an image location before the outcoupling aperture corresponds to a negative equivalent Fresnel number. A similarity transformation of the round-trip propagation matrix will move the image location past the outcoupling aperture, with no intervening focus. The appropriate similarity transformation corresponds to the placement of a lens with some focal length f1 immediately in front of the outcoupling aperture and a lens with focal length −f1 immediately behind the outcoupling aperture.
  12. E. A. Sziklas, A. E. Siegman, Appl. Opt. 14, 1874 (1975). [CrossRef] [PubMed]

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