Abstract

We analyze the resonant transmission of light through a photonic-crystal waveguide side coupled to a Kerr nonlinear cavity, and demonstrate how to design the structure geometry for achieving bistability and all-optical switching at ultralow powers in the slow-light regime. We show that the resonance quality factor in such structures scales inversely proportional to the group velocity of light at the resonant frequency and thus grows indefinitely in the slow-light regime. Accordingly, the power threshold required for all-optical switching in such structures scales as a square of the group velocity, rapidly vanishing in the slow-light regime.

© 2007 Optical Society of America

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  1. J.P. Dowling, M. Scalora, M.J. Bloemer, and C.M. Bowden, "The photonic band edge laser: A new aproach to gain enhancement," J. Appl. Phys. 75,1896-1899 (1994).
    [CrossRef]
  2. M. Roussey, M.-P. Bernal, N. Courjal, D. Van Labeke, F.I. Baida, and R. Salut, "Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons," Appl. Phys. Lett. 89,241110 (2006).
    [CrossRef]
  3. T. Suzuki and P.K.L. Yu, "Emission power of an electric dipole in the photonic band structure of the fcc lattice," J. Opt. Soc. Am. B 12,570-582 (1995).
  4. M. Scalora, J.P. Dowling, C.W. 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]
  5. J. Martorell, R. Vilaseca, and R. Corbalan, "Second-harmonic generation in a photonic crystal," Appl. Phys. Lett. 70,702-704 (1997).
    [CrossRef]
  6. M. Soljacic, S.G. Johnson, S.H. Fan, M. Ibanescu, E. Ippen, and J.D. Joannopoulos, "Photonic-crystal slow-light enhancement of nonlinear phase sensitivity," J. Opt. Soc. Am. B 19,2052-2059 (2002).
  7. Y. Chen and S. Blair, "Nonlinearity enhancement in finite coupled-resonator slow-light waveguides," Opt. Express 12,3353-3366 (2004).
    [CrossRef]
  8. J.B. Khurgin, "Optical buffers based on slow light in electromagnetically induced transparent media and coupled resonator structures: comparative analysis," J. Opt. Soc. Am. B 22,1062-1074 (2005).
    [CrossRef]
  9. F. Xia, L. Sekaric, and Yu. Vlasov, "Ultracompact optical buffers on a silicon chip," Nat. Photon. 1,65-72 (2007).
  10. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87,253902 (2001).
    [CrossRef]
  11. R.S. Jacobsen, A.V. Lavrinenko, L.H. Frandsen, C. Peucheret, B. Zsigri, G. Moulin, J.F. Pedersen, and P. I. Borel, "Direct experimental and numerical determination of extremely high group indices in photonic crystal waveguides," Opt. Express 13,7861-7871 (2005).
    [CrossRef]
  12. Y.A. Vlasov, M. O’Boyle, H.F. Hamann, and S.J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438,65-69 (2005).
    [CrossRef]
  13. H. Gersen, T.J. Karle, R.J.P. Engelen, W. Bogaerts, J.P. Korterik, N.F. van Hulst, T.F. Krauss, and L. Kuipers, "Near-field characterization of low-loss photonic crystal waveguides," Phys. Rev. Lett. 94,073903 (2005).
    [CrossRef]
  14. S. Assefa, S.J. McNab and Y.A. Vlasov, "Transmission of slow light through photonic crystal waveguide bends," Opt. Lett. 31,745-747 (2006).
    [CrossRef]
  15. Y.A. Vlasov and S.J. McNab, "Coupling into the slow light mode in slab-type photonic crystal waveguides," Opt. Lett. 31,50-52 (2006).
    [CrossRef]
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    [CrossRef]
  17. S.H. Fan, "Sharp asymmetric line shapes in side-coupled waveguide-cavity systems," Appl. Phys. Lett. 80,908- 910 (2002).
    [CrossRef]
  18. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431,1081-1084 (2004).
    [CrossRef]
  19. P. E. Barclay, K. Srinivasan, and O. Painter, "Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper," Opt. Express 13,801-820 (2005).
    [CrossRef]
  20. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching action of Si high-Q photonic-crystal nanocavities," Opt. Express 13,2678-2687 (2005).
    [CrossRef]
  21. T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, "All-optical switches on a silicon chip realized using photonic crystal nanocavities," Appl. Phys. Lett. 87,151112 (2005).
    [CrossRef]
  22. G. Priem, P. Dumon,W. Bogaerts, D. Van Thourhout, G. Morthier, and R. Baets, "Optical bistability and pulsating behaviour in Silicon-On-Insulator ring resonator structures," Opt. Express 13,9623-9528 (2005).
    [CrossRef]
  23. T. Uesugi, B. Song, T. Asano, and S. Noda, "Investigation of optical nonlinearities in an ultra-high-Q Si nanocavity in a two-dimensional photonic crystal slab," Opt. Express 14,377-386 (2006).
    [CrossRef]
  24. X. Yang, C. Husko, M. Yu, D.-L. Kwong, and C.W. Wong, "Observation of femto-joule optical bistability involving Fano resonances in high-Q/Vm silicon photonic crystal nanocavities," arXiv:physics/0703132 (2007).
  25. S. Hughes, L. Ramunno, J.F. Young, and J.E. Sipe, "Extrinsic optical scattering loss in photonic crystal waveguides: Role of fabrication disorder and photon group velocity," Phys. Rev. Lett. 94,033903 (2005).
    [CrossRef]
  26. S.F. Mingaleev, A.E. Miroshnichenko, Y.S. Kivshar, and K. Busch, "All-optical switching, bistability, and slowlight transmission in photonic crystal waveguide-resonator structures," Phys. Rev. E 74,046603 (2006).
    [CrossRef]
  27. K. Busch, S.F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, "Wannier function approach to photonic crystal circuits," J. Phys.: Condens. Matter. 15,R1233-R1256 (2003).
    [CrossRef]
  28. S.G. Johnson and J.D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8,173-190 (2001).
  29. A.E. Miroshnichenko, S.F. Mingaleev, S. Flach, and Yu.S. Kivshar, "Nonlinear Fano resonance and bistable wave transmission," Phys. Rev. E 71,036626 (2005).
    [CrossRef]
  30. M.F. Yanik, S.H. Fan, and M. Soljacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83,2739-2741 (2003).
    [CrossRef]

2007 (1)

F. Xia, L. Sekaric, and Yu. Vlasov, "Ultracompact optical buffers on a silicon chip," Nat. Photon. 1,65-72 (2007).

2006 (6)

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

M. Roussey, M.-P. Bernal, N. Courjal, D. Van Labeke, F.I. Baida, and R. Salut, "Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons," Appl. Phys. Lett. 89,241110 (2006).
[CrossRef]

S.F. Mingaleev, A.E. Miroshnichenko, Y.S. Kivshar, and K. Busch, "All-optical switching, bistability, and slowlight transmission in photonic crystal waveguide-resonator structures," Phys. Rev. E 74,046603 (2006).
[CrossRef]

Y.A. Vlasov and S.J. McNab, "Coupling into the slow light mode in slab-type photonic crystal waveguides," Opt. Lett. 31,50-52 (2006).
[CrossRef]

T. Uesugi, B. Song, T. Asano, and S. Noda, "Investigation of optical nonlinearities in an ultra-high-Q Si nanocavity in a two-dimensional photonic crystal slab," Opt. Express 14,377-386 (2006).
[CrossRef]

S. Assefa, S.J. McNab and Y.A. Vlasov, "Transmission of slow light through photonic crystal waveguide bends," Opt. Lett. 31,745-747 (2006).
[CrossRef]

2005 (10)

P. E. Barclay, K. Srinivasan, and O. Painter, "Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper," Opt. Express 13,801-820 (2005).
[CrossRef]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching action of Si high-Q photonic-crystal nanocavities," Opt. Express 13,2678-2687 (2005).
[CrossRef]

J.B. Khurgin, "Optical buffers based on slow light in electromagnetically induced transparent media and coupled resonator structures: comparative analysis," J. Opt. Soc. Am. B 22,1062-1074 (2005).
[CrossRef]

R.S. Jacobsen, A.V. Lavrinenko, L.H. Frandsen, C. Peucheret, B. Zsigri, G. Moulin, J.F. Pedersen, and P. I. Borel, "Direct experimental and numerical determination of extremely high group indices in photonic crystal waveguides," Opt. Express 13,7861-7871 (2005).
[CrossRef]

G. Priem, P. Dumon,W. Bogaerts, D. Van Thourhout, G. Morthier, and R. Baets, "Optical bistability and pulsating behaviour in Silicon-On-Insulator ring resonator structures," Opt. Express 13,9623-9528 (2005).
[CrossRef]

A.E. Miroshnichenko, S.F. Mingaleev, S. Flach, and Yu.S. Kivshar, "Nonlinear Fano resonance and bistable wave transmission," Phys. Rev. E 71,036626 (2005).
[CrossRef]

Y.A. Vlasov, M. O’Boyle, H.F. Hamann, and S.J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438,65-69 (2005).
[CrossRef]

H. Gersen, T.J. Karle, R.J.P. Engelen, W. Bogaerts, J.P. Korterik, N.F. van Hulst, T.F. Krauss, and L. Kuipers, "Near-field characterization of low-loss photonic crystal waveguides," Phys. Rev. Lett. 94,073903 (2005).
[CrossRef]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, "All-optical switches on a silicon chip realized using photonic crystal nanocavities," Appl. Phys. Lett. 87,151112 (2005).
[CrossRef]

S. Hughes, L. Ramunno, J.F. Young, and J.E. Sipe, "Extrinsic optical scattering loss in photonic crystal waveguides: Role of fabrication disorder and photon group velocity," Phys. Rev. Lett. 94,033903 (2005).
[CrossRef]

2004 (2)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431,1081-1084 (2004).
[CrossRef]

Y. Chen and S. Blair, "Nonlinearity enhancement in finite coupled-resonator slow-light waveguides," Opt. Express 12,3353-3366 (2004).
[CrossRef]

2003 (2)

M.F. Yanik, S.H. Fan, and M. Soljacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83,2739-2741 (2003).
[CrossRef]

K. Busch, S.F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, "Wannier function approach to photonic crystal circuits," J. Phys.: Condens. Matter. 15,R1233-R1256 (2003).
[CrossRef]

2002 (2)

2001 (2)

S.G. Johnson and J.D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8,173-190 (2001).

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87,253902 (2001).
[CrossRef]

1997 (1)

J. Martorell, R. Vilaseca, and R. Corbalan, "Second-harmonic generation in a photonic crystal," Appl. Phys. Lett. 70,702-704 (1997).
[CrossRef]

1995 (1)

1994 (2)

J.P. Dowling, M. Scalora, M.J. Bloemer, and C.M. Bowden, "The photonic band edge laser: A new aproach to gain enhancement," J. Appl. Phys. 75,1896-1899 (1994).
[CrossRef]

M. Scalora, J.P. Dowling, C.W. 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]

Appl. Phys. Lett. (5)

J. Martorell, R. Vilaseca, and R. Corbalan, "Second-harmonic generation in a photonic crystal," Appl. Phys. Lett. 70,702-704 (1997).
[CrossRef]

M. Roussey, M.-P. Bernal, N. Courjal, D. Van Labeke, F.I. Baida, and R. Salut, "Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons," Appl. Phys. Lett. 89,241110 (2006).
[CrossRef]

S.H. Fan, "Sharp asymmetric line shapes in side-coupled waveguide-cavity systems," Appl. Phys. Lett. 80,908- 910 (2002).
[CrossRef]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, "All-optical switches on a silicon chip realized using photonic crystal nanocavities," Appl. Phys. Lett. 87,151112 (2005).
[CrossRef]

M.F. Yanik, S.H. Fan, and M. Soljacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83,2739-2741 (2003).
[CrossRef]

J. Appl. Phys. (1)

J.P. Dowling, M. Scalora, M.J. Bloemer, and C.M. Bowden, "The photonic band edge laser: A new aproach to gain enhancement," J. Appl. Phys. 75,1896-1899 (1994).
[CrossRef]

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

J. Phys.: Condens. Matter. (1)

K. Busch, S.F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, "Wannier function approach to photonic crystal circuits," J. Phys.: Condens. Matter. 15,R1233-R1256 (2003).
[CrossRef]

Nat. Photon. (1)

F. Xia, L. Sekaric, and Yu. Vlasov, "Ultracompact optical buffers on a silicon chip," Nat. Photon. 1,65-72 (2007).

Nat. Phys. (1)

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

Nature (2)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431,1081-1084 (2004).
[CrossRef]

Y.A. Vlasov, M. O’Boyle, H.F. Hamann, and S.J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438,65-69 (2005).
[CrossRef]

Opt. Express (7)

Opt. Lett. (2)

Phys. Rev. E (2)

A.E. Miroshnichenko, S.F. Mingaleev, S. Flach, and Yu.S. Kivshar, "Nonlinear Fano resonance and bistable wave transmission," Phys. Rev. E 71,036626 (2005).
[CrossRef]

S.F. Mingaleev, A.E. Miroshnichenko, Y.S. Kivshar, and K. Busch, "All-optical switching, bistability, and slowlight transmission in photonic crystal waveguide-resonator structures," Phys. Rev. E 74,046603 (2006).
[CrossRef]

Phys. Rev. Lett. (4)

S. Hughes, L. Ramunno, J.F. Young, and J.E. Sipe, "Extrinsic optical scattering loss in photonic crystal waveguides: Role of fabrication disorder and photon group velocity," Phys. Rev. Lett. 94,033903 (2005).
[CrossRef]

M. Scalora, J.P. Dowling, C.W. 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]

H. Gersen, T.J. Karle, R.J.P. Engelen, W. Bogaerts, J.P. Korterik, N.F. van Hulst, T.F. Krauss, and L. Kuipers, "Near-field characterization of low-loss photonic crystal waveguides," Phys. Rev. Lett. 94,073903 (2005).
[CrossRef]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87,253902 (2001).
[CrossRef]

Other (1)

X. Yang, C. Husko, M. Yu, D.-L. Kwong, and C.W. Wong, "Observation of femto-joule optical bistability involving Fano resonances in high-Q/Vm silicon photonic crystal nanocavities," arXiv:physics/0703132 (2007).

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