Abstract

We consider a microcavity with degenerate dipole or hexapole eigenmodes. If the cavity is positioned between waveguides, degeneracy is lifted. However, we show that in a nonlinear microcavity the degeneracy is recovered at certain injected power. In application we consider a two-dimensional photonic crystal of GaAs rods holding two parallel waveguides and one defect made of Kerr media. We show that 100% efficiency channel dropping can be attained without a necessity to tune the resonant frequencies of the microcavity.

© 2013 Optical Society of America

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  1. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3, 4–11 (1998).
    [CrossRef]
  2. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999).
    [CrossRef]
  3. C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
    [CrossRef]
  4. M. Qiu and B. Jaskorzynska, “Design of a channel drop filter in a two-dimensional triangular photonic crystal,” Appl. Phys. Lett. 83, 1074–1076 (2003).
    [CrossRef]
  5. B. K. Min, J. E. Kim, and H. Y. Park, “Channel drop filters using resonant tunneling processes in two-dimensional triangular lattice photonic crystal slabs,” Opt. Commun. 237, 59–63 (2004).
    [CrossRef]
  6. Z. Zhang and M. Qiu, “Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs,” Opt. Express 12, 3988–3995 (2004).
    [CrossRef]
  7. Y. Akahane, T. Asano, H. Takano, B.-S. Song, Y. Takana, and S. Noda, “Two-dimensional photonic-crystal-slab channel-drop filter with flat-top response,” Opt. Express 13, 2512–2530 (2005).
    [CrossRef]
  8. K. H. Hwang and G. H. Song, “Design of a high-Q channel add-drop multiplexer based on the two-dimensional photonic-crystal membrane structure,” Opt. Express 13, 1948–1957 (2005).
    [CrossRef]
  9. A. Shinya, S. Mitsugi, E. Kuramochi, and M. Notomi, “Ultrasmall multi-channel resonant-tunneling filter using mode gap of width-tuned photonic-crystal waveguide,” Opt. Express 13, 4202–4209 (2005).
    [CrossRef]
  10. M. Djavid, A. Ghaffari, F. Monifi, and M. S. Abrishamian, “Heterostructure photonic crystal channel drop filters using mirror cavities,” J. Opt. A 10, 055203 (2008).
    [CrossRef]
  11. K. Fasihi and S. Mohammadnejad, “Highly efficient channel-drop filter with a coupled cavity-based wavelength-selective reflection feedback,” Opt. Express 17, 8983–8997 (2009).
    [CrossRef]
  12. J.-X. Fu, J. Lian, R.-J. Liu, L. Gan, and Z.-Y. Li, “Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides,” Appl. Phys. Lett. 98, 211104 (2011).
    [CrossRef]
  13. J. Romero-Vivas, D. N. Chigrin, A. V. Lavrinenko, and C. M. S. Torres, “Resonant add-drop filter based on a photonic quasicrystal,” Opt. Express 13, 826–835 (2005).
    [CrossRef]
  14. Z. Zhang and M. Qiu, “Compact in-plane channel drop filter design using a single cavity with two degenerate modes in 2D photonic crystal slabs,” Opt. Express 13, 2596–2604 (2005).
    [CrossRef]
  15. A. D’Orazio, M. De Sario, V. Marrocco, V. Petruzzelli, and F. Prudenzano, “Photonic crystal drop filter exploiting resonant cavity configuration,” IEEE Trans. Nanotechnol. 7, 10–13 (2008).
    [CrossRef]
  16. L. Shang, A. Wen, B. Li, and T. Wang, “Coupled spiral-shaped microring resonator-based unidirectional add–drop filters with gapless coupling,” J. Opt. 13, 015503 (2011).
    [CrossRef]
  17. Y.-N. Zhao, K.-Z. Li, X.-H. Wang, and C.-J. Jin, “A compact in-plane photonic crystal channel drop filter,” Chin. Phys. B 20, 047210 (2011).
    [CrossRef]
  18. H. Takano, B.-S. Song, T. Aasano, and S. Noda, “Highly effective in-plane channel-drop filters in two-dimensional heterostructure photonic-crystal slab,” Jpn. J. Appl. Phys. 45, 6078–6086 (2006).
    [CrossRef]
  19. J. Joannopoulos, R. D. Meade, and J. Winn, Photonic Crystals (Princeton University, 1995).
  20. M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002).
    [CrossRef]
  21. W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40, 1511–1518 (2004).
    [CrossRef]
  22. E. N. Bulgakov and A. F. Sadreev, “Symmetry breaking in photonic crystal waveguide coupled with the dipole modes of a nonlinear optical cavity,” J. Opt. Soc. Am. B 29, 2924–2928 (2012).
    [CrossRef]
  23. M. F. Yanik, S. Fan, and M. Soljačić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
    [CrossRef]
  24. E. N. Bulgakov and A. F. Sadreev, “All-optical manipulation of light in X- and T-shaped photonic crystal waveguides with a nonlinear dipole defect,” Phys. Rev. B 86, 075125 (2012).
    [CrossRef]

2012 (2)

E. N. Bulgakov and A. F. Sadreev, “Symmetry breaking in photonic crystal waveguide coupled with the dipole modes of a nonlinear optical cavity,” J. Opt. Soc. Am. B 29, 2924–2928 (2012).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, “All-optical manipulation of light in X- and T-shaped photonic crystal waveguides with a nonlinear dipole defect,” Phys. Rev. B 86, 075125 (2012).
[CrossRef]

2011 (3)

J.-X. Fu, J. Lian, R.-J. Liu, L. Gan, and Z.-Y. Li, “Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides,” Appl. Phys. Lett. 98, 211104 (2011).
[CrossRef]

L. Shang, A. Wen, B. Li, and T. Wang, “Coupled spiral-shaped microring resonator-based unidirectional add–drop filters with gapless coupling,” J. Opt. 13, 015503 (2011).
[CrossRef]

Y.-N. Zhao, K.-Z. Li, X.-H. Wang, and C.-J. Jin, “A compact in-plane photonic crystal channel drop filter,” Chin. Phys. B 20, 047210 (2011).
[CrossRef]

2009 (1)

2008 (2)

M. Djavid, A. Ghaffari, F. Monifi, and M. S. Abrishamian, “Heterostructure photonic crystal channel drop filters using mirror cavities,” J. Opt. A 10, 055203 (2008).
[CrossRef]

A. D’Orazio, M. De Sario, V. Marrocco, V. Petruzzelli, and F. Prudenzano, “Photonic crystal drop filter exploiting resonant cavity configuration,” IEEE Trans. Nanotechnol. 7, 10–13 (2008).
[CrossRef]

2006 (1)

H. Takano, B.-S. Song, T. Aasano, and S. Noda, “Highly effective in-plane channel-drop filters in two-dimensional heterostructure photonic-crystal slab,” Jpn. J. Appl. Phys. 45, 6078–6086 (2006).
[CrossRef]

2005 (5)

2004 (3)

B. K. Min, J. E. Kim, and H. Y. Park, “Channel drop filters using resonant tunneling processes in two-dimensional triangular lattice photonic crystal slabs,” Opt. Commun. 237, 59–63 (2004).
[CrossRef]

Z. Zhang and M. Qiu, “Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs,” Opt. Express 12, 3988–3995 (2004).
[CrossRef]

W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40, 1511–1518 (2004).
[CrossRef]

2003 (2)

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

M. Qiu and B. Jaskorzynska, “Design of a channel drop filter in a two-dimensional triangular photonic crystal,” Appl. Phys. Lett. 83, 1074–1076 (2003).
[CrossRef]

2002 (1)

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

1999 (2)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999).
[CrossRef]

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

1998 (1)

Aasano, T.

H. Takano, B.-S. Song, T. Aasano, and S. Noda, “Highly effective in-plane channel-drop filters in two-dimensional heterostructure photonic-crystal slab,” Jpn. J. Appl. Phys. 45, 6078–6086 (2006).
[CrossRef]

Abrishamian, M. S.

M. Djavid, A. Ghaffari, F. Monifi, and M. S. Abrishamian, “Heterostructure photonic crystal channel drop filters using mirror cavities,” J. Opt. A 10, 055203 (2008).
[CrossRef]

Akahane, Y.

Asano, T.

Bulgakov, E. N.

E. N. Bulgakov and A. F. Sadreev, “Symmetry breaking in photonic crystal waveguide coupled with the dipole modes of a nonlinear optical cavity,” J. Opt. Soc. Am. B 29, 2924–2928 (2012).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, “All-optical manipulation of light in X- and T-shaped photonic crystal waveguides with a nonlinear dipole defect,” Phys. Rev. B 86, 075125 (2012).
[CrossRef]

Chigrin, D. N.

D’Orazio, A.

A. D’Orazio, M. De Sario, V. Marrocco, V. Petruzzelli, and F. Prudenzano, “Photonic crystal drop filter exploiting resonant cavity configuration,” IEEE Trans. Nanotechnol. 7, 10–13 (2008).
[CrossRef]

De Sario, M.

A. D’Orazio, M. De Sario, V. Marrocco, V. Petruzzelli, and F. Prudenzano, “Photonic crystal drop filter exploiting resonant cavity configuration,” IEEE Trans. Nanotechnol. 7, 10–13 (2008).
[CrossRef]

Djavid, M.

M. Djavid, A. Ghaffari, F. Monifi, and M. S. Abrishamian, “Heterostructure photonic crystal channel drop filters using mirror cavities,” J. Opt. A 10, 055203 (2008).
[CrossRef]

Fan, S.

W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40, 1511–1518 (2004).
[CrossRef]

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

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999).
[CrossRef]

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

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3, 4–11 (1998).
[CrossRef]

Fasihi, K.

Fink, Y.

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

Fu, J.-X.

J.-X. Fu, J. Lian, R.-J. Liu, L. Gan, and Z.-Y. Li, “Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides,” Appl. Phys. Lett. 98, 211104 (2011).
[CrossRef]

Gan, L.

J.-X. Fu, J. Lian, R.-J. Liu, L. Gan, and Z.-Y. Li, “Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides,” Appl. Phys. Lett. 98, 211104 (2011).
[CrossRef]

Ghaffari, A.

M. Djavid, A. Ghaffari, F. Monifi, and M. S. Abrishamian, “Heterostructure photonic crystal channel drop filters using mirror cavities,” J. Opt. A 10, 055203 (2008).
[CrossRef]

Haus, H. A.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999).
[CrossRef]

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

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3, 4–11 (1998).
[CrossRef]

Hwang, K. H.

Ibanescu, M.

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

Jaskorzynska, B.

M. Qiu and B. Jaskorzynska, “Design of a channel drop filter in a two-dimensional triangular photonic crystal,” Appl. Phys. Lett. 83, 1074–1076 (2003).
[CrossRef]

Jin, C.-J.

Y.-N. Zhao, K.-Z. Li, X.-H. Wang, and C.-J. Jin, “A compact in-plane photonic crystal channel drop filter,” Chin. Phys. B 20, 047210 (2011).
[CrossRef]

Joannopoulos, J.

J. Joannopoulos, R. D. Meade, and J. Winn, Photonic Crystals (Princeton University, 1995).

Joannopoulos, J. D.

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

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

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3, 4–11 (1998).
[CrossRef]

Johnson, S. G.

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

Khan, M. J.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999).
[CrossRef]

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

Kim, J. E.

B. K. Min, J. E. Kim, and H. Y. Park, “Channel drop filters using resonant tunneling processes in two-dimensional triangular lattice photonic crystal slabs,” Opt. Commun. 237, 59–63 (2004).
[CrossRef]

Kuramochi, E.

Lavrinenko, A. V.

Li, B.

L. Shang, A. Wen, B. Li, and T. Wang, “Coupled spiral-shaped microring resonator-based unidirectional add–drop filters with gapless coupling,” J. Opt. 13, 015503 (2011).
[CrossRef]

Li, K.-Z.

Y.-N. Zhao, K.-Z. Li, X.-H. Wang, and C.-J. Jin, “A compact in-plane photonic crystal channel drop filter,” Chin. Phys. B 20, 047210 (2011).
[CrossRef]

Li, Z.-Y.

J.-X. Fu, J. Lian, R.-J. Liu, L. Gan, and Z.-Y. