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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 20 — Sep. 28, 2009
  • pp: 17934–17949

An accurate envelope equation for light propagation in photonic nanowires: new nonlinear effects

Truong X. Tran and Fabio Biancalana  »View Author Affiliations

Optics Express, Vol. 17, Issue 20, pp. 17934-17949 (2009)

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We derive a set of new unidirectional evolution equations for photonic nanowires, i.e. waveguides with sub-wavelength core diameter. Contrary to previous approaches, our formulation simultaneously takes into account both the vector nature of the electromagnetic field and the full variations of the effective modal profiles with wavelength. This leads to the discovery of new, previously unexplored nonlinear effects which have the potential to affect soliton propagation considerably. We specialize our theoretical considerations to the case of perfectly circular silica strands in air, and we support our analysis with detailed numerical simulations.

© 2009 Optical Society of America

OCIS Codes
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(190.3270) Nonlinear optics : Kerr effect
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(060.4005) Fiber optics and optical communications : Microstructured fibers

ToC Category:
Nonlinear Optics

Original Manuscript: August 6, 2009
Revised Manuscript: September 17, 2009
Manuscript Accepted: September 17, 2009
Published: September 22, 2009

Truong X. Tran and Fabio Biancalana, "An accurate envelope equation for light propagation in photonic nanowires: new nonlinear effects," Opt. Express 17, 17934-17949 (2009)

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  1. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, San Diego, 2007).
  2. A. Taflove and S. C. Hagness, Computational Electrodynamics, 3rd ed. (Artech House, London, 2005).
  3. A. Hasegawa and Y. Kodama, "Nonlinear pulse propagation in a monomode dielectric guide," IEEE J. Quantum Electron. 23, 510-524 (1987). [CrossRef]
  4. F. Biancalana, D. V. Skryabin, and P. St. J. Russell, "Four-wave mixing instabilities in photonic crystal and tapered fibers," Phys. Rev. E 68, 046603 (2003). [CrossRef]
  5. J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1986). [CrossRef] [PubMed]
  6. A. L. Gaeta, "Nonlinear propagation and continuum generation in microstructured optical fibers," Opt. Lett. 27, 924-926 (2002). [CrossRef]
  7. K. Shi, F. G. Omenetto, and Z. Liu, "Supercontinuum generation in an imaging fiber taper," Opt. Express 14, 12359-12364 (2006).
  8. P. St. J. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003). [CrossRef] [PubMed]
  9. J. M. Dudley, G. Genty and S. Coen, "Supercontinuum generation in photonic crystal fibers," Rev. Mod. Phys. 78, 1135-1184 (2006). [CrossRef]
  10. N. Akhmediev and M. Karlsson, "Cherenkov radiation emitted by solitons in optical fibers," Phys. Rev. A 51, 2602-2607 (1995). [CrossRef] [PubMed]
  11. D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, "Soliton self-frequency shift cancellation in photonic crystal fibers," Science 301, 1705-1707 (2003). [CrossRef] [PubMed]
  12. F. Biancalana, D. V. Skryabin, and A. V. Yulin, "Theory of the soliton self-frequency shift compensation by the resonant radiation in photonic crystal fibers," Phys. Rev. E 70, 016615 (2004). [CrossRef]
  13. T. Brabec and F. Krausz, "Nonlinear optical pulse propagation in the single-cycle regime," Phys. Rev. Lett. 78, 3282-3285 (1997). [CrossRef]
  14. T. G. Euser, J. S. Y. Chen, M. Scharrer, P. St. J. Russell, N. J. Farrer and P. J. Sadler, "Quantitative broadband chemical sensing in air-suspended solid-core fibers," J. Appl. Phys. 103, 103108 (2008). [CrossRef]
  15. F. Benabid, F. Biancalana, P. S. Light, F. Couny, A. Luiten, P. J. Roberts, J. Peng, A. V. Sokolov, "Fourth-order dispersion mediated solitonic radiations in HC-PCF cladding," Opt. Lett. 33,2680-2682 (2008). [CrossRef] [PubMed]
  16. S. Afshar V. and T. M. Monro, "A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity," Opt. Express 17,2298-2318 (2009). [CrossRef] [PubMed]
  17. M. D. Turner, T. M. Monro and S. Afshar V., "A full vectorial model for pulse propagation in emerging waveguides with sub-wavelength structures part II: Stimulated Raman Scattering," Opt. Express 17, 11565-11581 (2009). [CrossRef] [PubMed]
  18. M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, "Nonlinear optics in photonic nanowires," Opt. Express 16, 1300-1320 (2008). [CrossRef] [PubMed]
  19. M. A. Foster, K. D. Moll, and A. L. Gaeta, "Optimal waveguide dimensions for nonlinear interactions," Opt. Express 12,2880-2887 (2004). [CrossRef] [PubMed]
  20. A. Zheltikov, "Gaussian-mode analysis of waveguide-enhanced Kerr-type nonlinearity of optical fibers and photonic wires," J. Opt. Soc. Am. B 22,1100-1104 (2005). [CrossRef]
  21. S. Afshar V., W. Zhang and T. M. Monro, "Experimental confirmation of a generalized definition of the effective nonlinear coefficient in emerging waveguides with sub-wavelength structures," CThBB6, CLEO Conference, Baltimore, USA (2009).
  22. P. V. Mamyshev and S. V. Chernikov, "Ultrashort-pulse propagation in optical fibers," Opt. Lett. 15,1076-1078 (1990). [CrossRef] [PubMed]
  23. M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations," Phys. Rev. E 70, 036604 (2004). [CrossRef]
  24. J. Lægsgaard, "Mode profile dispersion in the generalised nonlinear Schrdinger equation," Opt. Express 15,16110-16123 (2007). [CrossRef] [PubMed]
  25. J. D. Jackson, Classical Electrodynamics (Wiley & Sons, New York, 1998).
  26. A. W. Snyder and J. Love, Optical Waveguide Theory (Kluwer, Boston, 1983).
  27. B. Kibler, J. M. Dudley, S. Coen, "Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area," Appl. Phys. B 81, 337-342 (2005). [CrossRef]
  28. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, San Diego, 2008).
  29. R. W. Hellwarth, "Third-order optical susceptibilities of liquids ans solids," Prog. Quantum Electron. 5,1-68 (1977). [CrossRef]
  30. F. Poletti and P. Horak, "Description of ultrashort pulse propagation in multimode optical fibers," J. Opt. Soc. Am. B 25, 1645-1654 (2008). [CrossRef]
  31. J. Santhanam and G. P. Agrawal, "Raman-induced spectral shifts in optical fibers: general theory based on the moment method," Opt. Commun. 222, 413-420 (2003). [CrossRef]
  32. F. Biancalana and Tr. X. Tran, in preparation.

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