Abstract

We compare the performance of two well-known all-optical switching schemes based on fiber Bragg gratings: a uniform grating and a grating with a π phase shift. We express their performance in terms of linear measures: the intensity enhancement inside the grating, which lowers the nonlinear threshold, and the relative resonance bandwidth, which determines the device’s response time. We show that in both grating types, the product of the enhancement and the relative bandwidth is proportional to the refractive index contrast, and that it is superior for a phase-shifted grating. We also evaluate the sensitivity of the devices to loss. We confirm results of our analysis by simulating nonlinear coupled-mode equations. More generally, our results indicate the advantage of structures with a high refractive- index contrast for all-optical switching.

© 2010 Optical Society of America

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  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]
  2. H. Lee and G. P. Agrawal, “Nonlinear switching of optical pulses in fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 508–515 (2003).
    [CrossRef]
  3. S. Radic, N. George, and G. P. Agrawal, “Theory of low-threshold optical switching in nonlinear phase-shifted periodic structures,” J. Opt. Soc. Am. B 12, 671–680 (1995).
    [CrossRef]
  4. R. Kashyap, Fiber Bragg Gratings (Academic, 1999).
  5. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge Univ. Press, 1997).
    [PubMed]
  6. S. Larochelle, Y. Hibino, V. Mizrahi, and G. I. Stegeman, “All-optical switching of grating transmission using cross-phase modulation in optical fibers,” Electron. Lett. 26, 1459–1460 (1990).
    [CrossRef]
  7. A. Melloni, M. Chinello, and M. Martinelli, “All-optical switching in phase-shifted fiber Bragg grating,” IEEE Photonics Technol. Lett. 12, 42–44 (2000).
    [CrossRef]
  8. I. V. Kabakova, B. Corcoran, J. A. Bolger, C. M. de Sterke, and B. J. Eggleton, “All-optical self-switching in optimized phase-shifted fiber Bragg grating,” Opt. Express 17, 5083–5089 (2009).
    [CrossRef] [PubMed]
  9. J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless slow light using gap soliton,” Nat. Phys. 2, 775–780 (2006).
    [CrossRef]
  10. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1991).
  11. Y. Nasu and S. Yamashita, “Multiple phase-shift superstructure fibre Bragg grating for DWDM systems,” Electron. Lett. 37, 1471–1472 (2001).
    [CrossRef]
  12. B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long superstructure Bragg gratings in optical fibers,” Electron. Lett. 30, 1621–1623 (1994).
    [CrossRef]
  13. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
    [CrossRef]
  14. M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
    [CrossRef] [PubMed]
  15. R. P. Stanley, R. Houdre, U. Oesterle, and M. Ilegems, “Impurity modes in one-dimensional periodic systems: the transition from photonic band gaps to microcavities,” Phys. Rev. A 48, 2246–2250 (1993).
    [CrossRef] [PubMed]
  16. N. G. R. Broderick, D. J. Richardson, and M. Ibsen, “Nonlinear switching in 20-cm-long fiber Bragg grating,” Opt. Lett. 25, 536–538 (2000).
    [CrossRef]
  17. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
    [CrossRef] [PubMed]
  18. A. Maitra, C. G. Poulton, J. Wang, J. Leuthold, and W. Freude, “Low switching threshold using nonlinearities in stopband-tapered waveguide Bragg gratings,” IEEE J. Quantum Electron. 41, 1303–1308 (2005).
    [CrossRef]
  19. M. Fujii, A. Mitra, C. Poulton, J. Leuthold, and W. Freude, “Non-reciprocal transmission and Schmitt trigger operation in strongly modulated asymmetric WBGs,” Opt. Express 14, 12782–12793 (2006).
    [CrossRef] [PubMed]
  20. J. H. Marburger and F. S. Felber, “Theory of lossless nonlinear Fabry–Perot interferometer,” Phys. Rev. A 17, 335–342 (1978).
    [CrossRef]
  21. A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, “Bistable optical element and its application,” Appl. Phys. Lett. 15, 376 (1969).
    [CrossRef]
  22. H. M. Gibbs, Optical Bistability (Academic, 1985).
  23. M. Yamada and K. Sakuda,“Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach,” Appl. Opt. 26, 3474–3478 (1987).
    [CrossRef] [PubMed]
  24. H. A. Haus and C. V. Shank, “Antisymmetric taper of distributed feedback lasers,” IEEE J. Quantum Electron. QE-12, 532–539 (1976).
    [CrossRef]
  25. D. Johlen, F. Knappe, H. Renner, and E. Brinkmeyer, “UV-induced absorption, scattering and transition losses in UV side-written fibers,” in Conference on Optical Fiber Communication (Optical Society of America, 1999), paper ThD1 .
  26. I. C. M. Littler, T. Grujic, and B. J. Eggleton, “Photothermal effects in fiber Bragg gratings,” Appl. Opt. 45, 4679–4685 (2006).
    [CrossRef] [PubMed]
  27. J. T. Mok, M. Ibsen, C. M. de Sterke, and B. J. Eggleton, “Dispersionless slow light with 5-pulse-width delay in fibre Bragg grating,” Electron. Lett. 43, 1418–1419 (2007).
    [CrossRef]
  28. C. M. de Sterke, K. R. Jackson, and B. D. Robert, “Nonlinear coupled mode equations on a finite interval: a numerical procedure,” J. Opt. Soc. Am. B 8, 403–412 (1991).
    [CrossRef]
  29. M. Shokooh-Saremi, V. G. Ta’eed, N. J. Baker, I. C. M. Littler, D. J. Moss, and B. J. Eggleton, “High-performance Bragg gratings in chalcogenide rib waveguides written with a modified Sagnac interferometer,” J. Opt. Soc. Am. B 23, 1323–1331 (2006).
    [CrossRef]
  30. C. M. de Sterke, L. C. Botten, A. A. Asatryan, T. P. White, and R. C. McPhedran, “Modes of coupled photonic crystal waveguide,” Opt. Lett. 29, 1384–1368 (2004).
    [CrossRef]

2009 (1)

2007 (1)

J. T. Mok, M. Ibsen, C. M. de Sterke, and B. J. Eggleton, “Dispersionless slow light with 5-pulse-width delay in fibre Bragg grating,” Electron. Lett. 43, 1418–1419 (2007).
[CrossRef]

2006 (4)

2005 (1)

A. Maitra, C. G. Poulton, J. Wang, J. Leuthold, and W. Freude, “Low switching threshold using nonlinearities in stopband-tapered waveguide Bragg gratings,” IEEE J. Quantum Electron. 41, 1303–1308 (2005).
[CrossRef]

2004 (1)

2003 (1)

H. Lee and G. P. Agrawal, “Nonlinear switching of optical pulses in fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 508–515 (2003).
[CrossRef]

2001 (1)

Y. Nasu and S. Yamashita, “Multiple phase-shift superstructure fibre Bragg grating for DWDM systems,” Electron. Lett. 37, 1471–1472 (2001).
[CrossRef]

2000 (2)

A. Melloni, M. Chinello, and M. Martinelli, “All-optical switching in phase-shifted fiber Bragg grating,” IEEE Photonics Technol. Lett. 12, 42–44 (2000).
[CrossRef]

N. G. R. Broderick, D. J. Richardson, and M. Ibsen, “Nonlinear switching in 20-cm-long fiber Bragg grating,” Opt. Lett. 25, 536–538 (2000).
[CrossRef]

1997 (1)

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

1996 (1)

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

1995 (1)

1994 (2)

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long superstructure Bragg gratings in optical fibers,” Electron. Lett. 30, 1621–1623 (1994).
[CrossRef]

1993 (1)

R. P. Stanley, R. Houdre, U. Oesterle, and M. Ilegems, “Impurity modes in one-dimensional periodic systems: the transition from photonic band gaps to microcavities,” Phys. Rev. A 48, 2246–2250 (1993).
[CrossRef] [PubMed]

1991 (1)

1990 (1)

S. Larochelle, Y. Hibino, V. Mizrahi, and G. I. Stegeman, “All-optical switching of grating transmission using cross-phase modulation in optical fibers,” Electron. Lett. 26, 1459–1460 (1990).
[CrossRef]

1987 (1)

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]

1978 (1)

J. H. Marburger and F. S. Felber, “Theory of lossless nonlinear Fabry–Perot interferometer,” Phys. Rev. A 17, 335–342 (1978).
[CrossRef]

1976 (1)

H. A. Haus and C. V. Shank, “Antisymmetric taper of distributed feedback lasers,” IEEE J. Quantum Electron. QE-12, 532–539 (1976).
[CrossRef]

1969 (1)

A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, “Bistable optical element and its application,” Appl. Phys. Lett. 15, 376 (1969).
[CrossRef]

Agrawal, G. P.

H. Lee and G. P. Agrawal, “Nonlinear switching of optical pulses in fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 508–515 (2003).
[CrossRef]

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

Asatryan, A. A.

Baker, N. J.

Bloemer, M. J.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

Bolger, J. A.

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge Univ. Press, 1997).
[PubMed]

Botten, L. C.

Bowden, C. M.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

Brinkmeyer, E.

D. Johlen, F. Knappe, H. Renner, and E. Brinkmeyer, “UV-induced absorption, scattering and transition losses in UV side-written fibers,” in Conference on Optical Fiber Communication (Optical Society of America, 1999), paper ThD1 .

Broderick, N. G. R.

Chinello, M.

A. Melloni, M. Chinello, and M. Martinelli, “All-optical switching in phase-shifted fiber Bragg grating,” IEEE Photonics Technol. Lett. 12, 42–44 (2000).
[CrossRef]

Corcoran, B.

Daneu, V.

A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, “Bistable optical element and its application,” Appl. Phys. Lett. 15, 376 (1969).
[CrossRef]

de Sterke, C. M.

I. V. Kabakova, B. Corcoran, J. A. Bolger, C. M. de Sterke, and B. J. Eggleton, “All-optical self-switching in optimized phase-shifted fiber Bragg grating,” Opt. Express 17, 5083–5089 (2009).
[CrossRef] [PubMed]

J. T. Mok, M. Ibsen, C. M. de Sterke, and B. J. Eggleton, “Dispersionless slow light with 5-pulse-width delay in fibre Bragg grating,” Electron. Lett. 43, 1418–1419 (2007).
[CrossRef]

J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless slow light using gap soliton,” Nat. Phys. 2, 775–780 (2006).
[CrossRef]

C. M. de Sterke, L. C. Botten, A. A. Asatryan, T. P. White, and R. C. McPhedran, “Modes of coupled photonic crystal waveguide,” Opt. Lett. 29, 1384–1368 (2004).
[CrossRef]

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

C. M. de Sterke, K. R. Jackson, and B. D. Robert, “Nonlinear coupled mode equations on a finite interval: a numerical procedure,” J. Opt. Soc. Am. B 8, 403–412 (1991).
[CrossRef]

Dowling, J. P.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

Eggleton, B. J.

I. V. Kabakova, B. Corcoran, J. A. Bolger, C. M. de Sterke, and B. J. Eggleton, “All-optical self-switching in optimized phase-shifted fiber Bragg grating,” Opt. Express 17, 5083–5089 (2009).
[CrossRef] [PubMed]

J. T. Mok, M. Ibsen, C. M. de Sterke, and B. J. Eggleton, “Dispersionless slow light with 5-pulse-width delay in fibre Bragg grating,” Electron. Lett. 43, 1418–1419 (2007).
[CrossRef]

M. Shokooh-Saremi, V. G. Ta’eed, N. J. Baker, I. C. M. Littler, D. J. Moss, and B. J. Eggleton, “High-performance Bragg gratings in chalcogenide rib waveguides written with a modified Sagnac interferometer,” J. Opt. Soc. Am. B 23, 1323–1331 (2006).
[CrossRef]

J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless slow light using gap soliton,” Nat. Phys. 2, 775–780 (2006).
[CrossRef]

I. C. M. Littler, T. Grujic, and B. J. Eggleton, “Photothermal effects in fiber Bragg gratings,” Appl. Opt. 45, 4679–4685 (2006).
[CrossRef] [PubMed]

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long superstructure Bragg gratings in optical fibers,” Electron. Lett. 30, 1621–1623 (1994).
[CrossRef]

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

Felber, F. S.

J. H. Marburger and F. S. Felber, “Theory of lossless nonlinear Fabry–Perot interferometer,” Phys. Rev. A 17, 335–342 (1978).
[CrossRef]

Freude, W.

M. Fujii, A. Mitra, C. Poulton, J. Leuthold, and W. Freude, “Non-reciprocal transmission and Schmitt trigger operation in strongly modulated asymmetric WBGs,” Opt. Express 14, 12782–12793 (2006).
[CrossRef] [PubMed]

A. Maitra, C. G. Poulton, J. Wang, J. Leuthold, and W. Freude, “Low switching threshold using nonlinearities in stopband-tapered waveguide Bragg gratings,” IEEE J. Quantum Electron. 41, 1303–1308 (2005).
[CrossRef]

Fujii, M.

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, N.

Gibbs, H. M.

H. M. Gibbs, Optical Bistability (Academic, 1985).

Goldhar, J.

A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, “Bistable optical element and its application,” Appl. Phys. Lett. 15, 376 (1969).
[CrossRef]

Grujic, T.

Haus, H. A.

H. A. Haus and C. V. Shank, “Antisymmetric taper of distributed feedback lasers,” IEEE J. Quantum Electron. QE-12, 532–539 (1976).
[CrossRef]

Hibino, Y.

S. Larochelle, Y. Hibino, V. Mizrahi, and G. I. Stegeman, “All-optical switching of grating transmission using cross-phase modulation in optical fibers,” Electron. Lett. 26, 1459–1460 (1990).
[CrossRef]

Houdre, R.

R. P. Stanley, R. Houdre, U. Oesterle, and M. Ilegems, “Impurity modes in one-dimensional periodic systems: the transition from photonic band gaps to microcavities,” Phys. Rev. A 48, 2246–2250 (1993).
[CrossRef] [PubMed]

Ibsen, M.

J. T. Mok, M. Ibsen, C. M. de Sterke, and B. J. Eggleton, “Dispersionless slow light with 5-pulse-width delay in fibre Bragg grating,” Electron. Lett. 43, 1418–1419 (2007).
[CrossRef]

N. G. R. Broderick, D. J. Richardson, and M. Ibsen, “Nonlinear switching in 20-cm-long fiber Bragg grating,” Opt. Lett. 25, 536–538 (2000).
[CrossRef]

Ilegems, M.

R. P. Stanley, R. Houdre, U. Oesterle, and M. Ilegems, “Impurity modes in one-dimensional periodic systems: the transition from photonic band gaps to microcavities,” Phys. Rev. A 48, 2246–2250 (1993).
[CrossRef] [PubMed]

Jackson, K. R.

Johlen, D.

D. Johlen, F. Knappe, H. Renner, and E. Brinkmeyer, “UV-induced absorption, scattering and transition losses in UV side-written fibers,” in Conference on Optical Fiber Communication (Optical Society of America, 1999), paper ThD1 .

Kabakova, I. V.

Kashyap, R.

R. Kashyap, Fiber Bragg Gratings (Academic, 1999).

Knappe, F.

D. Johlen, F. Knappe, H. Renner, and E. Brinkmeyer, “UV-induced absorption, scattering and transition losses in UV side-written fibers,” in Conference on Optical Fiber Communication (Optical Society of America, 1999), paper ThD1 .

Krug, P. A.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long superstructure Bragg gratings in optical fibers,” Electron. Lett. 30, 1621–1623 (1994).
[CrossRef]

Kurnit, N. A.

A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, “Bistable optical element and its application,” Appl. Phys. Lett. 15, 376 (1969).
[CrossRef]

Larochelle, S.

S. Larochelle, Y. Hibino, V. Mizrahi, and G. I. Stegeman, “All-optical switching of grating transmission using cross-phase modulation in optical fibers,” Electron. Lett. 26, 1459–1460 (1990).
[CrossRef]

Lee, H.

H. Lee and G. P. Agrawal, “Nonlinear switching of optical pulses in fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 508–515 (2003).
[CrossRef]

Leuthold, J.

M. Fujii, A. Mitra, C. Poulton, J. Leuthold, and W. Freude, “Non-reciprocal transmission and Schmitt trigger operation in strongly modulated asymmetric WBGs,” Opt. Express 14, 12782–12793 (2006).
[CrossRef] [PubMed]

A. Maitra, C. G. Poulton, J. Wang, J. Leuthold, and W. Freude, “Low switching threshold using nonlinearities in stopband-tapered waveguide Bragg gratings,” IEEE J. Quantum Electron. 41, 1303–1308 (2005).
[CrossRef]

Littler, I. C. M.

Maitra, A.

A. Maitra, C. G. Poulton, J. Wang, J. Leuthold, and W. Freude, “Low switching threshold using nonlinearities in stopband-tapered waveguide Bragg gratings,” IEEE J. Quantum Electron. 41, 1303–1308 (2005).
[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]

J. H. Marburger and F. S. Felber, “Theory of lossless nonlinear Fabry–Perot interferometer,” Phys. Rev. A 17, 335–342 (1978).
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1991).

Martinelli, M.

A. Melloni, M. Chinello, and M. Martinelli, “All-optical switching in phase-shifted fiber Bragg grating,” IEEE Photonics Technol. Lett. 12, 42–44 (2000).
[CrossRef]

McPhedran, R. C.

Melloni, A.

A. Melloni, M. Chinello, and M. Martinelli, “All-optical switching in phase-shifted fiber Bragg grating,” IEEE Photonics Technol. Lett. 12, 42–44 (2000).
[CrossRef]

Mitra, A.

Mizrahi, V.

S. Larochelle, Y. Hibino, V. Mizrahi, and G. I. Stegeman, “All-optical switching of grating transmission using cross-phase modulation in optical fibers,” Electron. Lett. 26, 1459–1460 (1990).
[CrossRef]

Mok, J. T.

J. T. Mok, M. Ibsen, C. M. de Sterke, and B. J. Eggleton, “Dispersionless slow light with 5-pulse-width delay in fibre Bragg grating,” Electron. Lett. 43, 1418–1419 (2007).
[CrossRef]

J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless slow light using gap soliton,” Nat. Phys. 2, 775–780 (2006).
[CrossRef]

Moss, D. J.

Nasu, Y.

Y. Nasu and S. Yamashita, “Multiple phase-shift superstructure fibre Bragg grating for DWDM systems,” Electron. Lett. 37, 1471–1472 (2001).
[CrossRef]

Oesterle, U.

R. P. Stanley, R. Houdre, U. Oesterle, and M. Ilegems, “Impurity modes in one-dimensional periodic systems: the transition from photonic band gaps to microcavities,” Phys. Rev. A 48, 2246–2250 (1993).
[CrossRef] [PubMed]

Ouellette, F.

B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long superstructure Bragg gratings in optical fibers,” Electron. Lett. 30, 1621–1623 (1994).
[CrossRef]

Poladian, L.

B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long superstructure Bragg gratings in optical fibers,” Electron. Lett. 30, 1621–1623 (1994).
[CrossRef]

Poulton, C.

Poulton, C. G.

A. Maitra, C. G. Poulton, J. Wang, J. Leuthold, and W. Freude, “Low switching threshold using nonlinearities in stopband-tapered waveguide Bragg gratings,” IEEE J. Quantum Electron. 41, 1303–1308 (2005).
[CrossRef]

Radic, S.

Renner, H.

D. Johlen, F. Knappe, H. Renner, and E. Brinkmeyer, “UV-induced absorption, scattering and transition losses in UV side-written fibers,” in Conference on Optical Fiber Communication (Optical Society of America, 1999), paper ThD1 .

Richardson, D. J.

Robert, B. D.

Sakuda, K.

Scalora, M.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

Shank, C. V.

H. A. Haus and C. V. Shank, “Antisymmetric taper of distributed feedback lasers,” IEEE J. Quantum Electron. QE-12, 532–539 (1976).
[CrossRef]

Shokooh-Saremi, M.

Sipe, J. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

Slusher, R. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

Stanley, R. P.

R. P. Stanley, R. Houdre, U. Oesterle, and M. Ilegems, “Impurity modes in one-dimensional periodic systems: the transition from photonic band gaps to microcavities,” Phys. Rev. A 48, 2246–2250 (1993).
[CrossRef] [PubMed]

Stegeman, G. I.

S. Larochelle, Y. Hibino, V. Mizrahi, and G. I. Stegeman, “All-optical switching of grating transmission using cross-phase modulation in optical fibers,” Electron. Lett. 26, 1459–1460 (1990).
[CrossRef]

Szoke, A.

A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, “Bistable optical element and its application,” Appl. Phys. Lett. 15, 376 (1969).
[CrossRef]

Ta’eed, V. G.

Wang, J.

A. Maitra, C. G. Poulton, J. Wang, J. Leuthold, and W. Freude, “Low switching threshold using nonlinearities in stopband-tapered waveguide Bragg gratings,” IEEE J. Quantum Electron. 41, 1303–1308 (2005).
[CrossRef]

White, T. P.

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]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge Univ. Press, 1997).
[PubMed]

Yamada, M.

Yamashita, S.

Y. Nasu and S. Yamashita, “Multiple phase-shift superstructure fibre Bragg grating for DWDM systems,” Electron. Lett. 37, 1471–1472 (2001).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

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]

A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, “Bistable optical element and its application,” Appl. Phys. Lett. 15, 376 (1969).
[CrossRef]

Electron. Lett. (4)

S. Larochelle, Y. Hibino, V. Mizrahi, and G. I. Stegeman, “All-optical switching of grating transmission using cross-phase modulation in optical fibers,” Electron. Lett. 26, 1459–1460 (1990).
[CrossRef]

Y. Nasu and S. Yamashita, “Multiple phase-shift superstructure fibre Bragg grating for DWDM systems,” Electron. Lett. 37, 1471–1472 (2001).
[CrossRef]

B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long superstructure Bragg gratings in optical fibers,” Electron. Lett. 30, 1621–1623 (1994).
[CrossRef]

J. T. Mok, M. Ibsen, C. M. de Sterke, and B. J. Eggleton, “Dispersionless slow light with 5-pulse-width delay in fibre Bragg grating,” Electron. Lett. 43, 1418–1419 (2007).
[CrossRef]

IEEE J. Quantum Electron. (3)

H. A. Haus and C. V. Shank, “Antisymmetric taper of distributed feedback lasers,” IEEE J. Quantum Electron. QE-12, 532–539 (1976).
[CrossRef]

H. Lee and G. P. Agrawal, “Nonlinear switching of optical pulses in fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 508–515 (2003).
[CrossRef]

A. Maitra, C. G. Poulton, J. Wang, J. Leuthold, and W. Freude, “Low switching threshold using nonlinearities in stopband-tapered waveguide Bragg gratings,” IEEE J. Quantum Electron. 41, 1303–1308 (2005).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

A. Melloni, M. Chinello, and M. Martinelli, “All-optical switching in phase-shifted fiber Bragg grating,” IEEE Photonics Technol. Lett. 12, 42–44 (2000).
[CrossRef]

J. Lightwave Technol. (1)

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

J. Opt. Soc. Am. B (3)

Nat. Phys. (1)

J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless slow light using gap soliton,” Nat. Phys. 2, 775–780 (2006).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (2)

R. P. Stanley, R. Houdre, U. Oesterle, and M. Ilegems, “Impurity modes in one-dimensional periodic systems: the transition from photonic band gaps to microcavities,” Phys. Rev. A 48, 2246–2250 (1993).
[CrossRef] [PubMed]

J. H. Marburger and F. S. Felber, “Theory of lossless nonlinear Fabry–Perot interferometer,” Phys. Rev. A 17, 335–342 (1978).
[CrossRef]

Phys. Rev. Lett. (2)

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

Other (5)

R. Kashyap, Fiber Bragg Gratings (Academic, 1999).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge Univ. Press, 1997).
[PubMed]

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1991).

H. M. Gibbs, Optical Bistability (Academic, 1985).

D. Johlen, F. Knappe, H. Renner, and E. Brinkmeyer, “UV-induced absorption, scattering and transition losses in UV side-written fibers,” in Conference on Optical Fiber Communication (Optical Society of America, 1999), paper ThD1 .

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Figures (7)

Fig. 1
Fig. 1

Principle of AOS in Bragg gratings: (a) optical pulse at wavelength λ p is coupled into the fiber with FBG (b). At low intensities λ p is just outside the grating bandgap, at first reflection zero (c), resulting in high transmission and (d). At high input intensities, the band edge shifts to the longer wavelength due to nonlinear effects (c) and the pulse falls into the bandgap, leading to low transmission (d). The intensity enhancement inside the grating at resonance (e) helps to reduce the threshold required for AOS.

Fig. 2
Fig. 2

Illustration of AOS schemes. Solid curve represents a spectrum of a uniform FBG, dotted curve shows a spectrum of a grating with a π phase shift. Labels 1, 2 show wavelength regions of each scheme, respectively.

Fig. 3
Fig. 3

Scheme of a FBG with the boundary conditions used to solve the CMEs [Eq. (6)].

Fig. 4
Fig. 4

(a) Numerically calculated transmission spectra for grating A with κ A = 200 m 1 (solid curve), and grating B with κ B = 400 m 1 (dotted curve). Both gratings have length of L = 1 cm . (b) Corresponding intensity envelopes inside the gratings are calculated at detunings corresponding to the first reflection zero δ A and δ B for gratings A and B, respectively.

Fig. 5
Fig. 5

(a) Calculated transmission spectra for phase-shifted grating A with parameters κ A L = 2 (solid curve) and phase-shifted grating B with κ B L = 4 (dotted curve). (b) Corresponding intensity envelope inside the gratings A and B, calculated at Bragg wavelength (detuning δ A , B = 0 ) for both gratings.

Fig. 6
Fig. 6

Switching curves on resonance for a phase-shifted (1) and uniform (2) FBGs. Both gratings have the same resonance width of Δ δ = 10.12 m 1 and strength κ L = 4 .

Fig. 7
Fig. 7

Switching of 2 ns pulses in a uniform (a) and phase-shifted (b) FBGs. Letters indicate input (I), reflected (R), and transmitted (T) pulses. Both gratings have the same resonance width of Δ δ = 10.12 m 1 and strength κ L = 4 . The pulse input peak intensity is 1 GW cm 2 .

Tables (1)

Tables Icon

Table 1 Comparison of Three Resonant Structures: a FP Etalon, a Uniform FBG and Phase-shifted FBG

Equations (27)

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Δ λ B = 2 n 2 E I 0 Λ .
E ( FP ) = 1 + R 1 R .
Δ λ ( FP ) λ m = 1 R m f π R 1 R m f π .
Δ λ ( FP ) λ m × E ( FP ) = 2 π 1 m f ,
E ( z , t ) = E + ( z , t ) exp [ i ( k z ω t ) ] + E ( z , t ) exp [ i ( k z ω t ) ] + c.c. ,
± i E ± z + δ E ± + κ E = 0 .
( E + ( z ) E ( z ) ) = M ( z ) ( E + ( 0 ) E ( 0 ) ) .
M ( z ) = ( β cosh ( β z ) + i δ sinh ( β z ) i e i ψ κ sinh ( β z ) i e i ψ κ sinh ( β z ) β cosh ( β z ) i δ sinh ( β z ) ) ,
T ( UG ) = β 2 β 2 cosh 2 ( β L ) + δ 2 sinh 2 ( β L ) .
E ( UG ) = | E + ( L 2 ) | 2 + | E ( L 2 ) | 2 | E 0 | 2 = 2 ( κ L π ) 2 + 1 ,
Δ λ ( UG ) λ B × E ( UG ) = Δ n n 0 1 κ L = π 2 1 N ,
M = M ( ψ = 0 ) L 2 M ( ψ = π ) L 2 .
T ( PS ) = ( 1 + 4 δ 2 κ 2 sinh 4 ( L 2 [ κ δ 2 2 κ ] ) ) 1 .
| E + ( z ) | = E 0 cosh ( κ ( L 2 | L 2 z | ) ) ,
| E ( z ) | = E 0 sinh ( κ ( L 2 | L 2 z | ) ) .
E ( PS ) = | E + ( L 2 ) | 2 + | E ( L 2 ) | 2 | E 0 | 2 = cosh ( κ L ) .
Δ λ ( PS ) = κ λ B 2 2 π n 0 sinh 2 ( κ L 2 ) .
Δ λ ( PS ) λ B × E ( PS ) = Δ n n 0 .
U = 0 L 2 ( | E + ( z ) | 2 + | E ( z ) | 2 ) d z .
U ( UG ) = L 2 ( 1 + ( κ L π ) 2 ) | E 0 | 2 ,
U ( PS ) = sinh ( κ L ) 2 κ | E 0 | 2 .
Δ UG = E ( α = 0 ) E ( α 0 ) E ( α = 0 ) = α L E ( α = 0 ) 2 ,
Δ PS = α E ( α = 0 ) 2 κ = Δ UG κ L .
E UG I UG = E PS I PS .
d d z ( | E + | 2 | E | 2 ) = 2 δ i ( | E + | 2 + | E | 2 ) ,
| E + ( z ) | 2 | E ( z ) | 2 = 2 δ i 0 z ( | E + ( z ) | 2 + | E ( z ) | 2 ) d z .
U = 0 L 2 ( | E + ( z ) | 2 + | E ( z ) | 2 ) d z .

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