Abstract

A photonic crystal waveguide-cavity structure with a partially reflecting element is exploited to achieve optical bistability. Analysis of the theoretical model and validation of the numerical simulation indicate that this structure shows an asymmetrical lineshape and a novel switching characteristic, with the nonlinear transmission power varying sharply in a very narrow linewidth range. The characteristic power can be decreased from 6.35mWμm of the symmetrical lineshape to 0.604mWμm of the asymmetrical one. Through the study of the quality factor of the cavity, the results show that the lower switch power of an asymmetrical lineshape is essentially due to the increased Q-factor, which causes more and more energy to be stored in the cavity.

© 2009 Optical Society of America

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987).
    [CrossRef] [PubMed]
  3. J. Joannopoulos, S. Johnson, J. Winn, and R. Meade, Photonic Crystals Molding the Flow of Light, 2nd. ed. (Princeton U. Press, 2008).
  4. Z. Wang and S. Fan, “Compact all-pass filters in photonic crystals as the building block for high-capacity optical delay lines,” Phys. Rev. E 68, 066616 (2003).
    [CrossRef]
  5. S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960-963 (1998).
    [CrossRef]
  6. H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  7. M. Soljačić, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
    [CrossRef]
  8. C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322-1331 (1999).
    [CrossRef]
  9. M. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2741-2743 (2003).
    [CrossRef]
  10. S. Fan, “Sharp asymmetric lineshapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80, 908-910 (2002).
    [CrossRef]
  11. C. Chao and L. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83, 1527-1529 (2003).
    [CrossRef]
  12. S. Fan, W. Suh, and J. Joannopoulos, “Temporal coupled mode theory for Fano resonances in optical resonators,” J. Opt. Soc. Am. A 20, 569-573 (2003).
    [CrossRef]
  13. Y. Xu, Y. LI, R. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E 62, 7389-7403 (2000).
    [CrossRef]
  14. S. Johnson and J. Joannopoulos, FDTD software, http://ab-initio.mit.edu/meep.
  15. B. Maes, P. Bienstman, and R. Baets, “Symmetry breaking with coupled Fano resonances,” Opt. Express 16, 3069-3076 (2008).
    [CrossRef] [PubMed]
  16. P. Villeneuve, S. Fan, and J. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability and coupling efficiency,” Phys. Rev. B 54, 7837-7842 (1996).
    [CrossRef]
  17. A. Mekis, S. Fan, and J. Joannopoulos, “Absorbing boundary conditions for FDTD simulations of photonic crystal waveguides,” IEEE Microw. Guid. Wave Lett. 9, 502-504 (1999).
    [CrossRef]

2008 (2)

J. Joannopoulos, S. Johnson, J. Winn, and R. Meade, Photonic Crystals Molding the Flow of Light, 2nd. ed. (Princeton U. Press, 2008).

B. Maes, P. Bienstman, and R. Baets, “Symmetry breaking with coupled Fano resonances,” Opt. Express 16, 3069-3076 (2008).
[CrossRef] [PubMed]

2003 (4)

M. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2741-2743 (2003).
[CrossRef]

C. Chao and L. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83, 1527-1529 (2003).
[CrossRef]

S. Fan, W. Suh, and J. Joannopoulos, “Temporal coupled mode theory for Fano resonances in optical resonators,” J. Opt. Soc. Am. A 20, 569-573 (2003).
[CrossRef]

Z. Wang and S. Fan, “Compact all-pass filters in photonic crystals as the building block for high-capacity optical delay lines,” Phys. Rev. E 68, 066616 (2003).
[CrossRef]

2002 (2)

M. Soljačić, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

S. Fan, “Sharp asymmetric lineshapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80, 908-910 (2002).
[CrossRef]

2000 (1)

Y. Xu, Y. LI, R. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E 62, 7389-7403 (2000).
[CrossRef]

1999 (2)

A. Mekis, S. Fan, and J. Joannopoulos, “Absorbing boundary conditions for FDTD simulations of photonic crystal waveguides,” IEEE Microw. Guid. Wave Lett. 9, 502-504 (1999).
[CrossRef]

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322-1331 (1999).
[CrossRef]

1998 (1)

S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960-963 (1998).
[CrossRef]

1996 (1)

P. Villeneuve, S. Fan, and J. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability and coupling efficiency,” Phys. Rev. B 54, 7837-7842 (1996).
[CrossRef]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

1984 (1)

H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

Baets, R.

Bienstman, P.

Chao, C.

C. Chao and L. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83, 1527-1529 (2003).
[CrossRef]

Fan, S.

M. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2741-2743 (2003).
[CrossRef]

S. Fan, W. Suh, and J. Joannopoulos, “Temporal coupled mode theory for Fano resonances in optical resonators,” J. Opt. Soc. Am. A 20, 569-573 (2003).
[CrossRef]

Z. Wang and S. Fan, “Compact all-pass filters in photonic crystals as the building block for high-capacity optical delay lines,” Phys. Rev. E 68, 066616 (2003).
[CrossRef]

S. Fan, “Sharp asymmetric lineshapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80, 908-910 (2002).
[CrossRef]

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322-1331 (1999).
[CrossRef]

A. Mekis, S. Fan, and J. Joannopoulos, “Absorbing boundary conditions for FDTD simulations of photonic crystal waveguides,” IEEE Microw. Guid. Wave Lett. 9, 502-504 (1999).
[CrossRef]

S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960-963 (1998).
[CrossRef]

P. Villeneuve, S. Fan, and J. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability and coupling efficiency,” Phys. Rev. B 54, 7837-7842 (1996).
[CrossRef]

Fink, Y.

M. Soljačić, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

Guo, L.

C. Chao and L. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83, 1527-1529 (2003).
[CrossRef]

Haus, H.

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322-1331 (1999).
[CrossRef]

S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960-963 (1998).
[CrossRef]

H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

Ibanescu, M.

M. Soljačić, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

Joannopoulos, J.

J. Joannopoulos, S. Johnson, J. Winn, and R. Meade, Photonic Crystals Molding the Flow of Light, 2nd. ed. (Princeton U. Press, 2008).

S. Fan, W. Suh, and J. Joannopoulos, “Temporal coupled mode theory for Fano resonances in optical resonators,” J. Opt. Soc. Am. A 20, 569-573 (2003).
[CrossRef]

M. Soljačić, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322-1331 (1999).
[CrossRef]

A. Mekis, S. Fan, and J. Joannopoulos, “Absorbing boundary conditions for FDTD simulations of photonic crystal waveguides,” IEEE Microw. Guid. Wave Lett. 9, 502-504 (1999).
[CrossRef]

S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960-963 (1998).
[CrossRef]

P. Villeneuve, S. Fan, and J. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability and coupling efficiency,” Phys. Rev. B 54, 7837-7842 (1996).
[CrossRef]

S. Johnson and J. Joannopoulos, FDTD software, http://ab-initio.mit.edu/meep.

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Johnson, S.

J. Joannopoulos, S. Johnson, J. Winn, and R. Meade, Photonic Crystals Molding the Flow of Light, 2nd. ed. (Princeton U. Press, 2008).

M. Soljačić, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

S. Johnson and J. Joannopoulos, FDTD software, http://ab-initio.mit.edu/meep.

Khan, M.

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322-1331 (1999).
[CrossRef]

Lee, R.

Y. Xu, Y. LI, R. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E 62, 7389-7403 (2000).
[CrossRef]

LI, Y.

Y. Xu, Y. LI, R. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E 62, 7389-7403 (2000).
[CrossRef]

Maes, B.

Manolatou, C.

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322-1331 (1999).
[CrossRef]

Meade, R.

J. Joannopoulos, S. Johnson, J. Winn, and R. Meade, Photonic Crystals Molding the Flow of Light, 2nd. ed. (Princeton U. Press, 2008).

Mekis, A.

A. Mekis, S. Fan, and J. Joannopoulos, “Absorbing boundary conditions for FDTD simulations of photonic crystal waveguides,” IEEE Microw. Guid. Wave Lett. 9, 502-504 (1999).
[CrossRef]

Soljacic, M.

M. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2741-2743 (2003).
[CrossRef]

M. Soljačić, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

Suh, W.

Villeneuve, P.

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322-1331 (1999).
[CrossRef]

S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960-963 (1998).
[CrossRef]

P. Villeneuve, S. Fan, and J. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability and coupling efficiency,” Phys. Rev. B 54, 7837-7842 (1996).
[CrossRef]

Wang, Z.

Z. Wang and S. Fan, “Compact all-pass filters in photonic crystals as the building block for high-capacity optical delay lines,” Phys. Rev. E 68, 066616 (2003).
[CrossRef]

Winn, J.

J. Joannopoulos, S. Johnson, J. Winn, and R. Meade, Photonic Crystals Molding the Flow of Light, 2nd. ed. (Princeton U. Press, 2008).

Xu, Y.

Y. Xu, Y. LI, R. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E 62, 7389-7403 (2000).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Yanik, M.

M. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2741-2743 (2003).
[CrossRef]

Yariv, A.

Y. Xu, Y. LI, R. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E 62, 7389-7403 (2000).
[CrossRef]

Appl. Phys. Lett. (3)

M. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2741-2743 (2003).
[CrossRef]

S. Fan, “Sharp asymmetric lineshapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80, 908-910 (2002).
[CrossRef]

C. Chao and L. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83, 1527-1529 (2003).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322-1331 (1999).
[CrossRef]

IEEE Microw. Guid. Wave Lett. (1)

A. Mekis, S. Fan, and J. Joannopoulos, “Absorbing boundary conditions for FDTD simulations of photonic crystal waveguides,” IEEE Microw. Guid. Wave Lett. 9, 502-504 (1999).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Phys. Rev. B (1)

P. Villeneuve, S. Fan, and J. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability and coupling efficiency,” Phys. Rev. B 54, 7837-7842 (1996).
[CrossRef]

Phys. Rev. E (3)

M. Soljačić, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

Y. Xu, Y. LI, R. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E 62, 7389-7403 (2000).
[CrossRef]

Z. Wang and S. Fan, “Compact all-pass filters in photonic crystals as the building block for high-capacity optical delay lines,” Phys. Rev. E 68, 066616 (2003).
[CrossRef]

Phys. Rev. Lett. (3)

S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960-963 (1998).
[CrossRef]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Other (3)

J. Joannopoulos, S. Johnson, J. Winn, and R. Meade, Photonic Crystals Molding the Flow of Light, 2nd. ed. (Princeton U. Press, 2008).

H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

S. Johnson and J. Joannopoulos, FDTD software, http://ab-initio.mit.edu/meep.

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Figures (6)

Fig. 1
Fig. 1

Schematic of the waveguide-cavity system with two partially reflecting elements in waveguide.

Fig. 2
Fig. 2

Theoretical transmission spectra with different reflection amplitudes of the PRE for the system in Fig. 1. The spectra are calculated from linear Eq. (9) in which the phase shift 2 θ is set to ( 2 n + 1 2 ) π .

Fig. 3
Fig. 3

Input versus output power with different reflection amplitudes of the PRE and the detuning d for the optical system shown in Fig. 1. The curves are calculated using nonlinear Eq. (10), and the open circles are obtained from the numerical simulation.

Fig. 4
Fig. 4

Structure of a waveguide in a 2-D PhC composed of dielectric rods in air. Right: waveguide guide mode of TM modes of the PhC in the gap.

Fig. 5
Fig. 5

Schematic of waveguide-cavity PhC system simulated in this paper.

Fig. 6
Fig. 6

Reflection power for partially reflecting element in the waveguide with different radii of rods.

Tables (1)

Tables Icon

Table 1 Parameters of Cavity with or without Partially Reflecting Element in Waveguide

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

[ S 1 S 2 ] = [ r j t j t r ] [ S 1 + S 2 + ] ,
[ S 2 + S 2 ] = T PRE [ S 1 + S 1 ] = 1 j 1 r 2 [ r 1 1 r ] [ S 1 + S 1 ] .
d a d t = ( j ω 0 γ ) a + γ s 2 + + γ s 3 + ,
s 2 = s 3 + + γ a ,
s 3 = s 2 + + γ a ,
a = γ ( s 2 + + s 3 + ) γ j ( ω ω 0 ) .
s 3 + = j γ ( ω ω 0 ) s 2 + + [ 1 j γ ( ω ω 0 ) ] s 2 ,
s 3 = [ 1 + j γ ( ω ω 0 ) ] s 2 + + j γ ( ω ω 0 ) s 2 .
[ s 3 + s 3 ] = T cavity [ s 2 + s 2 ] = [ j γ ( ω ω 0 ) 1 j γ ( ω ω 0 ) 1 + j γ ( ω ω 0 ) j γ ( ω ω 0 ) ] [ s 2 + s 2 ] .
[ s 4 + s 4 ] = T all [ s 1 + s 1 ] ,
T 0 = [ 0 e j θ e j θ 0 ] ,
t s = ( r 2 1 ) e i 2 θ ( ω ω 0 ) e i 4 θ r 2 ( ω ω 0 i γ ) 2 e i 2 θ ( i γ ) r + ω ω 0 + i γ .
T = t s 2 = ( r 2 1 ) 2 ( ω ω 0 ) 2 ( r 2 + 1 2 r cos 2 θ ) [ ( r 2 + 1 + 2 r cos 2 θ ) ( ω ω 0 ) 2 + 4 γ r ( ω ω 0 ) sin 2 θ + γ 2 ( r 2 + 1 2 r cos 2 θ ) ] .
P out P 0 P in P 0 = ( r 2 1 ) 2 ( P ref P 0 δ ) 2 ( r 2 + 1 2 r cos 2 θ ) [ ( r 2 + 1 + 2 r cos 2 θ ) ( P ref P 0 δ ) 2 + 4 r ( P ref P 0 δ ) sin 2 θ + ( r 2 + 1 2 r cos 2 θ ) ] .

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