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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 17, Iss. 4 — Apr. 1, 2000
  • pp: 555–560

Propagation and transformation properties of an elliptic Gaussian optical beam with a Kerr-law nonlinear graded-index rod lens

Yucui Li  »View Author Affiliations

JOSA B, Vol. 17, Issue 4, pp. 555-560 (2000)

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An elliptic Gaussian optical beam (EGB) in a Kerr-law nonlinear graded-index rod lens is treated as two dependent optical beams. Two coupled differential equations of the dimensionless beam-width parameters of two beams in the rod lens are derived by a variational approach and then solved for what is to my knowledge the first time. Investigations of the propagation and the collapse of the EGB in the rod lens and the transformation of the EGB by the rod lens are presented. It is concluded that the properties of propagation, collapse, and transformation are largely determined by the power and initial ellipticity of the incident EGB. The field derived also applies to the EGB propagating in a nonlinear graded-index fiber.

© 2000 Optical Society of America

OCIS Codes
(060.2350) Fiber optics and optical communications : Fiber optics imaging
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(110.2760) Imaging systems : Gradient-index lenses
(140.3510) Lasers and laser optics : Lasers, fiber
(190.3270) Nonlinear optics : Kerr effect
(190.4370) Nonlinear optics : Nonlinear optics, fibers

Yucui Li, "Propagation and transformation properties of an elliptic Gaussian optical beam with a Kerr-law nonlinear graded-index rod lens," J. Opt. Soc. Am. B 17, 555-560 (2000)

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  1. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).
  2. G. I. Stegeman and R. H. Stolen, “Waveguides and fibers for nonlinear optics,” J. Opt. Soc. Am. B 6, 652–662 (1989). [CrossRef]
  3. P. Tran, “All-optical switching with a nonlinear chiral photonic bandgap structure,” J. Opt. Soc. Am. B 16, 70–73 (1999). [CrossRef]
  4. E. Desurvire, Erbium-Doped Fiber Amplifiers: Principles and Applications (Wiley, New York, 1994).
  5. R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, “Nonlinear refractive index in erbium doped optical fiber: theory and experiment,” IEEE J. Quantum Electron. 27, 908–913 (1991). [CrossRef]
  6. R. A. Sammut and C. Pask, “Gaussian and equivalent-step-index approximations for nonlinear waveguides,” J. Opt. Soc. Am. B 8, 395–402 (1991). [CrossRef]
  7. M. Karlsson and D. Anderson, “Super-Gaussian approximation of the fundamental radial mode in nonlinear parabolic-index optical fibers,” J. Opt. Soc. Am. B 9, 1558–1562 (1992). [CrossRef]
  8. Z. Chen and H. Lai, “Imaging properties of Gaussian beams with a nonlinear graded-index rod lens,” J. Opt. Soc. Am. B 9, 2248–2251 (1992). [CrossRef]
  9. Z. Chen, X. Chen, and H. Lai, “Effect of beam power on imaging characteristics of Gaussian beams with a defocusing GRIN rod lens,” IEE Proc. J. 139, 309–312 (1992).
  10. L. Gagnon and C. Paré, “Nonlinear radiation modes connected to parabolic graded-index profiles by the lens transformation,” J. Opt. Soc. Am. A 8, 601–607 (1991). [CrossRef]
  11. F. Cornolti, M. Lucchesi, and B. Zambon, “Elliptic Gaussian beam self-focusing in nonlinear media,” Opt. Commun. 75, 129–135 (1990). [CrossRef]
  12. C. R. Giuliano, J. H. Marburger, and A. Yariv, “Enhancement of self-focusing threshold in sapphire with elliptical beams,” Appl. Phys. Lett. 21, 58–60 (1972). [CrossRef]
  13. S. Konar and A. Sengupta, “Propagation of an elliptic Gaussian laser beam in a medium with saturable nonlinearity,” J. Opt. Soc. Am. B 11, 1644–1646 (1994). [CrossRef]
  14. S. M. Mian, B. Taheri, and J. P. Wicksted, “Effects of beam ellipticity on Z-scan measurement,” J. Opt. Soc. Am. B 13, 856–863 (1996). [CrossRef]
  15. A. Yariv, Introduction to Optical Electronics (Holt, Rinehart & Winston, New York, 1976), Chaps. 2 and 3.
  16. F. H. Berkshire and J. D. Gibbon, “Collapse in the n-dimensional nonlinear Schrödinger equation—a parallel with Sundman’s results in the N-body problem,” Stud. Appl. Math. 69, 229–262 (1983).
  17. J. R. Ray and J. L. Reid, “More exact invariants for the time-dependent harmonic oscillator,” Phys. Lett. 71A, 317–318 (1979). [CrossRef]

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