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Optics Letters

Optics Letters


  • Vol. 19, Iss. 8 — Apr. 15, 1994
  • pp: 524–526

Spatial solitons of Maxwell’s equations

Allan W. Snyder, D. John Mitchell, and Yijiang Chen  »View Author Affiliations

Optics Letters, Vol. 19, Issue 8, pp. 524-526 (1994)

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Spatial solitons of Maxwell’s equations propagating in an isotropic Kerr material differ significantly from the classical soliton of the nonlinear Schrödinger equation unless the electric field is linearly polarized along a geometric axis of the soliton intensity pattern. In general the polarization state changes continuously as the beam propagates, with a period of millimeters for highly nonlinear materials. This effect is due to the form birefringence of the soliton-induced waveguide. Equivalently, a soliton of Maxwell’s equations is composed of both the TE and TM modes of the axially uniform waveguide it induces. Modal beating leads to the polarization dynamics.

© 1994 Optical Society of America

Original Manuscript: September 20, 1993
Published: April 15, 1994

Allan W. Snyder, D. John Mitchell, and Yijiang Chen, "Spatial solitons of Maxwell’s equations," Opt. Lett. 19, 524-526 (1994)

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  1. R. Chaio, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964). [CrossRef]
  2. A. W. Snyder, W. R. Young, J. Opt. Soc. Am. 68, 297 (1978). [CrossRef]
  3. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 13 and 32.
  4. P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964). Their case of B = 0 applies for materials with zero nonlinear intrinsic birefringence. [CrossRef]
  5. A. W. Snyder, D. J. Mitchell, L. Poladian, F. Ladouceur, Opt. Lett. 16, 21 (1991); A. W. Snyder, D. J. Mitchell, Opt. Lett. 18, 101 (1993). [CrossRef] [PubMed]
  6. D. Pohl, Opt. Commun. 2, 305 (1970). This paper suggests that TM solitons do not exist, but their existence is established in Ref. 7. [CrossRef]
  7. Y. Chen, A. W. Snyder, Electron. Lett. 27, 565 (1991). [CrossRef]
  8. Beam propagation is accomplished with the pair of equations Lψy = 0 andLψx=-∂∂x(ψx∂ ln n2∂x),where L = i2kn0(∂/∂z) + ∇t2 + k2δn2, with n2 = n02 + δn2(|E|2) and E = (x̂ψx + ŷψy)exp(ikn0z).
  9. V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
  10. A. W. Snyder, S. J. Hewlett, D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994). [CrossRef] [PubMed]

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