OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 4 — Feb. 16, 2009
  • pp: 2298–2318

A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity

Shahraam Afshar V. and Tanya M. Monro  »View Author Affiliations

Optics Express, Vol. 17, Issue 4, pp. 2298-2318 (2009)

View Full Text Article

Enhanced HTML    Acrobat PDF (2826 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The propagation of pulses through waveguides with sub-wavelength features, inhomogeneous transverse structure, and high index contrast cannot be described accurately using existing models in the presence of nonlinear effects. Here we report the development of a generalised full vectorial model of nonlinear pulse propagation and demonstrate that, unlike the standard pulse propagation formulation, the z-component of guided modes plays a key role for these new structures, and results in generalised definitions of the nonlinear coefficient γ, Aeff , and mode orthognality. While new definitions reduce to standard definitions in some limits, significant differences are predicted, including a factor of ~2 higher value for γ, for emerging waveguides and microstructured fibers.

© 2009 Optical Society of America

OCIS Codes
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(130.4310) Integrated optics : Nonlinear
(190.3270) Nonlinear optics : Kerr effect
(190.4360) Nonlinear optics : Nonlinear optics, devices
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(060.4005) Fiber optics and optical communications : Microstructured fibers

ToC Category:
Nonlinear Optics

Original Manuscript: November 19, 2008
Revised Manuscript: January 22, 2009
Manuscript Accepted: February 4, 2009
Published: February 5, 2009

