Abstract

We present detailed theoretical and numerical analysis of certain novel non-linear optical phenomena enabled by photonic bandgap fibers. In particular, we demonstrate the feasibility of optical bistability in an axially modulated nonlinear photonic bandgap fiber through analytical theory and detailed numerical experiments. At 1.55µm carrier wavelength, the in-fiber devices we propose can operate with only a few tens of mW of power, have a nearly instantaneous response and recovery time, and be shorter than 100µm. Furthermore, we predict existence of gap-like solitons (which have thus-far been described only in axially periodic systems) in axially uniform photonic bandgap fibers.

© 2004 Optical Society of America

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2003 (2)

2002 (5)

Jeffrey M. Harbold, F. Ömer Ilday, Frank W. Wise, and Bruce G. Aitken, “Highly Nonlinear Ge-As-Se and Ge-As-S-Se Glasses for All-Optical Switching,” IEEE Photon. Technol. Lett. 14, 822–824, (2002).
[CrossRef]

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14, 483–485, (2002).
[CrossRef]

S.D. Hart, G.R. Maskaly, B. Temelkuran, P.H. Prideaux, J.D. Joannopoulos, and Y. Fink, “External Reflection from Omnidirectional Dielectric Mirror Fibers,” Science 296, 510–513, (2002).
[CrossRef] [PubMed]

B. Temelkuran, S.D. Hart, G. Benoit, J.D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420, 650–653, (2002).
[CrossRef] [PubMed]

Marin Soljačić, Mihai Ibanescu, Steven G. Johnson, Yoel Fink, and J.D. Joannopoulos, “Optimal Bistable Switching in Non-Linear Photonic Crystals,” Phys. Rev. E 66, 055601(R) (2002).
[CrossRef]

2001 (3)

2000 (1)

1999 (4)

J.E. Heebner and R. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt. Lett. 24, 847–849, (1999).
[CrossRef]

S. Coen and M. Haelterman, “Competition between modulational instability and switching in optical bistability,” Opt. Lett. 24, 80–82, (1999).
[CrossRef]

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “Guiding optical light in air using an all-dielectric structure,” J. Lightwave. Technol. 17, 2039–2041, (1999).
[CrossRef]

R.F. Gregan, B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, P.J. Roberts, and D.C. Allan, “Single-Mode Photonic Band Gap Guidance of Light in Air,” Science 285, 1537–1539, (1999).
[CrossRef]

1998 (1)

1997 (3)

E. Lidorikis, K. Busch, Qiming Li, C.T. Chan, and C.M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090–15099, (1997).
[CrossRef]

B.J. Eggleton, C. Martijn de Sterke, and R.E. Slusher, “Nonlinear pulse propagation in Bragg gratings,” J. Opt. Soc. Am. B 14, 2980–2993, (1997).
[CrossRef]

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145, (1997).
[CrossRef]

1995 (2)

Stojan Radić, Nicholas George, and Govind P. Agrawal, “Theory of low-threshold optical switching in nonlinear phase-shifted periodic structures,” J. Opt. Soc. Am. B 12, 671–680, (1995).
[CrossRef]

S. Janz, J. He, Z.R. Wasilewski, and M. Cada, “Low threshold optical bistable switching in an asymmetric ¼-shifted distributed-feedback heterostructure,” Appl. Phys. Lett. 67, 1051–1053, (1995).
[CrossRef]

1990 (1)

C. Martijn de Sterke and J.E. Sipe, “Switching dynamics of finite periodic nonlinear media: A numerical study,” Phys. Rev. A 42, 2858–2869, (1990).
[CrossRef]

1989 (1)

D.N. Christodoulides and R.I Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62, 1746–1749, (1989).
[CrossRef] [PubMed]

1988 (1)

C. Martijn de Sterke and J.E. Sipe, “Envelope-function approach for the electrodynamics of nonlinear periodic structures,” Phys. Rev. A 38, 5149–5165, (1988).
[CrossRef]

1987 (1)

Wei Chen and D.L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. 58, 160–163, (1987).
[CrossRef] [PubMed]

1979 (1)

H.G. Winful, J.H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381, (1979).
[CrossRef]

Aggarwal, I. D.

Agrawal, G. P.

G. P. Agrawal, Nonlinear fiber optics (Academic Press, London, UK, 1995); Applications of nonlinear fiber optics (Academic Press, London, UK, 2001).

Agrawal, Govind P.

Aitken, Bruce G.

Jeffrey M. Harbold, F. Ömer Ilday, Frank W. Wise, and Bruce G. Aitken, “Highly Nonlinear Ge-As-Se and Ge-As-S-Se Glasses for All-Optical Switching,” IEEE Photon. Technol. Lett. 14, 822–824, (2002).
[CrossRef]

Allan, D.C.

R.F. Gregan, B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, P.J. Roberts, and D.C. Allan, “Single-Mode Photonic Band Gap Guidance of Light in Air,” Science 285, 1537–1539, (1999).
[CrossRef]

Benoit, G.

B. Temelkuran, S.D. Hart, G. Benoit, J.D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420, 650–653, (2002).
[CrossRef] [PubMed]

Birks, T.A.

R.F. Gregan, B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, P.J. Roberts, and D.C. Allan, “Single-Mode Photonic Band Gap Guidance of Light in Air,” Science 285, 1537–1539, (1999).
[CrossRef]

Boyd, R.

Broderick, N.G.R.

Busch, K.

E. Lidorikis, K. Busch, Qiming Li, C.T. Chan, and C.M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090–15099, (1997).
[CrossRef]

Cada, M.

S. Janz, J. He, Z.R. Wasilewski, and M. Cada, “Low threshold optical bistable switching in an asymmetric ¼-shifted distributed-feedback heterostructure,” Appl. Phys. Lett. 67, 1051–1053, (1995).
[CrossRef]

Chan, C.T.

E. Lidorikis, K. Busch, Qiming Li, C.T. Chan, and C.M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090–15099, (1997).
[CrossRef]

Chen, C.

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “Guiding optical light in air using an all-dielectric structure,” J. Lightwave. Technol. 17, 2039–2041, (1999).
[CrossRef]

Chen, Wei

Wei Chen and D.L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. 58, 160–163, (1987).
[CrossRef] [PubMed]

Cheong, S.-W.

Christodoulides, D.N.

D.N. Christodoulides and R.I Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62, 1746–1749, (1989).
[CrossRef] [PubMed]

Coen, S.

Eggleton, B.J.

B.J. Eggleton, C. Martijn de Sterke, and R.E. Slusher, “Nonlinear pulse propagation in Bragg gratings,” J. Opt. Soc. Am. B 14, 2980–2993, (1997).
[CrossRef]

C. Kerbage and B.J. Eggleton, “Microstructured Optical Fibers,” Optics&Photonics News 38–42, (September 2002).

Engeness, Torkel D.

Fan, S.

S.G. Johnson, S. Fan, A. Mekis, and J.D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388–3390, (2001).
[CrossRef]

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “Guiding optical light in air using an all-dielectric structure,” J. Lightwave. Technol. 17, 2039–2041, (1999).
[CrossRef]

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145, (1997).
[CrossRef]

Ferrera, J.

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145, (1997).
[CrossRef]

Fink, Y.

S.D. Hart, G.R. Maskaly, B. Temelkuran, P.H. Prideaux, J.D. Joannopoulos, and Y. Fink, “External Reflection from Omnidirectional Dielectric Mirror Fibers,” Science 296, 510–513, (2002).
[CrossRef] [PubMed]

B. Temelkuran, S.D. Hart, G. Benoit, J.D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420, 650–653, (2002).
[CrossRef] [PubMed]

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “Guiding optical light in air using an all-dielectric structure,” J. Lightwave. Technol. 17, 2039–2041, (1999).
[CrossRef]

Fink, Yoel

Marin Soljačić, Mihai Ibanescu, Steven G. Johnson, Yoel Fink, and J.D. Joannopoulos, “Optimal Bistable Switching in Non-Linear Photonic Crystals,” Phys. Rev. E 66, 055601(R) (2002).
[CrossRef]

Steven G. Johnson, Mihai Ibanescu, M. Skorobogatiy, Ori Weisberg, Torkel D. Engeness, Marin Soljačić, Steven A. Jacobs, J. D. Joannopoulos, and Yoel Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–779, (2001).
[CrossRef] [PubMed]

Elefterios Lidorikis, Marin Soljacic, Mihai Ibanescu, Yoel Fink, and J.D. Joannopoulos, “Gap solitons and optical switching in axially uniform systems,” Opt. Lett., in press.

Fink, Yoel:

Foresi, J.S.

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145, (1997).
[CrossRef]

Garmire, E.

H.G. Winful, J.H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381, (1979).
[CrossRef]

George, Nicholas

Gregan, R.F.

R.F. Gregan, B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, P.J. Roberts, and D.C. Allan, “Single-Mode Photonic Band Gap Guidance of Light in Air,” Science 285, 1537–1539, (1999).
[CrossRef]

Haelterman, M.

Harbold, Jeffrey M.

Jeffrey M. Harbold, F. Ömer Ilday, Frank W. Wise, and Bruce G. Aitken, “Highly Nonlinear Ge-As-Se and Ge-As-S-Se Glasses for All-Optical Switching,” IEEE Photon. Technol. Lett. 14, 822–824, (2002).
[CrossRef]

Hart, S.D.

B. Temelkuran, S.D. Hart, G. Benoit, J.D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420, 650–653, (2002).
[CrossRef] [PubMed]

S.D. Hart, G.R. Maskaly, B. Temelkuran, P.H. Prideaux, J.D. Joannopoulos, and Y. Fink, “External Reflection from Omnidirectional Dielectric Mirror Fibers,” Science 296, 510–513, (2002).
[CrossRef] [PubMed]

Haus, H.A.

H.A. Haus, Waves And Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, NJ, 1984).

He, J.

S. Janz, J. He, Z.R. Wasilewski, and M. Cada, “Low threshold optical bistable switching in an asymmetric ¼-shifted distributed-feedback heterostructure,” Appl. Phys. Lett. 67, 1051–1053, (1995).
[CrossRef]

Heebner, J.E.

Hwang, H. Y.

Ibanescu, Mihai

Marin Soljačić, Mihai Ibanescu, Steven G. Johnson, J.D. Joannopoulos, and Yoel: Fink“Optical Bistability in Axially Modulated OmniGuide Fibers,” Opt. Lett. 28, 516–518, (2003).
[CrossRef]

Marin Soljačić, Mihai Ibanescu, Steven G. Johnson, Yoel Fink, and J.D. Joannopoulos, “Optimal Bistable Switching in Non-Linear Photonic Crystals,” Phys. Rev. E 66, 055601(R) (2002).
[CrossRef]

Steven G. Johnson, Mihai Ibanescu, M. Skorobogatiy, Ori Weisberg, Torkel D. Engeness, Marin Soljačić, Steven A. Jacobs, J. D. Joannopoulos, and Yoel Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–779, (2001).
[CrossRef] [PubMed]

Elefterios Lidorikis, Marin Soljacic, Mihai Ibanescu, Yoel Fink, and J.D. Joannopoulos, “Gap solitons and optical switching in axially uniform systems,” Opt. Lett., in press.

Ibsen, M.

Ippen, E.P.

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145, (1997).
[CrossRef]

Jacobs, Steven A.

Janz, S.

S. Janz, J. He, Z.R. Wasilewski, and M. Cada, “Low threshold optical bistable switching in an asymmetric ¼-shifted distributed-feedback heterostructure,” Appl. Phys. Lett. 67, 1051–1053, (1995).
[CrossRef]

Joannopoulos, J. D.

Joannopoulos, J.D.

Marin Soljačić, Mihai Ibanescu, Steven G. Johnson, J.D. Joannopoulos, and Yoel: Fink“Optical Bistability in Axially Modulated OmniGuide Fibers,” Opt. Lett. 28, 516–518, (2003).
[CrossRef]

Marin Soljačić, Mihai Ibanescu, Steven G. Johnson, Yoel Fink, and J.D. Joannopoulos, “Optimal Bistable Switching in Non-Linear Photonic Crystals,” Phys. Rev. E 66, 055601(R) (2002).
[CrossRef]

B. Temelkuran, S.D. Hart, G. Benoit, J.D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420, 650–653, (2002).
[CrossRef] [PubMed]

S.D. Hart, G.R. Maskaly, B. Temelkuran, P.H. Prideaux, J.D. Joannopoulos, and Y. Fink, “External Reflection from Omnidirectional Dielectric Mirror Fibers,” Science 296, 510–513, (2002).
[CrossRef] [PubMed]

S.G. Johnson, S. Fan, A. Mekis, and J.D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388–3390, (2001).
[CrossRef]

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145, (1997).
[CrossRef]

Elefterios Lidorikis, Marin Soljacic, Mihai Ibanescu, Yoel Fink, and J.D. Joannopoulos, “Gap solitons and optical switching in axially uniform systems,” Opt. Lett., in press.

Johnson, S.G.

S.G. Johnson, S. Fan, A. Mekis, and J.D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388–3390, (2001).
[CrossRef]

Johnson, Steven G.

Joseph, R.I

D.N. Christodoulides and R.I Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62, 1746–1749, (1989).
[CrossRef] [PubMed]

Katsufuji, T.

Kerbage, C.

C. Kerbage and B.J. Eggleton, “Microstructured Optical Fibers,” Optics&Photonics News 38–42, (September 2002).

Kimerling, L.C.

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145, (1997).
[CrossRef]

Knight, J.C.

R.F. Gregan, B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, P.J. Roberts, and D.C. Allan, “Single-Mode Photonic Band Gap Guidance of Light in Air,” Science 285, 1537–1539, (1999).
[CrossRef]

Laming, R.I.

Lenz, G.

Li, Qiming

E. Lidorikis, K. Busch, Qiming Li, C.T. Chan, and C.M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090–15099, (1997).
[CrossRef]

Lidorikis, E.

E. Lidorikis, K. Busch, Qiming Li, C.T. Chan, and C.M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090–15099, (1997).
[CrossRef]

Lidorikis, Elefterios

Elefterios Lidorikis, Marin Soljacic, Mihai Ibanescu, Yoel Fink, and J.D. Joannopoulos, “Gap solitons and optical switching in axially uniform systems,” Opt. Lett., in press.

Lines, M. E.

Mangan, B.J.

R.F. Gregan, B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, P.J. Roberts, and D.C. Allan, “Single-Mode Photonic Band Gap Guidance of Light in Air,” Science 285, 1537–1539, (1999).
[CrossRef]

Marburger, J.H.

H.G. Winful, J.H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381, (1979).
[CrossRef]

Martijn de Sterke, C.

B.J. Eggleton, C. Martijn de Sterke, and R.E. Slusher, “Nonlinear pulse propagation in Bragg gratings,” J. Opt. Soc. Am. B 14, 2980–2993, (1997).
[CrossRef]

C. Martijn de Sterke and J.E. Sipe, “Switching dynamics of finite periodic nonlinear media: A numerical study,” Phys. Rev. A 42, 2858–2869, (1990).
[CrossRef]

C. Martijn de Sterke and J.E. Sipe, “Envelope-function approach for the electrodynamics of nonlinear periodic structures,” Phys. Rev. A 38, 5149–5165, (1988).
[CrossRef]

Maskaly, G.R.

S.D. Hart, G.R. Maskaly, B. Temelkuran, P.H. Prideaux, J.D. Joannopoulos, and Y. Fink, “External Reflection from Omnidirectional Dielectric Mirror Fibers,” Science 296, 510–513, (2002).
[CrossRef] [PubMed]

Mekis, A.

S.G. Johnson, S. Fan, A. Mekis, and J.D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388–3390, (2001).
[CrossRef]

Mills, D.L.

Wei Chen and D.L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. 58, 160–163, (1987).
[CrossRef] [PubMed]

Ömer Ilday, F.

Jeffrey M. Harbold, F. Ömer Ilday, Frank W. Wise, and Bruce G. Aitken, “Highly Nonlinear Ge-As-Se and Ge-As-S-Se Glasses for All-Optical Switching,” IEEE Photon. Technol. Lett. 14, 822–824, (2002).
[CrossRef]

Prideaux, P.H.

S.D. Hart, G.R. Maskaly, B. Temelkuran, P.H. Prideaux, J.D. Joannopoulos, and Y. Fink, “External Reflection from Omnidirectional Dielectric Mirror Fibers,” Science 296, 510–513, (2002).
[CrossRef] [PubMed]

Radic, Stojan

Richardson, D.J.

Ripin, D. J.

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “Guiding optical light in air using an all-dielectric structure,” J. Lightwave. Technol. 17, 2039–2041, (1999).
[CrossRef]

Roberts, P.J.

R.F. Gregan, B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, P.J. Roberts, and D.C. Allan, “Single-Mode Photonic Band Gap Guidance of Light in Air,” Science 285, 1537–1539, (1999).
[CrossRef]

Russell, P.

P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[CrossRef] [PubMed]

Russell, P.St.J.

R.F. Gregan, B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, P.J. Roberts, and D.C. Allan, “Single-Mode Photonic Band Gap Guidance of Light in Air,” Science 285, 1537–1539, (1999).
[CrossRef]

Saleh, B.E.A.

B.E.A. Saleh and M.C. Teich, Fundamentals Of Photonics (John Wiley&Sons, 1991).
[CrossRef]

Sanghera, J. S.

Sipe, J.E.

C. Martijn de Sterke and J.E. Sipe, “Switching dynamics of finite periodic nonlinear media: A numerical study,” Phys. Rev. A 42, 2858–2869, (1990).
[CrossRef]

C. Martijn de Sterke and J.E. Sipe, “Envelope-function approach for the electrodynamics of nonlinear periodic structures,” Phys. Rev. A 38, 5149–5165, (1988).
[CrossRef]

Skorobogatiy, M.

Slusher, R. E.

Slusher, R.E.

Smith, H.I.

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145, (1997).
[CrossRef]

Soljacic, Marin

Marin Soljačić, Mihai Ibanescu, Steven G. Johnson, J.D. Joannopoulos, and Yoel: Fink“Optical Bistability in Axially Modulated OmniGuide Fibers,” Opt. Lett. 28, 516–518, (2003).
[CrossRef]

Marin Soljačić, Mihai Ibanescu, Steven G. Johnson, Yoel Fink, and J.D. Joannopoulos, “Optimal Bistable Switching in Non-Linear Photonic Crystals,” Phys. Rev. E 66, 055601(R) (2002).
[CrossRef]

Steven G. Johnson, Mihai Ibanescu, M. Skorobogatiy, Ori Weisberg, Torkel D. Engeness, Marin Soljačić, Steven A. Jacobs, J. D. Joannopoulos, and Yoel Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–779, (2001).
[CrossRef] [PubMed]

Elefterios Lidorikis, Marin Soljacic, Mihai Ibanescu, Yoel Fink, and J.D. Joannopoulos, “Gap solitons and optical switching in axially uniform systems,” Opt. Lett., in press.

Soukoulis, C.M.

E. Lidorikis, K. Busch, Qiming Li, C.T. Chan, and C.M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090–15099, (1997).
[CrossRef]

Spälter, S.

Steinmeyer, G.

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145, (1997).
[CrossRef]

Taflove, A.

For a review, see A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1995).

Taverner, D.

Teich, M.C.

B.E.A. Saleh and M.C. Teich, Fundamentals Of Photonics (John Wiley&Sons, 1991).
[CrossRef]

Temelkuran, B.

S.D. Hart, G.R. Maskaly, B. Temelkuran, P.H. Prideaux, J.D. Joannopoulos, and Y. Fink, “External Reflection from Omnidirectional Dielectric Mirror Fibers,” Science 296, 510–513, (2002).
[CrossRef] [PubMed]

B. Temelkuran, S.D. Hart, G. Benoit, J.D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420, 650–653, (2002).
[CrossRef] [PubMed]

Thoen, E.R.

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145, (1997).
[CrossRef]

Thomas, E. L.

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “Guiding optical light in air using an all-dielectric structure,” J. Lightwave. Technol. 17, 2039–2041, (1999).
[CrossRef]

Villeneuve, P.R.

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145, (1997).
[CrossRef]

Wasilewski, Z.R.

S. Janz, J. He, Z.R. Wasilewski, and M. Cada, “Low threshold optical bistable switching in an asymmetric ¼-shifted distributed-feedback heterostructure,” Appl. Phys. Lett. 67, 1051–1053, (1995).
[CrossRef]

Weisberg, Ori

Winful, H.G.

H.G. Winful, J.H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381, (1979).
[CrossRef]

Wise, Frank W.

Jeffrey M. Harbold, F. Ömer Ilday, Frank W. Wise, and Bruce G. Aitken, “Highly Nonlinear Ge-As-Se and Ge-As-S-Se Glasses for All-Optical Switching,” IEEE Photon. Technol. Lett. 14, 822–824, (2002).
[CrossRef]

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A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14, 483–485, (2002).
[CrossRef]

Zimmerman, J.

Appl. Phys. Lett. (3)

S.G. Johnson, S. Fan, A. Mekis, and J.D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388–3390, (2001).
[CrossRef]

H.G. Winful, J.H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381, (1979).
[CrossRef]

S. Janz, J. He, Z.R. Wasilewski, and M. Cada, “Low threshold optical bistable switching in an asymmetric ¼-shifted distributed-feedback heterostructure,” Appl. Phys. Lett. 67, 1051–1053, (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

Jeffrey M. Harbold, F. Ömer Ilday, Frank W. Wise, and Bruce G. Aitken, “Highly Nonlinear Ge-As-Se and Ge-As-S-Se Glasses for All-Optical Switching,” IEEE Photon. Technol. Lett. 14, 822–824, (2002).
[CrossRef]

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14, 483–485, (2002).
[CrossRef]

J. Lightwave. Technol. (1)

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “Guiding optical light in air using an all-dielectric structure,” J. Lightwave. Technol. 17, 2039–2041, (1999).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nature (2)

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145, (1997).
[CrossRef]

B. Temelkuran, S.D. Hart, G. Benoit, J.D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420, 650–653, (2002).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. A (2)

C. Martijn de Sterke and J.E. Sipe, “Switching dynamics of finite periodic nonlinear media: A numerical study,” Phys. Rev. A 42, 2858–2869, (1990).
[CrossRef]

C. Martijn de Sterke and J.E. Sipe, “Envelope-function approach for the electrodynamics of nonlinear periodic structures,” Phys. Rev. A 38, 5149–5165, (1988).
[CrossRef]

Phys. Rev. B (1)

E. Lidorikis, K. Busch, Qiming Li, C.T. Chan, and C.M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090–15099, (1997).
[CrossRef]

Phys. Rev. E (1)

Marin Soljačić, Mihai Ibanescu, Steven G. Johnson, Yoel Fink, and J.D. Joannopoulos, “Optimal Bistable Switching in Non-Linear Photonic Crystals,” Phys. Rev. E 66, 055601(R) (2002).
[CrossRef]

Phys. Rev. Lett. (2)

D.N. Christodoulides and R.I Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62, 1746–1749, (1989).
[CrossRef] [PubMed]

Wei Chen and D.L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. 58, 160–163, (1987).
[CrossRef] [PubMed]

Science (3)

P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[CrossRef] [PubMed]

S.D. Hart, G.R. Maskaly, B. Temelkuran, P.H. Prideaux, J.D. Joannopoulos, and Y. Fink, “External Reflection from Omnidirectional Dielectric Mirror Fibers,” Science 296, 510–513, (2002).
[CrossRef] [PubMed]

R.F. Gregan, B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, P.J. Roberts, and D.C. Allan, “Single-Mode Photonic Band Gap Guidance of Light in Air,” Science 285, 1537–1539, (1999).
[CrossRef]

Other (7)

This special kind of modal cutoff is different from the ones found in many simple waveguiding systems which appear very close to the light line (k≠0) and thus are very lossy (no fedback) and do not have zero group velocity solutions.

Elefterios Lidorikis, Marin Soljacic, Mihai Ibanescu, Yoel Fink, and J.D. Joannopoulos, “Gap solitons and optical switching in axially uniform systems,” Opt. Lett., in press.

G. P. Agrawal, Nonlinear fiber optics (Academic Press, London, UK, 1995); Applications of nonlinear fiber optics (Academic Press, London, UK, 2001).

B.E.A. Saleh and M.C. Teich, Fundamentals Of Photonics (John Wiley&Sons, 1991).
[CrossRef]

For a review, see A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1995).

H.A. Haus, Waves And Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, NJ, 1984).

C. Kerbage and B.J. Eggleton, “Microstructured Optical Fibers,” Optics&Photonics News 38–42, (September 2002).

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Figures (6)

Fig. 1.
Fig. 1.

Schematic of a non-linear OmniGuide device in which we demonstrate optical bistability. The left panel presents a longitudinal cross-section; the panel on the right presents a transverse cross-section.

Fig. 2.
Fig. 2.

Numerical experiments with launching temporal-gaussian pulses into the non-linear system of Fig. 1. The upper-left panel shows the transmission as a function of the incoming pulse energy. The colored lines in the upper-right panel display the output spectra for a few pulses, corresponding to the colored dots in the upper-left panel; the spectrum of each pulse is normalized to its peak incoming power; i.e. the input pulse, normalized in the same manner is displayed with the gray dashed line. The lower panels show the output shapes for the incoming pulses denoted with the green, and blue dots in the upper-left panel respectively.

Fig. 3.
Fig. 3.

Plot of the observed POUTS vs. PINS for the device from Fig. 1, when δ=3.2. The squares are points obtained from numerical experiments. The line is the analytical prediction, which clearly matches the numerical experiments; the dotted part of the line is unstable and therefore physically unobservable.

Fig. 4.
Fig. 4.

(a) 2D simulation system: cladding consists of alternating dielectric layers of high-(2.8) and low-(1.5) index with thickness 0.3a and 0.7a, where a is the period. The core diameter is d=1.2a and index n′=n 0+n 2| E |2, where n 0=1.6. (b) Linear dispersion relations calculated by the FDTD method. The cutoff frequency is ωc =0.26215. Gray areas represent cladding and radiation modes.

Fig. 5.
Fig. 5.

(a) Transmission vs input flux S̃ for the L=5a system and ωa/2πc=0.26. The normalized flux S̃ is defined as S̃=n 0·n 2·s, where S is the electromagnetic flux through the fiber’s cross section. Both 2D FDTD (dots) and 1D model (red line) results are shown. The unstable solutions (physically unobservable) of the 1D model are represented by the dashed line. (b) Output flux during switch-up (path marked by the up-pointing arrow) for the L=5a system. (c) and (d) Same as (a) and (b), but for the L=8a system.

Fig. 6.
Fig. 6.

(a) Linear transmission coefficient vs frequency for the L=5a system. (b) Normalized intensity (or local index change δn=n 2| E |2) along the nonlinear core for the L=5a system.

Equations (6)

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κ ( c ω RES ) d * VOL d d r [ E ( r ) · E ( r ) 2 + 2 E ( r ) · E * ( r ) 2 ] n 2 ( r ) n 2 ( r ) [ VOL d d r E ( r ) 2 n 2 ( r ) ] 2 n 2 ( r ) MAX
P OUT S P IN S = T P 1 + ( P OUT S P 0 δ ) 2 ,
P 0 T P κ Q 2 ( ω RES c ) d 1 n 2 ( r ) MAX .
ω ( E 2 , k ) = ω c + α · k 2 + δ ω ( E 2 ) , ω ( k ) = ω c + α · k 2
δ ω ( z ) = ω 0 4 n 2 ( x , y ) n 0 ( x , y ) ( F · F 2 + 2 F 4 ) dxdy n 0 ( x , y ) 2 F 2 dxdy A ( z ) 2 γ A ( z ) 2 ,
A t i α 2 A z 2 i γ A 2 A = 0 .

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