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] [PubMed]
  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] [PubMed]
  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).
  9. F. Xia, L. Sekaric, and Yu. Vlasov, "Ultracompact optical buffers on a silicon chip," Nat. Photon. 1,65-72 (2007).
    [CrossRef]
  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] [PubMed]
  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] [PubMed]
  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] [PubMed]
  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] [PubMed]
  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] [PubMed]
  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] [PubMed]
  16. 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]
  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] [PubMed]
  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] [PubMed]
  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] [PubMed]
  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] [PubMed]
  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] [PubMed]
  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] [PubMed]
  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).
  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).
    [CrossRef] [PubMed]
  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).
  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).
[CrossRef]

2006 (6)

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

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] [PubMed]

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]

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] [PubMed]

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).

2005 (10)

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] [PubMed]

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] [PubMed]

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] [PubMed]

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]

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] [PubMed]

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).

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] [PubMed]

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] [PubMed]

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] [PubMed]

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).

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] [PubMed]

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

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)

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] [PubMed]

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).
[CrossRef] [PubMed]

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)

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] [PubMed]

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]

Appl. Phys. Lett. (5)

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]

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

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] [PubMed]

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] [PubMed]

Opt. Express (7)

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] [PubMed]

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] [PubMed]

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] [PubMed]

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

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).
[CrossRef] [PubMed]

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] [PubMed]

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] [PubMed]

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).

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).

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] [PubMed]

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] [PubMed]

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] [PubMed]

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] [PubMed]

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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Figures (4)

Fig. 1.
Fig. 1.

Frequencies of localized cavity modes created by changing the radius r def of (a) single defect rod and (b) two neighboring defect rods in the photonic crystal created by a triangular lattice of rods with ε=12 and radius r=0.25a in air, a is the lattice spacing. (c) Dispersion of the W1 photonic-crystal waveguide created by removing a row of rods in the same photonic crystal. Results are calculated using 11 maximally localized Wannier functions [27] (blue lines) and the supercell plane-waves method [28] (red circles).

Fig. 2.
Fig. 2.

Single-defect waveguide-cavity structure with the radius of the defect rod r def: (a) Electric field at the resonance reflection for r def=0.102a; (b) Transmission spectra for different values of r def: 0.1a (black), 0.101a (blue), 0.102a (red), 0.1025a (green). For convenience, in addition to the light frequency on the bottom axis, we indicate on the top axis the complementary group velocity, vg (ω), of the waveguide’s guided mode.

Fig. 3.
Fig. 3.

Double-defect waveguide-cavity structure with the cavity created by two defect rods with the radius r def: (a) Electric field at the resonance reflection for r def=0.121a; (b) Transmission spectra for different values of r def: 0.119a (black), 0.120a (blue), 0.121a (red), 0.1213a (green).

Fig. 4.
Fig. 4.

(a) Quality factor Q vs. group velocity vg at resonance for the structure shown in Fig. 3; (b) Nonlinear bistable transmission in the same structure at the frequencies with 80% of linear light transmission vs. the incoming light power for different values of r def: 0.119a (black), 0.120a (blue), 0.121a (red), 0.1214a (green); (c) Switch-off bistability threshold Pth vs. the group velocity vg at resonance for the same structure.

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