Shahraam Afshar V. and Tanya 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)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. Q. Lin, O. J. Painter, and G. P. Agrawal, "Nonlinear Optical Phenomena in Silicon Waveguides: Modeling and Applications," Opt. Express 15, 16,604 (2007). [CrossRef]
  2. J. C. Knight and D. V. Skryabin, "Nonlinear Waveguide Optics and Photonic Crystal Fibers," Opt. Express 15, 15,365 (2007). [CrossRef]
  3. M. A. Foster, A. C. Turner,M. Lipson, and A. L. Gaeta, "Nonlinear Optics in Photonic Nanowires," Opt. Express 16, 1300 (2008). [CrossRef] [PubMed]
  4. C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, "Nonlinear silicon-on-insulator waveguides for all-optical signal processing," Opt. Express 15, 5976-5990 (2007). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-10-5976. [CrossRef] [PubMed]
  5. A. Fuerbach, P. Steinvurzel, J. Bolger, and B. Eggleton, "Nonlinear pulse propagation at zero dispersion wavelength in anti-resonant photonic crystal fibers," Opt. Express 13, 2977-2987 (2005). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-13-8-2977. [CrossRef] [PubMed]
  6. S. Yiou, P. Delaye, A. Rouvie, J. Chinaud, R. Frey, G. Roosen, P. Viale, S. Février, P. Roy, J.-L. Auguste, and J.-M. Blondy, "Stimulated Raman scattering in an ethanol core microstructured optical fiber," Opt. Express 13, 4786-4791 (2005). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-13-12-4786. [CrossRef] [PubMed]
  7. F. M. Cox, A. Argyros, and M. C. J. Large, "Liquid-filled hollow core microstructured polymer optical fiber," Opt. Express 14, 4135-4140 (2006). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-14-9-4135. [CrossRef] [PubMed]
  8. R. Zhang, J. Teipel, and H. Giessen, "Theoretical design of a liquid-core photonic crystal fiber for supercontinuum generation," Opt. Express 14, 6800-6812 (2006). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-14-15-6800 [CrossRef] [PubMed]
  9. M. R. Perrone, V. Piccinno, G. de Nunzio, and V. Nassisi, "Dependence of Rotational and Vibrational Raman Scattering on Focusing Geometry," IEEE. J. Quantum Electron. 33, 938-944 (1997). [CrossRef]
  10. F. D. Tomasi, "Stimulated Rotational and Vibrational Raman Scattering by Elliptical Polarized Pump Radiation," Phys. Rev. A 64, 023,812 (2001).
  11. L. S. Meng, P. A. Roos, and J. L. Carlsten, "Continuous-Wave Rotational Raman Laser in H2," Opt. Lett. 27, 1226 (2002). [CrossRef]
  12. F. Benabid, G. Bouwmans, J. C. Knight, and P. S. J. Russell, "Ultrahigh Efficiency Laser Wavelength Conversion in a Gas-Filled Hollow Core Photonic Crystal Fiber by Pure Stimulated Rotational Raman Scattering in Molecular Hydrogen," Phys. Rev. Lett. 93, 123,903-1 (2004). [CrossRef]
  13. F. Benabid, F. Couny, J. C. Knight, T. A. Birks, and P. S. J. Russell, "Compact, Stable and Efficient All-Fibre Gas Cells using Hollow-Core Photonic Crystal Fibres," Nature 434, 488 (2005). [CrossRef] [PubMed]
  14. C. A. Barrios, "High-Performance All-Optical Silicon Microswitch," Electron Lett. 40, 862 (2004). [CrossRef]
  15. S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, "Resonant Optical Interactions with Molecules Confined in Photonic Band-Gap Fibers," Phys. Rev. Lett.  94, 093902 (2005). URL http://link.aps.org/abstract/PRL/v94/e093902. [CrossRef] [PubMed]
  16. F. Benabid, P. Light, F. Couny, and P. Russell, "Electromagnetically-induced transparency grid in acetylene-filled hollow-core PCF," Opt. Express 13, 5694-5703 (2005). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-13-15-5694. [CrossRef] [PubMed]
  17. S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, "Low-Light-Level Optical Interactions with Rubidium Vapor in a Photonic Band-Gap Fiber," Phys. Rev. Lett. 97, 023603 (2006). URL http://link.aps.org/abstract/PRL/v97/e023603. [CrossRef] [PubMed]
  18. P. S. Light, F. Benabid, F. Couny, M. Maric, and A. N. Luiten, "Electromagnetically induced transparency in Rb-filled coated hollow-core photonic crystal fiber," Opt. Lett.  32, 1323-1325 (2007). URL http://ol.osa.org/abstract.cfm?URI=ol-32-10-1323. [CrossRef] [PubMed]
  19. J. E. Debs, H. Ebendorff-Heidepriem, J. S. Quinton, and T. M. Monro, "A Fundamental Study Into the Surface Functionalization of Soft Glass Microstructured Optical Fibers Via Silane Coupling Agents," J. Lightwave Technol., Accepted (2008).
  20. M. Foster, K. Moll, and A. Gaeta, "Optimal waveguide dimensions for nonlinear interactions," Opt. Express 12, 2880-2887 (2004). [CrossRef] [PubMed]
  21. Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, "Experimental Demonstration of Guiding and Confining Light in Nanometer-Size Low-Refractive-Index Material," Opt. Lett. 29, 1626 (2004). [CrossRef] [PubMed]
  22. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, "Guiding and Confining Light in Void Nanostructure," Opt. Lett. 29, 1209 (2004). [CrossRef] [PubMed]
  23. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-Optical Control of Light on a Silicon Chip," Nature 43, 1081 (2004). [CrossRef]
  24. V. Almeida, C. Barrios, R. Panepucci, M. Lipson, M. Foster, D. Ouzounov, and A. Gaeta, "All-optical switching on a silicon chip," Opt. Lett. 29, 2867-2869 (2004). [CrossRef]
  25. M. Foster, J. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. Gaeta, "Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation," Appl. Phys. B-Lasers Opt. 81, 363-367 (2005). [CrossRef]
  26. P. Mullner and R. Hainberger, "Structural Optimization of Silicon-on-Insulator Slot Waveguides," IEEE Photon. Technol. Lett. 18, 2557 (2006). [CrossRef]
  27. E. C. Magi, L. B. Fu, H. C. Nguyen, M. R. E. Lamont, D. I. Yeom, and B. J. Eggleton, "Enhanced Kerr Nonlinearity in Sub-Wavelength Diameter As2Se3 Chalcogenide Fiber Tapers," Opt. Express 15, 10,324 (2007). [CrossRef]
  28. M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, "Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides," Opt. Express 15, 12,949-12,958 (2007). [CrossRef]
  29. R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, "All-Optical Regeneration on Silicon Chip," Opt. Express 15, 7802 (2007). [CrossRef] [PubMed]
  30. M. Nagel, A. Marchewka, and H. Kurz, "Low-index discontinuity terahertz waveguides," Opt. Express 14, 9944-9954 (2006). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-14-21-9944. [CrossRef] [PubMed]
  31. G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, and H. L. Fragnito, "Field Enhancement within an Optical Fibre with a Subwavelength Air Core," Nat. Photonics 1, 115 (2007). [CrossRef]
  32. S. Afshar. V., S. C. Warren-Smith, and T. M. Monro, "Enhancement of fluorescence-based sensing using microstructured optical fibres," Opt. Express 15,17,891-17,901 (2007). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-26-17891. [CrossRef]
  33. S. Atakaramians, S. Afshar. V., B. M . Fischer, D . Abbott, and T. M. Monro, "Porous fibers: a novel approach to low loss THz waveguides," Opt. Express 16, 8845-8854 (2008). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-16-12-8845. [CrossRef] [PubMed]
  34. N. Karasawa, S. Nakamura, N. Nakagawa, M. Shibata, R. Morita, H. Shigekawa, and M. Yamashita, "Comparison between Theory and Experiment of Nonlinear Propagation for a-Few-Cycle and Ultrabroadband Optical Pulses in a Fused-Silica Fiber," IEEE J. of Quantum Electron. 37, 398 (2001). [CrossRef]
  35. O. Boyraz, T. Indukuri, and B. Jalali, "Self-Pahse-Modulation Induced Spectral Broadening in Silicon Waveguides," Opt. Express 12, 829 (2004). [CrossRef] [PubMed]
  36. O. Boyraz, P. Koonath, V. Raghunathan, and B. Jalali, "All Optical Switching and Continuum Generation in Silicon Waveguides," Opt. Express 12, 4094 (2004). [CrossRef] [PubMed]
  37. A. Zheltikov, "Gaussian-Mode Analysis of Waveguide-Enhanced Kerr-Type Nonlinearity of Optical Fibers and Photonic Wires," J. Opt. Soc. Am. B 22, 1100 (2005). [CrossRef]
  38. B. Kibler, J. M. Dudley, and 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]
  39. J. Y. Y. Leong, P. Petropoulos, J. H. V. Price, H. Ebendorff-Heidepriem, S. Asimakis, R. C. Moore, K. E. Frampton, V. Finazzi, X. Feng, T. M. Monro, and D. J. Richardson, "High-Nonlinearity Dispersion-Shifted Lead-Silicate Holey Fibers for Efficient 1-m Pumped Supercontinuum Generation," IEEE J. Lightwave Technol.  24, 183 (2006). URL http://jlt.osa.org/abstract.cfm?URI=JLT-24-1-183. [CrossRef]
  40. G. Genty, P. Kinsler, B. Kibler, and J. M. Dudley, "Nonlinear Envelope Equation Modeling of Sub-Cycle Dynamics and Harmonic Generation in Nonlinear Waveguides," Opt. Express 15, 5382 (2007). [CrossRef] [PubMed]
  41. J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, "Optical solitons in a silicon waveguide," Opt. Express 15, 7682-7688 (2007). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-12-7682. [CrossRef] [PubMed]
  42. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).
  43. M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations," Phys. Rev. E 70, 036,604 (2004). [CrossRef]
  44. M. Kolesik, E. M. Wright, and J. V. Moloney, "Simulation of Femtosecond Pulse Propagation in Sub-Micron Diameter Tapered Fibers," Appl. Phys. B 79, 293 (2004). [CrossRef]
  45. X. Chen, N. C. Panoiu, and R. M. Osgood, "Theory of Raman-Mediated Pulsed Amplification in Silicon-Wire Waveguides," IEEE J. Quantum Electron. 42, 160 (2006). [CrossRef]
  46. J. Laegsgaard, "Mode profile dispersion in the generalised nonlinear Schr¨odinger equation," Opt. Express 15, 16,110-16,123 (2007). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-24-16110. [CrossRef]
  47. J. L. Dadap, N. C. Panoiu, X. Chen, I.-W. Hsieh, X. Liu, C.-Y. Chou, E. Dulkeith, S. J. McNab, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. O. Jr., "Nonlinear-Optical Phase Modification in Dispersion-Engineered Si Photonic Wires," Opt. Express 16, 1280 (2008). [CrossRef] [PubMed]
  48. T. Fujisawa and M. Koshiba, "Guided Modes of Nonlinear Slot Waveguides," IEEE Photon. Technol. Lett. 18, 1530 (2006). [CrossRef]
  49. S. Afshar V. and T. M. Monro, "Kerr Nonlinearity in Small Core Optical Fibres and Nanowires: A Generalised Model, and Application to Microstructured Fibres", Joint OECC/ACOFT 2008 conference, IEEE conference proceeding.
  50. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and hall, 2-6 Boundary Row, London SE1 8HN, UK, 1995).
  51. K. Okamoto, Fundamentals of Optical Waveguides, 1st ed., (Academic Press, 2000).
  52. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, "Multipole method for microstructured optical fibers. I. Formulation," J. Opt. Soc. Am. B 19, 2322-2330 (2002). [CrossRef]
  53. URL http://josab.osa.org/abstract.cfm?URI=josab-19-10-2322. [CrossRef]
  54. B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. M. de Sterke, and R. C. McPhedran, "Multipole method for microstructured optical fibers. II. Implementation and results," J. Opt. Soc. Am. B 19, 2331-2340 (2002). [CrossRef]
  55. URL http://josab.osa.org/abstract.cfm?URI=josab-19-10-2331. [CrossRef]
  56. M. Kolesik, J. V. Moloney, and M. Mlejnek, "Unidirectional Optical Pulse Propagation Equation," Phys. Rev. Lett. 89, 283,902-1 (2002). [CrossRef]
  57. M. J. Steel, T. P. White, C. M. de Sterke, R. C. McPhedran, and L. C. Botten, "Symmetry and Degeneracy in Microstructured Optical Fibers," Opt. Lett. 26, 488 (2001). [CrossRef]
  58. K. J. Blow and D. Wood, "Theoretical Description of Transient Stimulated Raman Scattering in Optical Fibers," IEEE J. Quantum Electron. 25, 2665 (1989). [CrossRef]
  59. P. V. Mamyshev and S. V. Chernikov, "Ultrashort-Pulse Propagation in Optical Fibers," Opt. Lett. 19, 1076 (1990). [CrossRef] [PubMed]
  60. T. Brabec and F. Krausz, "Nonlinear Optical Pulse Ropagation in the Single-Cycle Regime," Phys. Rev. Lett. 78, 3282 (1997). [CrossRef]
  61. A. L. Gaeta, "Catastrophic Collapse of Ultrashort Pulses," Phys. Rev. Lett. 84, 3582 (2000). [CrossRef]
  62. J. M. Dudley and S. Coen, "Coherence Properties of Supercontinuum Spectra Generated in Photonic Crystal and Tapered Optical Fibers," Opt. Lett. 27, 1180 (2002). [CrossRef] [PubMed]
  63. F. Biancalana, D. V. Skryabin, and P. S. J. Russell, "Four-Wave Mixing Instabilities in Photonic-Crystal and Tapered Fibers," Phys. Rev. E 68, 046,603-1 (2003).
  64. G. Chang, T. B. Norris, and H. G. Winful, "Optimization of Supercontinuum Generation in Photonic Crystal Fibers for Pulse Compression," Opt. Lett. 28, 546 (2003). [CrossRef]
  65. P. N. Butch, and D. Cotter, The Elements of Nonlinear Optics (Cambridge University Press, Cambridge CB2 1RP UK, 1990). [CrossRef]
  66. P. Roussignol, D. Ricard, J. Lukasik, and C. Flytzanis, "New results on optical phaseconjugation in semiconductor-doped glasses," J. Opt. Soc. Am. B 4, 5-13 (1987). [CrossRef]
  67. G. I. Stegeman and R. H. Stolen, "Waveguides and fibers for nonlinear optics," J. Opt. Soc. Am. B 6, 652-662 (1989). URL http://josab.osa.org/abstract.cfm?URI=josab-6-4-652. [CrossRef]
  68. S. Gatz and J. Herrmann, "Soliton propagation in materials with saturable nonlinearity," J. Opt. Soc. Am. B 8, 2296-2302 (1991). URL http://josab.osa.org/abstract.cfm?URI=josab-8-11-2296. [CrossRef]
  69. J.-L. Coutaz and M. Kull, "Saturation of the nonlinear index of refraction in semiconductor-doped glass," J. Opt. Soc. Am. B 8, 95-98 (1991). URL http://josab.osa.org/abstract.cfm?URI=josab-8-1-95.
  70. S. Konar, S. Jana, and M. Mishra, "Induced focusing and all optical switching in cubic quintic nonlinear media," Opt. Commun 255, 114-129 (2005). [CrossRef]
  71. R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, CA, 2003). [CrossRef] [PubMed]
  72. Q. Lin and G. P. Agrawal, "Vector Theory of Cross-Phase Modulation: Role of Nonlinear Polarization Rotation," IEEE J. Quantum Electron. 40, 958 (2004). [CrossRef] [PubMed]
  73. H. Ebendorff-Heidepriem, P. Petropoulos, S. Asimakis, V. Finazzi, R. Moore, K. Frampton, F. Koizumi, D. Richardson, and T. Monro, "Bismuth glass holey fibers with high nonlinearity," Opt. Express 12, 5082-5087 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-21-5082. [CrossRef]
  74. H. Ebendorff-Heidepriem, P. Petropoulos, S. Asimakis, V. Finazzi, R. C. Moore, K. Frampton, F. Koizumi, D. J. Richardson, and T. M. Monro, "Bismuth Glass Holey Fibers with High Nonlinearity," Opt. Express 12, 5082 (2004). [CrossRef] [PubMed]
  75. M. Dinu, F. Quochi, and H. Garcia, "Third-Order Nonlinearities in Silicon at TelecomWavelengths," App. Phys. Lett. 82, 2954 (2003).
  76. M. Steel, "Reflection symmetry and mode transversality in microstructured fibers," Opt. Express 12, 1497-1509 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-8-1497.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited