Abstract

We develop a full theoretical analysis of the nonlinear interactions of the two polarizations of a waveguide by means of a vectorial model of pulse propagation which applies to high index subwavelength waveguides. In such waveguides there is an anisotropy in the nonlinear behavior of the two polarizations that originates entirely from the waveguide structure, and leads to switching properties. We determine the stability properties of the steady state solutions by means of a Lagrangian formulation. We find all static solutions of the nonlinear system, including those that are periodic with respect to the optical fiber length as well as nonperiodic soliton solutions, and analyze these solutions by means of a Hamiltonian formulation. We discuss in particular the switching solutions which lie near the unstable steady states, since they lead to self-polarization flipping which can in principle be employed to construct fast optical switches and optical logic gates.

© 2012 OSA

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  1. R. H. Stolen, J. Botineau, and A. Ashkin, “Intensity discrimination of optical pulses with birefringent fibers,” Opt. Lett.7, 512–514 (1982).
    [CrossRef] [PubMed]
  2. F. Matera and S. Wabnitz, “Nonlinear polarization evolution and instability in a twisted birefringent fiber,” Opt. Lett.11, 467–469 (1986).
    [CrossRef] [PubMed]
  3. H. G. Winful, “Polarization instabilities in birefringent nonlinear media: application to fiber-optic devices,” Opt. Lett.11, 33–35 (1986).
    [CrossRef] [PubMed]
  4. C. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron.23, 174–176 (1987).
    [CrossRef]
  5. S. F. Feldman, D. A. Weinberger, and H. G. Winful, “Polarization instability in a twisted birefringent optical fiber,” J. Opt. Soc. Am. B10, 1191–1201 (1993).
    [CrossRef]
  6. G. Millot, E. Seve, and S. Wabnitz, “Polarization symmetry breaking and pulse train generation from the modulation of light waves,” Phys. Rev. Lett.79, 661–664 (1997).
    [CrossRef]
  7. G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, “Dark-soliton-like pulse-train generation from induced modulational polarization instability in a birefringent fiber,” Opt. Lett.23, 511–513 (1998).
    [CrossRef]
  8. S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counterpropagating laser beams,” Phys. Rev. Lett.81, 1409–1412 (1998).
    [CrossRef]
  9. S. Pitois, G. Millot, and S. Wabnitz, “Nonlinear polarization dynamics of counterpropagating waves in an isotropic optical fiber: theory and experiments,” J. Opt. Soc. Am. B18, 432–443 (2001).
    [CrossRef]
  10. S. Wabnitz, “Polarization domain wall solitons in elliptically birefringent optical fibers,” PIERS ONLINE5, 621–624 (2009).
    [CrossRef]
  11. V. V. Kozlov and S. Wabnitz, “Theoretical study of polarization attraction in high-birefringence and spun fibers,” Opt. Lett.35, 3949–3951 (2010).
    [CrossRef] [PubMed]
  12. J. Fatome, S. Pitois, P. Morin, and G. Millot, “Observation of light-by-light polarization control and stabilization in optical fibre for telecommunication applications,” Opt. Express18, 15311–15317 (2010).
    [CrossRef] [PubMed]
  13. V. V. Kozlov, J. Nuño, and S. Wabnitz, “Theory of lossless polarization attraction in telecommunication fibers,” J. Opt. Soc. Am. B28, 100–108 (2011).
    [CrossRef]
  14. V. E. Zakharov and A. V. Mikhailov, “Polarization domains in nonlinear optics,” JETP Lett.45, 349–352 (1987).
  15. S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett.70, 88–94 (2005).
    [CrossRef]
  16. S. Pitois, J. Fatome, and G. Millot, “Polarization attraction using counter-propagating waves in optical fiber at telecommunication wavelengths,” Opt. Express16, 6646–6651 (2008).
    [CrossRef] [PubMed]
  17. S. Wabnitz, “Cross-polarization modulation domain wall solitons for WDM signals in birefringent optical fibers,” IEEE Photon. Technol. Lett.21, 875–877 (2009).
    [CrossRef]
  18. E. Seve, G. Millot, S. Trillo, and S. Wabnitz, “Large-signal enhanced frequency conversion in birefringent optical fibers: theory and experiments,” J. Opt. Soc. Am. B15, 2537–2551 (1998).
    [CrossRef]
  19. G. Gregori and S. Wabnitz, “New exact solutions and bifurcations in the spatial distribution of polarization in third-order nonlinear optical interactions,” Phys. Rev. Lett.56, 600–603 (1986).
    [CrossRef] [PubMed]
  20. S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron.18, 1580–1583 (1982).
    [CrossRef]
  21. C. M. de Sterke and J. E. Sipe, “Polarization instability in a waveguide geometry,” Opt. Lett.16, 202–204 (1991).
    [CrossRef] [PubMed]
  22. Y. Wang and W. Wang, “Nonlinear optical pulse coupling dynamics,” J. Lightwave Technol.24, 2458–2464 (2006).
    [CrossRef]
  23. Y. S. Kivshar, “Switching dynamics of solitons in fiber directional couplers,” Opt. Lett.18, 7–9 (1993).
    [CrossRef] [PubMed]
  24. D. C. Hutchings, J. S. Aitchison, and J. M. Arnold, “Nonlinear refractive coupling and vector solitons in anisotropic cubic media,” J. Opt. Soc. Am. B14, 869–879 (1997).
    [CrossRef]
  25. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett.81, 3383–3386 (1998).
    [CrossRef]
  26. U. Peschel, R. Morandotti, J. M. Arnold, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, T. Pertsch, and F. Lederer, “Optical discrete solitons in waveguide arrays. 2. dynamic properties,” J. Opt. Soc. Am. B19, 2637–2644 (2002).
    [CrossRef]
  27. K. R. Khan, T. X. Wu, D. N. Christodoulides, and G. I. Stegeman, “Soliton switching and multi-frequency generation in a nonlinear photonic crystal fiber coupler,” Opt. Express16, 9417–9428 (2008).
    [CrossRef] [PubMed]
  28. C. C. Yang, “All-optical ultrafast logic gates that use asymmetric nonlinear directional couplers,” Opt. Lett.16, 1641–1643 (1991).
    [CrossRef] [PubMed]
  29. T. Fujisawa and M. Koshiba, “All-optical logic gates based on nonlinear slot-waveguide couplers,” J. Opt. Soc. Am. B23, 684–691 (2006).
    [CrossRef]
  30. W. Fraga, J. Menezes, M. da Silva, C. Sobrinho, and A. Sombra, “All optical logic gates based on an asymmetric nonlinear directional coupler,” Opt. Commun.262, 32–37 (2006).
    [CrossRef]
  31. D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zinc-blende semiconductors,” Phys. Rev. B52, 8150–8159 (1995).
    [CrossRef]
  32. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).
  33. 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. Express17, 2298–2318 (2009).
    [CrossRef] [PubMed]
  34. J. B. Driscoll, X. Liu, S. Yasseri, I. Hsieh, J. I. Dadap, and R. M. Osgood, “Large longitudinal electric fields (Ez) in silicon nanowire waveguides,” Opt. Express17, 2797–2804 (2009).
    [CrossRef] [PubMed]
  35. B. A. Daniel and G. P. Agrawal, “Vectorial nonlinear propagation in silicon nanowire waveguides: polarization effects,” J. Opt. Soc. Am. B27, 956–965 (2010).
    [CrossRef]
  36. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett.29, 1209–1211 (2004).
    [CrossRef] [PubMed]
  37. O. Boyraz, P. Koonath, V. Raghunathan, and B. Jalali, “All optical switching and continuum generation in silicon waveguides,” Opt. Express12, 4094–4102 (2004).
    [CrossRef] [PubMed]
  38. C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon.3, 216–219 (2009).
    [CrossRef]
  39. W. Astar, J. B. Driscoll, X. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and R. M. Osgood, “Tunable wavelength conversion by XPM in a silicon nanowire, and the potential for XPM-multicasting,” J. Lightwave Technol.28, 2499–2511 (2010).
    [CrossRef]
  40. R. K. W. Lau, M. Ménard, Y. Okawachi, M. A. Foster, A. C. Turner-Foster, R. Salem, M. Lipson, and A. L. Gaeta, “Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides,” Opt. Lett.36, 1263–1265 (2011).
    [CrossRef] [PubMed]
  41. M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photon.3, 139–143 (2009).
    [CrossRef]
  42. X. Gai, T. Han, A. Prasad, S. Madden, D.-Y. Choi, R. Wang, D. Bulla, and B. Luther-Davies, “Progress in optical waveguides fabricated from chalcogenide glasses,” Opt. Express18, 26635–26646 (2010).
    [CrossRef] [PubMed]
  43. B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photon.5, 141–148 (2011).
  44. P. Petropoulos, T. M. Monro, W. Belardi, K. Furusawa, J. H. Lee, and D. J. Richardson, “2R-regenerative all-optical switch based on a highly nonlinear holey fiber,” Opt. Lett.26, 1233–1235 (2001).
    [CrossRef]
  45. 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. Express12, 5082–5087 (2004).
    [CrossRef] [PubMed]
  46. S. Afshar V., W. Q. Zhang, H. Ebendorff-Heidepriem, and T. M. Monro, “Small core optical waveguides are more nonlinear than expected: experimental confirmation,” Opt. Lett.34, 3577–3579 (2009).
    [CrossRef] [PubMed]
  47. G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Highly nonlinear tellurite microstructured fibers for broadband wavelength conversion and flattened supercontinuum generation,” J. Appl. Phys.107, 043108 (2010).
    [CrossRef]
  48. F. Poletti, X. Feng, G. M. Ponzo, M. N. Petrovich, W. H. Loh, and D. J. Richardson, “All-solid highly nonlinear singlemode fibers with a tailored dispersion profile,” Opt. Express19, 66–80 (2011).
    [CrossRef] [PubMed]
  49. M. D. Turner, T. M. Monro, and S. Afshar V., “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part II: Stimulated Raman scattering,” Opt. Express17, 11565–11581 (2009).
    [CrossRef] [PubMed]
  50. W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “Nonlinear polarization bistability in optical nanowires,” Opt. Lett.36, 588–590 (2011).
    [CrossRef] [PubMed]
  51. S. Afshar V., W. Q. Zhang, and T. M. Monro, “Structurally-based nonlinear birefringence in waveguides with subwavelength structures and high index materials,” in “ACOFT 2009 Proceeding,” (Australian Optical Society, 2009), 374–375.
  52. E. Mägi, L. Fu, H. Nguyen, M. Lamont, D. Yeom, and B. Eggleton, “Enhanced Kerr nonlinearity in sub-wavelength diameter As2Se3 chalcogenide fiber tapers,” Opt. Express15, 10324–10329 (2007).
    [CrossRef] [PubMed]
  53. S. Coleman, “Classical lumps and their quantum descendents,” in New Phenomena in Subnuclear Physics Ed. A. Zichichi (New York, 1977), 185–264.
  54. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic Press, 2003)
  55. W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “Nonlinear self-flipping of polarization states in asymmetric waveguides,” arXiv:1203.6416
  56. W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “Nonlinear polarization self-flipping and optical switching,” in Proceedings of the International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim 2011, (Optical Society of America, 2011), paper C370.
    [PubMed]
  57. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press, 1965).
  58. W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “New regimes of polarization bistability in linear birefringent waveguides and optical logic gates,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper NThD4.

