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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 22, Iss. 2 — Feb. 1, 2005
  • pp: 306–309

Ince–Gaussian beams in a quadratic-index medium

Julio C. Gutiérrez-Vega and Miguel A. Bandres  »View Author Affiliations


JOSA A, Vol. 22, Issue 2, pp. 306-309 (2005)
http://dx.doi.org/10.1364/JOSAA.22.000306


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Abstract

The propagation of Ince–Gaussian beams in media where the refractive index varies quadratically with the distance from the optical axis is studied. Explicit expressions for the complex beam parameter and the longitudinal phase shift are derived and discussed. Ince–Gaussian eigenmodes with constant width can be obtained by satisfying a relation between the beam width and the quadratic-medium coefficient. The derivation has included the possibility of propagation of Ince–Gaussian beams in complex lenslike media having quadratic transverse variations of the index of refraction and the gain or loss.

© 2005 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(140.3300) Lasers and laser optics : Laser beam shaping
(140.3410) Lasers and laser optics : Laser resonators
(260.1960) Physical optics : Diffraction theory
(350.5500) Other areas of optics : Propagation

History
Original Manuscript: July 23, 2004
Manuscript Accepted: August 24, 2004
Published: February 1, 2005

Citation
Julio C. Gutiérrez-Vega and Miguel A. Bandres, "Ince–Gaussian beams in a quadratic-index medium," J. Opt. Soc. Am. A 22, 306-309 (2005)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-2-306


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References

  1. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  2. M. A. Bandres, J. C. Gutiérrez-Vega, “Ince–Gaussian beams,” Opt. Lett. 29, 144–146 (2004). [CrossRef] [PubMed]
  3. M. A. Bandres, J. C. Gutiérrez-Vega, “Ince–Gaussian modes of the paraxial wave equation and stable resonators,” J. Opt. Soc. Am. A 21, 873–880 (2004). [CrossRef]
  4. M. A. Bandres, “Elegant Ince–Gaussian beams,” Opt. Lett. 29, 1724–1726 (2004). [CrossRef] [PubMed]
  5. U. T. Schwarz, M. A. Bandres, J. C. Gutiérrez-Vega, “Observation of Ince–Gaussian modes in stable resonators,” Opt. Lett. 29, 1870–1872 (2004). [CrossRef] [PubMed]
  6. P. K. Tien, J. P. Gordon, J. R. Whinnery, “Focusing of light beam of Gaussian field distribution in continuous and periodic lenslike media,” Proc. IEEE 53, 129–136 (1965). [CrossRef]
  7. M. Newstein, K. Lin, “Laguerre–Gaussian periodically focusing beams in a quadratic index medium,” IEEE J. Quantum Electron. 23, 481–482 (1987). [CrossRef]
  8. F. M. Arscott, Periodic Differential Equations (Pergamon, Oxford, UK, 1964).
  9. 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]
  10. M. A. Bandres, J. C. Gutiérrez-Vega, “Ince–Gaussian series representation of the two-dimensional fractional Fourier transform,” Opt. Lett. (to be published).

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