2011

2010

2009

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon.3, 216–219 (2009).
[CrossRef]

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photon.3, 139–143 (2009).
[CrossRef]

S. Wabnitz, “Polarization domain wall solitons in elliptically birefringent optical fibers,” PIERS ONLINE5, 621–624 (2009).
[CrossRef]

S. Wabnitz, “Cross-polarization modulation domain wall solitons for WDM signals in birefringent optical fibers,” IEEE Photon. Technol. Lett.21, 875–877 (2009).
[CrossRef]

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. Express17, 2298–2318 (2009).
[CrossRef] [PubMed]

J. B. Driscoll, X. Liu, S. Yasseri, I. Hsieh, J. I. Dadap, and R. M. Osgood, “Large longitudinal electric fields (Ez) in silicon nanowire waveguides,” Opt. Express17, 2797–2804 (2009).
[CrossRef] [PubMed]

M. D. Turner, T. M. Monro, and S. Afshar V., “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part II: Stimulated Raman scattering,” Opt. Express17, 11565–11581 (2009).
[CrossRef] [PubMed]

S. Afshar V., W. Q. Zhang, H. Ebendorff-Heidepriem, and T. M. Monro, “Small core optical waveguides are more nonlinear than expected: experimental confirmation,” Opt. Lett.34, 3577–3579 (2009).
[CrossRef] [PubMed]

2008

2007

2006

2005

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett.70, 88–94 (2005).
[CrossRef]

2004

2002

2001

1998

E. Seve, G. Millot, S. Trillo, and S. Wabnitz, “Large-signal enhanced frequency conversion in birefringent optical fibers: theory and experiments,” J. Opt. Soc. Am. B15, 2537–2551 (1998).
[CrossRef]

G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, “Dark-soliton-like pulse-train generation from induced modulational polarization instability in a birefringent fiber,” Opt. Lett.23, 511–513 (1998).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett.81, 3383–3386 (1998).
[CrossRef]

S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counterpropagating laser beams,” Phys. Rev. Lett.81, 1409–1412 (1998).
[CrossRef]

1997

G. Millot, E. Seve, and S. Wabnitz, “Polarization symmetry breaking and pulse train generation from the modulation of light waves,” Phys. Rev. Lett.79, 661–664 (1997).
[CrossRef]

D. C. Hutchings, J. S. Aitchison, and J. M. Arnold, “Nonlinear refractive coupling and vector solitons in anisotropic cubic media,” J. Opt. Soc. Am. B14, 869–879 (1997).
[CrossRef]

1995

D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zinc-blende semiconductors,” Phys. Rev. B52, 8150–8159 (1995).
[CrossRef]

1993

1991

1987

C. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron.23, 174–176 (1987).
[CrossRef]

V. E. Zakharov and A. V. Mikhailov, “Polarization domains in nonlinear optics,” JETP Lett.45, 349–352 (1987).

1986

1982

Afshar V., S.

W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “Nonlinear polarization bistability in optical nanowires,” Opt. Lett.36, 588–590 (2011).
[CrossRef] [PubMed]

M. D. Turner, T. M. Monro, and S. Afshar V., “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part II: Stimulated Raman scattering,” Opt. Express17, 11565–11581 (2009).
[CrossRef] [PubMed]

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. Express17, 2298–2318 (2009).
[CrossRef] [PubMed]

S. Afshar V., W. Q. Zhang, H. Ebendorff-Heidepriem, and T. M. Monro, “Small core optical waveguides are more nonlinear than expected: experimental confirmation,” Opt. Lett.34, 3577–3579 (2009).
[CrossRef] [PubMed]

W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “Nonlinear self-flipping of polarization states in asymmetric waveguides,” arXiv:1203.6416

W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “Nonlinear polarization self-flipping and optical switching,” in Proceedings of the International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim 2011, (Optical Society of America, 2011), paper C370.
[PubMed]

S. Afshar V., W. Q. Zhang, and T. M. Monro, “Structurally-based nonlinear birefringence in waveguides with subwavelength structures and high index materials,” in “ACOFT 2009 Proceeding,” (Australian Optical Society, 2009), 374–375.

W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “New regimes of polarization bistability in linear birefringent waveguides and optical logic gates,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper NThD4.

Agrawal, G. P.

B. A. Daniel and G. P. Agrawal, “Vectorial nonlinear propagation in silicon nanowire waveguides: polarization effects,” J. Opt. Soc. Am. B27, 956–965 (2010).
[CrossRef]

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic Press, 2003)

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).

Aitchison, J. S.

Almeida, V. R.

Arnold, J. M.

Ashkin, A.

Asimakis, S.

Astar, W.

Baets, R.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon.3, 216–219 (2009).
[CrossRef]

Barrios, C. A.

Belardi, W.

Biaggio, I.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon.3, 216–219 (2009).
[CrossRef]

Bogaerts, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon.3, 216–219 (2009).
[CrossRef]

Botineau, J.

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett.81, 3383–3386 (1998).
[CrossRef]

Boyraz, O.

Bulla, D.

Bulla, D. A.

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photon.3, 139–143 (2009).
[CrossRef]

Carter, G. M.

Choi, D.-Y.

X. Gai, T. Han, A. Prasad, S. Madden, D.-Y. Choi, R. Wang, D. Bulla, and B. Luther-Davies, “Progress in optical waveguides fabricated from chalcogenide glasses,” Opt. Express18, 26635–26646 (2010).
[CrossRef] [PubMed]

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photon.3, 139–143 (2009).
[CrossRef]

Christodoulides, D. N.

Coleman, S.

S. Coleman, “Classical lumps and their quantum descendents,” in New Phenomena in Subnuclear Physics Ed. A. Zichichi (New York, 1977), 185–264.

da Silva, M.

W. Fraga, J. Menezes, M. da Silva, C. Sobrinho, and A. Sombra, “All optical logic gates based on an asymmetric nonlinear directional coupler,” Opt. Commun.262, 32–37 (2006).
[CrossRef]

Dadap, J. I.

Daniel, B. A.

de Sterke, C. M.

Diederich, F.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon.3, 216–219 (2009).
[CrossRef]

Driscoll, J. B.

Dumon, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon.3, 216–219 (2009).
[CrossRef]

Ebendorff-Heidepriem, H.

Eggleton, B.

Eggleton, B. J.

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photon.5, 141–148 (2011).

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photon.3, 139–143 (2009).
[CrossRef]

Eisenberg, H. S.

U. Peschel, R. Morandotti, J. M. Arnold, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, T. Pertsch, and F. Lederer, “Optical discrete solitons in waveguide arrays. 2. dynamic properties,” J. Opt. Soc. Am. B19, 2637–2644 (2002).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett.81, 3383–3386 (1998).
[CrossRef]

Esembeson, B.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon.3, 216–219 (2009).
[CrossRef]

Fatome, J.

Feldman, S. F.

Feng, X.

Finazzi, V.

Foster, M. A.

Fraga, W.

W. Fraga, J. Menezes, M. da Silva, C. Sobrinho, and A. Sombra, “All optical logic gates based on an asymmetric nonlinear directional coupler,” Opt. Commun.262, 32–37 (2006).
[CrossRef]

Frampton, K.

Freude, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon.3, 216–219 (2009).
[CrossRef]

Fu, L.

Fujisawa, T.

Furusawa, K.

Gaeta, A. L.

Gai, X.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press, 1965).

Green, W. M. J.

Gregori, G.

G. Gregori and S. Wabnitz, “New exact solutions and bifurcations in the spatial distribution of polarization in third-order nonlinear optical interactions,” Phys. Rev. Lett.56, 600–603 (1986).
[CrossRef] [PubMed]

Haelterman, M.

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett.70, 88–94 (2005).
[CrossRef]

G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, “Dark-soliton-like pulse-train generation from induced modulational polarization instability in a birefringent fiber,” Opt. Lett.23, 511–513 (1998).
[CrossRef]

Han, T.

Hsieh, I.

Hutchings, D. C.

D. C. Hutchings, J. S. Aitchison, and J. M. Arnold, “Nonlinear refractive coupling and vector solitons in anisotropic cubic media,” J. Opt. Soc. Am. B14, 869–879 (1997).
[CrossRef]

D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zinc-blende semiconductors,” Phys. Rev. B52, 8150–8159 (1995).
[CrossRef]

Jalali, B.

Jauslin, H. R.

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett.70, 88–94 (2005).
[CrossRef]

Jensen, S. M.

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron.18, 1580–1583 (1982).
[CrossRef]

Khan, K. R.

Kito, C.

G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Highly nonlinear tellurite microstructured fibers for broadband wavelength conversion and flattened supercontinuum generation,” J. Appl. Phys.107, 043108 (2010).
[CrossRef]

Kivshar, Y. S.

Y. S. Kivshar, “Switching dynamics of solitons in fiber directional couplers,” Opt. Lett.18, 7–9 (1993).
[CrossRef] [PubMed]

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic Press, 2003)

Koizumi, F.

Koonath, P.

Koos, C.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon.3, 216–219 (2009).
[CrossRef]

Koshiba, M.

Kozlov, V. V.

Lamont, M.

Lamont, M. R. E.

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photon.3, 139–143 (2009).
[CrossRef]

Lau, R. K. W.

Lederer, F.

Lee, J. H.

Leuthold, J.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon.3, 216–219 (2009).
[CrossRef]

Liao, M.

G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Highly nonlinear tellurite microstructured fibers for broadband wavelength conversion and flattened supercontinuum generation,” J. Appl. Phys.107, 043108 (2010).
[CrossRef]

Lipson, M.

Liu, X.

Loh, W. H.

Lohe, M. A.

W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “Nonlinear polarization bistability in optical nanowires,” Opt. Lett.36, 588–590 (2011).
[CrossRef] [PubMed]

W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “New regimes of polarization bistability in linear birefringent waveguides and optical logic gates,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper NThD4.

W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “Nonlinear self-flipping of polarization states in asymmetric waveguides,” arXiv:1203.6416

W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “Nonlinear polarization self-flipping and optical switching,” in Proceedings of the International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim 2011, (Optical Society of America, 2011), paper C370.
[PubMed]

Luan, F.

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photon.3, 139–143 (2009).
[CrossRef]

Luther-Davies, B.

Luther-Davis, B.

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photon.3, 139–143 (2009).
[CrossRef]

Madden, S.

Madden, S. J.

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photon.3, 139–143 (2009).
[CrossRef]

Mägi, E.

Matera, F.

Ménard, M.

Menezes, J.

W. Fraga, J. Menezes, M. da Silva, C. Sobrinho, and A. Sombra, “All optical logic gates based on an asymmetric nonlinear directional coupler,” Opt. Commun.262, 32–37 (2006).
[CrossRef]

Menyuk, C.

C. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron.23, 174–176 (1987).
[CrossRef]

Michinobu, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon.3, 216–219 (2009).
[CrossRef]

Mikhailov, A. V.

V. E. Zakharov and A. V. Mikhailov, “Polarization domains in nonlinear optics,” JETP Lett.45, 349–352 (1987).

Millot, G.

J. Fatome, S. Pitois, P. Morin, and G. Millot, “Observation of light-by-light polarization control and stabilization in optical fibre for telecommunication applications,” Opt. Express18, 15311–15317 (2010).
[CrossRef] [PubMed]

S. Pitois, J. Fatome, and G. Millot, “Polarization attraction using counter-propagating waves in optical fiber at telecommunication wavelengths,” Opt. Express16, 6646–6651 (2008).
[CrossRef] [PubMed]

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett.70, 88–94 (2005).
[CrossRef]

S. Pitois, G. Millot, and S. Wabnitz, “Nonlinear polarization dynamics of counterpropagating waves in an isotropic optical fiber: theory and experiments,” J. Opt. Soc. Am. B18, 432–443 (2001).
[CrossRef]

G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, “Dark-soliton-like pulse-train generation from induced modulational polarization instability in a birefringent fiber,” Opt. Lett.23, 511–513 (1998).
[CrossRef]

S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counterpropagating laser beams,” Phys. Rev. Lett.81, 1409–1412 (1998).
[CrossRef]

E. Seve, G. Millot, S. Trillo, and S. Wabnitz, “Large-signal enhanced frequency conversion in birefringent optical fibers: theory and experiments,” J. Opt. Soc. Am. B15, 2537–2551 (1998).
[CrossRef]

G. Millot, E. Seve, and S. Wabnitz, “Polarization symmetry breaking and pulse train generation from the modulation of light waves,” Phys. Rev. Lett.79, 661–664 (1997).
[CrossRef]

Monro, T. M.

W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “Nonlinear polarization bistability in optical nanowires,” Opt. Lett.36, 588–590 (2011).
[CrossRef] [PubMed]

M. D. Turner, T. M. Monro, and S. Afshar V., “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part II: Stimulated Raman scattering,” Opt. Express17, 11565–11581 (2009).
[CrossRef] [PubMed]

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. Express17, 2298–2318 (2009).
[CrossRef] [PubMed]

S. Afshar V., W. Q. Zhang, H. Ebendorff-Heidepriem, and T. M. Monro, “Small core optical waveguides are more nonlinear than expected: experimental confirmation,” Opt. Lett.34, 3577–3579 (2009).
[CrossRef] [PubMed]

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. Express12, 5082–5087 (2004).
[CrossRef] [PubMed]

P. Petropoulos, T. M. Monro, W. Belardi, K. Furusawa, J. H. Lee, and D. J. Richardson, “2R-regenerative all-optical switch based on a highly nonlinear holey fiber,” Opt. Lett.26, 1233–1235 (2001).
[CrossRef]

W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “Nonlinear self-flipping of polarization states in asymmetric waveguides,” arXiv:1203.6416

W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “Nonlinear polarization self-flipping and optical switching,” in Proceedings of the International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim 2011, (Optical Society of America, 2011), paper C370.
[PubMed]

S. Afshar V., W. Q. Zhang, and T. M. Monro, “Structurally-based nonlinear birefringence in waveguides with subwavelength structures and high index materials,” in “ACOFT 2009 Proceeding,” (Australian Optical Society, 2009), 374–375.

W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “New regimes of polarization bistability in linear birefringent waveguides and optical logic gates,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper NThD4.

Moore, R. C.

Morandotti, R.

U. Peschel, R. Morandotti, J. M. Arnold, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, T. Pertsch, and F. Lederer, “Optical discrete solitons in waveguide arrays. 2. dynamic properties,” J. Opt. Soc. Am. B19, 2637–2644 (2002).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett.81, 3383–3386 (1998).
[CrossRef]

Mori, A.

G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Highly nonlinear tellurite microstructured fibers for broadband wavelength conversion and flattened supercontinuum generation,” J. Appl. Phys.107, 043108 (2010).
[CrossRef]

Morin, P.

Nguyen, H.

Nuño, J.

Ohishi, Y.

G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Highly nonlinear tellurite microstructured fibers for broadband wavelength conversion and flattened supercontinuum generation,” J. Appl. Phys.107, 043108 (2010).
[CrossRef]

Okawachi, Y.

Osgood, R. M.

Pelusi, M.

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photon.3, 139–143 (2009).
[CrossRef]

Pertsch, T.

Peschel, U.

Petropoulos, P.

Petrovich, M. N.

Picozzi, A.

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett.70, 88–94 (2005).
[CrossRef]

Pitois, S.

Poletti, F.

Ponzo, G. M.

Prasad, A.

Qin, G.

G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Highly nonlinear tellurite microstructured fibers for broadband wavelength conversion and flattened supercontinuum generation,” J. Appl. Phys.107, 043108 (2010).
[CrossRef]

Raghunathan, V.

Richardson, D. J.

Richardson, K.

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photon.5, 141–148 (2011).

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press, 1965).

Salem, R.

Seve, E.

Silberberg, Y.

U. Peschel, R. Morandotti, J. M. Arnold, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, T. Pertsch, and F. Lederer, “Optical discrete solitons in waveguide arrays. 2. dynamic properties,” J. Opt. Soc. Am. B19, 2637–2644 (2002).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett.81, 3383–3386 (1998).
[CrossRef]

Sipe, J. E.

Sobrinho, C.

W. Fraga, J. Menezes, M. da Silva, C. Sobrinho, and A. Sombra, “All optical logic gates based on an asymmetric nonlinear directional coupler,” Opt. Commun.262, 32–37 (2006).
[CrossRef]

Sombra, A.

W. Fraga, J. Menezes, M. da Silva, C. Sobrinho, and A. Sombra, “All optical logic gates based on an asymmetric nonlinear directional coupler,” Opt. Commun.262, 32–37 (2006).
[CrossRef]

Stegeman, G. I.

Stolen, R. H.

Suzuki, T.

G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Highly nonlinear tellurite microstructured fibers for broadband wavelength conversion and flattened supercontinuum generation,” J. Appl. Phys.107, 043108 (2010).
[CrossRef]

Trillo, S.

Turner, M. D.

Turner-Foster, A. C.

Vallaitis, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon.3, 216–219 (2009).
[CrossRef]

Vlasov, Y. A.

Vo, T. D.

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photon.3, 139–143 (2009).
[CrossRef]

Vorreau, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon.3, 216–219 (2009).
[CrossRef]

Wabnitz, S.

V. V. Kozlov, J. Nuño, and S. Wabnitz, “Theory of lossless polarization attraction in telecommunication fibers,” J. Opt. Soc. Am. B28, 100–108 (2011).
[CrossRef]

V. V. Kozlov and S. Wabnitz, “Theoretical study of polarization attraction in high-birefringence and spun fibers,” Opt. Lett.35, 3949–3951 (2010).
[CrossRef] [PubMed]

S. Wabnitz, “Cross-polarization modulation domain wall solitons for WDM signals in birefringent optical fibers,” IEEE Photon. Technol. Lett.21, 875–877 (2009).
[CrossRef]

S. Wabnitz, “Polarization domain wall solitons in elliptically birefringent optical fibers,” PIERS ONLINE5, 621–624 (2009).
[CrossRef]

S. Pitois, G. Millot, and S. Wabnitz, “Nonlinear polarization dynamics of counterpropagating waves in an isotropic optical fiber: theory and experiments,” J. Opt. Soc. Am. B18, 432–443 (2001).
[CrossRef]

E. Seve, G. Millot, S. Trillo, and S. Wabnitz, “Large-signal enhanced frequency conversion in birefringent optical fibers: theory and experiments,” J. Opt. Soc. Am. B15, 2537–2551 (1998).
[CrossRef]

G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, “Dark-soliton-like pulse-train generation from induced modulational polarization instability in a birefringent fiber,” Opt. Lett.23, 511–513 (1998).
[CrossRef]

S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counterpropagating laser beams,” Phys. Rev. Lett.81, 1409–1412 (1998).
[CrossRef]

G. Millot, E. Seve, and S. Wabnitz, “Polarization symmetry breaking and pulse train generation from the modulation of light waves,” Phys. Rev. Lett.79, 661–664 (1997).
[CrossRef]

F. Matera and S. Wabnitz, “Nonlinear polarization evolution and instability in a twisted birefringent fiber,” Opt. Lett.11, 467–469 (1986).
[CrossRef] [PubMed]

G. Gregori and S. Wabnitz, “New exact solutions and bifurcations in the spatial distribution of polarization in third-order nonlinear optical interactions,” Phys. Rev. Lett.56, 600–603 (1986).
[CrossRef] [PubMed]

Wang, R.

Wang, W.

Wang, Y.

Weinberger, D. A.

Wherrett, B. S.

D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zinc-blende semiconductors,” Phys. Rev. B52, 8150–8159 (1995).
[CrossRef]

Winful, H. G.

Wu, T. X.

Xu, Q.

Yan, X.

G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Highly nonlinear tellurite microstructured fibers for broadband wavelength conversion and flattened supercontinuum generation,” J. Appl. Phys.107, 043108 (2010).
[CrossRef]

Yang, C. C.

Yasseri, S.

Yeom, D.

Zakharov, V. E.

V. E. Zakharov and A. V. Mikhailov, “Polarization domains in nonlinear optics,” JETP Lett.45, 349–352 (1987).

Zhang, W. Q.

W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “Nonlinear polarization bistability in optical nanowires,” Opt. Lett.36, 588–590 (2011).
[CrossRef] [PubMed]

S. Afshar V., W. Q. Zhang, H. Ebendorff-Heidepriem, and T. M. Monro, “Small core optical waveguides are more nonlinear than expected: experimental confirmation,” Opt. Lett.34, 3577–3579 (2009).
[CrossRef] [PubMed]

W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “Nonlinear polarization self-flipping and optical switching,” in Proceedings of the International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim 2011, (Optical Society of America, 2011), paper C370.
[PubMed]

W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “Nonlinear self-flipping of polarization states in asymmetric waveguides,” arXiv:1203.6416

W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “New regimes of polarization bistability in linear birefringent waveguides and optical logic gates,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper NThD4.

S. Afshar V., W. Q. Zhang, and T. M. Monro, “Structurally-based nonlinear birefringence in waveguides with subwavelength structures and high index materials,” in “ACOFT 2009 Proceeding,” (Australian Optical Society, 2009), 374–375.

Europhys. Lett.

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett.70, 88–94 (2005).
[CrossRef]

IEEE J. Quantum Electron.

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron.18, 1580–1583 (1982).
[CrossRef]

C. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron.23, 174–176 (1987).
[CrossRef]

IEEE Photon. Technol. Lett.

S. Wabnitz, “Cross-polarization modulation domain wall solitons for WDM signals in birefringent optical fibers,” IEEE Photon. Technol. Lett.21, 875–877 (2009).
[CrossRef]

J. Appl. Phys.

G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Highly nonlinear tellurite microstructured fibers for broadband wavelength conversion and flattened supercontinuum generation,” J. Appl. Phys.107, 043108 (2010).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

T. Fujisawa and M. Koshiba, “All-optical logic gates based on nonlinear slot-waveguide couplers,” J. Opt. Soc. Am. B23, 684–691 (2006).
[CrossRef]

B. A. Daniel and G. P. Agrawal, “Vectorial nonlinear propagation in silicon nanowire waveguides: polarization effects,” J. Opt. Soc. Am. B27, 956–965 (2010).
[CrossRef]

V. V. Kozlov, J. Nuño, and S. Wabnitz, “Theory of lossless polarization attraction in telecommunication fibers,” J. Opt. Soc. Am. B28, 100–108 (2011).
[CrossRef]

D. C. Hutchings, J. S. Aitchison, and J. M. Arnold, “Nonlinear refractive coupling and vector solitons in anisotropic cubic media,” J. Opt. Soc. Am. B14, 869–879 (1997).
[CrossRef]

S. F. Feldman, D. A. Weinberger, and H. G. Winful, “Polarization instability in a twisted birefringent optical fiber,” J. Opt. Soc. Am. B10, 1191–1201 (1993).
[CrossRef]

S. Pitois, G. Millot, and S. Wabnitz, “Nonlinear polarization dynamics of counterpropagating waves in an isotropic optical fiber: theory and experiments,” J. Opt. Soc. Am. B18, 432–443 (2001).
[CrossRef]

E. Seve, G. Millot, S. Trillo, and S. Wabnitz, “Large-signal enhanced frequency conversion in birefringent optical fibers: theory and experiments,” J. Opt. Soc. Am. B15, 2537–2551 (1998).
[CrossRef]

U. Peschel, R. Morandotti, J. M. Arnold, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, T. Pertsch, and F. Lederer, “Optical discrete solitons in waveguide arrays. 2. dynamic properties,” J. Opt. Soc. Am. B19, 2637–2644 (2002).
[CrossRef]

JETP Lett.

V. E. Zakharov and A. V. Mikhailov, “Polarization domains in nonlinear optics,” JETP Lett.45, 349–352 (1987).

Nat. Photon.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon.3, 216–219 (2009).
[CrossRef]

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photon.3, 139–143 (2009).
[CrossRef]

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photon.5, 141–148 (2011).

Opt. Commun.

W. Fraga, J. Menezes, M. da Silva, C. Sobrinho, and A. Sombra, “All optical logic gates based on an asymmetric nonlinear directional coupler,” Opt. Commun.262, 32–37 (2006).
[CrossRef]

Opt. Express

O. Boyraz, P. Koonath, V. Raghunathan, and B. Jalali, “All optical switching and continuum generation in silicon waveguides,” Opt. Express12, 4094–4102 (2004).
[CrossRef] [PubMed]

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. Express12, 5082–5087 (2004).
[CrossRef] [PubMed]

J. Fatome, S. Pitois, P. Morin, and G. Millot, “Observation of light-by-light polarization control and stabilization in optical fibre for telecommunication applications,” Opt. Express18, 15311–15317 (2010).
[CrossRef] [PubMed]

F. Poletti, X. Feng, G. M. Ponzo, M. N. Petrovich, W. H. Loh, and D. J. Richardson, “All-solid highly nonlinear singlemode fibers with a tailored dispersion profile,” Opt. Express19, 66–80 (2011).
[CrossRef] [PubMed]

E. Mägi, L. Fu, H. Nguyen, M. Lamont, D. Yeom, and B. Eggleton, “Enhanced Kerr nonlinearity in sub-wavelength diameter As2Se3 chalcogenide fiber tapers,” Opt. Express15, 10324–10329 (2007).
[CrossRef] [PubMed]

S. Pitois, J. Fatome, and G. Millot, “Polarization attraction using counter-propagating waves in optical fiber at telecommunication wavelengths,” Opt. Express16, 6646–6651 (2008).
[CrossRef] [PubMed]

K. R. Khan, T. X. Wu, D. N. Christodoulides, and G. I. Stegeman, “Soliton switching and multi-frequency generation in a nonlinear photonic crystal fiber coupler,” Opt. Express16, 9417–9428 (2008).
[CrossRef] [PubMed]

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. Express17, 2298–2318 (2009).
[CrossRef] [PubMed]

J. B. Driscoll, X. Liu, S. Yasseri, I. Hsieh, J. I. Dadap, and R. M. Osgood, “Large longitudinal electric fields (Ez) in silicon nanowire waveguides,” Opt. Express17, 2797–2804 (2009).
[CrossRef] [PubMed]

M. D. Turner, T. M. Monro, and S. Afshar V., “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part II: Stimulated Raman scattering,” Opt. Express17, 11565–11581 (2009).
[CrossRef] [PubMed]

X. Gai, T. Han, A. Prasad, S. Madden, D.-Y. Choi, R. Wang, D. Bulla, and B. Luther-Davies, “Progress in optical waveguides fabricated from chalcogenide glasses,” Opt. Express18, 26635–26646 (2010).
[CrossRef] [PubMed]

Opt. Lett.

V. V. Kozlov and S. Wabnitz, “Theoretical study of polarization attraction in high-birefringence and spun fibers,” Opt. Lett.35, 3949–3951 (2010).
[CrossRef] [PubMed]

S. Afshar V., W. Q. Zhang, H. Ebendorff-Heidepriem, and T. M. Monro, “Small core optical waveguides are more nonlinear than expected: experimental confirmation,” Opt. Lett.34, 3577–3579 (2009).
[CrossRef] [PubMed]

W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “Nonlinear polarization bistability in optical nanowires,” Opt. Lett.36, 588–590 (2011).
[CrossRef] [PubMed]

R. K. W. Lau, M. Ménard, Y. Okawachi, M. A. Foster, A. C. Turner-Foster, R. Salem, M. Lipson, and A. L. Gaeta, “Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides,” Opt. Lett.36, 1263–1265 (2011).
[CrossRef] [PubMed]

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett.29, 1209–1211 (2004).
[CrossRef] [PubMed]

P. Petropoulos, T. M. Monro, W. Belardi, K. Furusawa, J. H. Lee, and D. J. Richardson, “2R-regenerative all-optical switch based on a highly nonlinear holey fiber,” Opt. Lett.26, 1233–1235 (2001).
[CrossRef]

G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, “Dark-soliton-like pulse-train generation from induced modulational polarization instability in a birefringent fiber,” Opt. Lett.23, 511–513 (1998).
[CrossRef]

R. H. Stolen, J. Botineau, and A. Ashkin, “Intensity discrimination of optical pulses with birefringent fibers,” Opt. Lett.7, 512–514 (1982).
[CrossRef] [PubMed]

H. G. Winful, “Polarization instabilities in birefringent nonlinear media: application to fiber-optic devices,” Opt. Lett.11, 33–35 (1986).
[CrossRef] [PubMed]

F. Matera and S. Wabnitz, “Nonlinear polarization evolution and instability in a twisted birefringent fiber,” Opt. Lett.11, 467–469 (1986).
[CrossRef] [PubMed]

C. M. de Sterke and J. E. Sipe, “Polarization instability in a waveguide geometry,” Opt. Lett.16, 202–204 (1991).
[CrossRef] [PubMed]

C. C. Yang, “All-optical ultrafast logic gates that use asymmetric nonlinear directional couplers,” Opt. Lett.16, 1641–1643 (1991).
[CrossRef] [PubMed]

Y. S. Kivshar, “Switching dynamics of solitons in fiber directional couplers,” Opt. Lett.18, 7–9 (1993).
[CrossRef] [PubMed]

Phys. Rev. B

D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zinc-blende semiconductors,” Phys. Rev. B52, 8150–8159 (1995).
[CrossRef]

Phys. Rev. Lett.

G. Gregori and S. Wabnitz, “New exact solutions and bifurcations in the spatial distribution of polarization in third-order nonlinear optical interactions,” Phys. Rev. Lett.56, 600–603 (1986).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett.81, 3383–3386 (1998).
[CrossRef]

G. Millot, E. Seve, and S. Wabnitz, “Polarization symmetry breaking and pulse train generation from the modulation of light waves,” Phys. Rev. Lett.79, 661–664 (1997).
[CrossRef]

S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counterpropagating laser beams,” Phys. Rev. Lett.81, 1409–1412 (1998).
[CrossRef]

PIERS ONLINE

S. Wabnitz, “Polarization domain wall solitons in elliptically birefringent optical fibers,” PIERS ONLINE5, 621–624 (2009).
[CrossRef]

Other

S. Coleman, “Classical lumps and their quantum descendents,” in New Phenomena in Subnuclear Physics Ed. A. Zichichi (New York, 1977), 185–264.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic Press, 2003)

W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “Nonlinear self-flipping of polarization states in asymmetric waveguides,” arXiv:1203.6416

W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “Nonlinear polarization self-flipping and optical switching,” in Proceedings of the International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim 2011, (Optical Society of America, 2011), paper C370.
[PubMed]

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press, 1965).

W. Q. Zhang, M. A. Lohe, T. M. Monro, and S. Afshar V., “New regimes of polarization bistability in linear birefringent waveguides and optical logic gates,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper NThD4.

S. Afshar V., W. Q. Zhang, and T. M. Monro, “Structurally-based nonlinear birefringence in waveguides with subwavelength structures and high index materials,” in “ACOFT 2009 Proceeding,” (Australian Optical Society, 2009), 374–375.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).

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Figures (6)

Fig. 1
Fig. 1

Contour plots as functions of the elliptical waveguide dimensions x, y of (i) log10 b; (ii) a as defined in Eq. (21) for P0 = 1W; (iii) C = (γ2γc)/γc where C < 0 to the left of the white line; (iv) the birefringence Δβ.

Fig. 2
Fig. 2

The a, b plane showing: (i) the regions of existence for the solutions Eq. (24), either 1 < a < 2b−1 (red), or 2b−1 < a < 1 (green); (ii) the regions of existence for the unstable solutions consisting of Eq. (24) (red), and Eq. (25) for which 2b + 1 < a < −1 (orange), together with Eqs. (26) and (27) for which |a| < 1 or |a − 2b| < 1 (light blue).

Fig. 3
Fig. 3

The potential V plotted as a function of (i) θ, a for b = 0.8; (ii) θ, b for a = 0.

Fig. 4
Fig. 4

(i) a as a function of P0 for Δβ < 0 (blue solid line) and Δβ > 0 (red solid line). The green lines mark the boundaries of the (red) region of instability in the a, b plane shown in Fig. 2(i); (ii) contour plot of log10( P 0 min) as a function of x, y, showing the minimum total power P 0 min (in units W) required to access unstable steady states, where they exist.

Fig. 5
Fig. 5

Contours in the θ, v plane of constant H for (i) a = 1, b = 4; (ii) a = b = 2, with steady states marked by green dots (stable) and red or orange dots (unstable). The separatrix, which identifies the soliton trajectories, is shown in red.

Fig. 6
Fig. 6

Switching solutions v and cos θ 2 = cos Δ ϕ as functions of τ for: (i) a = 1, b = 4 and v0 = ε, θ0 = 0; (ii) a = b = 2 and v 0 = 1 2, θ0 = ε where ε = 10−4. The insets show the polarization vectors associated with the values cosΔϕ = ±1.

Equations (51)

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E i ( x , y , z , t ) = A i ( z , t ) e i ( x , y ) , i = 1 , 2 ,
A ν z + n = 1 i n 1 β ν ( n ) n ! n A ν t n = i ( γ ν | A ν | 2 + γ μ ν | A μ | 2 ) A ν + i γ μ ν A μ 2 A ν * e 2 i ( β ν β μ ) z + i γ μ ν ( 1 ) A μ * A ν 2 e i ( β μ β ν ) z + i γ μ ν ( 2 ) A μ | A ν | 2 e i ( β μ β ν ) z + i γ μ ν ( 3 ) A μ | A μ | 2 e i ( β μ β ν ) z
γ ν = ( k ε 0 4 μ 0 ) 1 3 N ν 2 n 2 ( x , y ) n 2 ( x , y ) [ 2 | e ν | 4 + | e ν 2 | 2 ] d A ,
γ μ ν = ( k ε 0 4 μ 0 ) 2 3 N ν N μ n 2 ( x , y ) n 2 ( x , y ) [ | e ν e μ * | 2 + | e ν e μ | 2 + | e ν | 2 | e μ | 2 ] d A ,
γ μ ν = ( k ε 0 4 μ 0 ) 1 3 N ν N μ n 2 ( x , y ) n 2 ( x , y ) [ 2 ( e μ e ν * ) 2 + ( e μ ) 2 ( e ν ) 2 ] d A ,
γ μ ν ( 1 ) = ( k ε 0 4 μ 0 ) 1 3 N ν 3 N μ n 2 ( x , y ) n 2 ( x , y ) [ 2 | e ν | 2 ( e μ * e ν ) + ( e ν ) 2 ( e μ * e ν * ) ] d A ,
γ μ ν ( 2 ) = ( k ε 0 4 μ 0 ) 2 3 N ν 3 N μ n 2 ( x , y ) n 2 ( x , y ) [ 2 | e ν | 2 ( e μ e ν * ) + ( e ν * ) 2 ( e μ e ν ) ] d A ,
γ μ ν ( 3 ) = ( k ε 0 4 μ 0 ) 1 3 N μ 3 N ν n 2 ( x , y ) n 2 ( x , y ) [ 2 | e μ | 2 ( e μ e ν * ) + ( e μ ) 2 ( e μ * e ν * ) ] d A .
N μ = 1 2 | e μ × h μ * z ^ d A |
A ν z + n = 1 i n 1 n ! β ν ( n ) n A ν t n = i ( γ ν | A ν | 2 + γ μ ν | A μ | 2 ) A ν + i γ μ ν A μ 2 A ν * e 2 i ( β ν β μ ) z .
γ 1 = γ 2 = 3 γ c / 2 = 3 γ c ,
d A 1 d z = i ( γ 1 | A 1 | 2 + γ c | A 2 | 2 ) A 1 + i γ c A 2 2 A 1 * e 2 i Δ β z
d A 2 d z = i ( γ 2 | A 2 | 2 + γ c | A 1 | 2 ) A 2 + i γ c A 1 2 A 2 * e 2 i Δ β z ,
A 1 = P 1 e i ϕ 1 , A 2 = P 2 e i ϕ 2 ,
Δ ϕ = ϕ 1 ϕ 2 + z Δ β , θ = 2 Δ ϕ ,
d P 1 d z = 2 γ c P 1 P 2 sin θ
d P 2 d z = 2 γ c P 1 P 2 sin θ
d θ d z = 2 Δ β + 2 P 1 ( γ 1 γ c γ c cos θ ) 2 P 2 ( γ 2 γ c γ c cos θ )
d ϕ 1 d z = γ 1 P 1 + P 2 ( γ c + γ c cos θ ) .
v = P 1 P 0 = P 1 P 1 + P 2 , τ = 2 γ c P 0 z ,
a = Δ β γ c P 0 γ c γ 2 γ c , b = γ 1 + γ 2 2 γ c 2 γ c .
v ˙ d v d τ = v ( 1 v ) sin θ ,
θ ˙ d θ d τ = a + 2 b v + ( 1 2 v ) cos θ .
cos θ = 1 , v = a 1 2 ( b 1 )
cos θ = 1 , v = a + 1 2 ( b + 1 )
cos θ = a , v = 0
cos θ = a + 2 b , v = 1
v = θ ˙ + a cos θ 2 ( b cos θ ) ,
2 ( b cos θ ) θ ¨ sin θ θ ˙ 2 + sin θ ( a cos θ ) ( a 2 b + cos θ ) = 0 .
L = T V = 1 2 M ( θ ) θ ˙ 2 V ( θ )
M ( θ ) θ ¨ + 1 2 M ( θ ) θ ˙ 2 + V ( θ ) = 0 ,
M ( θ ) = 2 | b cos θ | , V ( θ ) = | b cos θ | ( a b ) 2 | b cos θ | .
θ ˙ 2 = ( b cos θ ) 2 + ( a b ) 2 + c ( b cos θ ) ,
γ c + γ c γ 1 < Δ β P 0 < γ 2 γ c γ c .
H ( v , θ ) = a v + b v 2 + v ( 1 v ) cos θ
v ˙ = H θ , θ ˙ = H v .
cos θ = H 0 + a v b v 2 v ( 1 v ) ,
v ˙ 2 = Q ( v ) ,
Q ( v ) = v 2 ( 1 v ) 2 ( H 0 + a v b v 2 ) 2 .
Q ( v ) = [ ( b + 1 ) v 2 ( a + 1 ) v H 0 ] [ ( b 1 ) v 2 ( a 1 ) v H 0 ] ,
v min v d u Q ( u ) = τ τ 0 , T = 2 v min v max d u Q ( u ) ,
V 0 = 1 b ( a b ) 2 b 1 .
S ( θ , θ ˙ ) = [ 1 2 M ( θ ) θ ˙ 2 + U ( θ ) ] d τ .
S = 1 2 M [ θ ˙ 2 U M ] 2 d τ ± M 2 U M θ ˙ d τ .
θ ˙ = ± 2 U M ,
cos θ = 1 + 2 κ 1 ( κ + 1 ) cosh 2 κ ( τ τ 0 ) ,
κ = ( a 1 ) ( a + 2 b 1 ) 2 ( b 1 ) .
v = a 1 2 ( b 1 ) + κ a b ± ( b 1 ) κ + 1 cosh κ ( τ τ 0 ) ,
v ( τ ) = 1 a 2 1 a b + | b a | cosh [ 1 a 2 ( τ τ 0 ) ] ,
cos θ ( τ ) = a 1 a 2 a + η cosh [ 1 a 2 ( τ τ 0 ) ] ,
v ( τ ) = 2 b + 1 + ( b 1 ) ( τ τ 0 ) 2 , cos θ = 1 2 1 + ( τ τ 0 ) 2 .

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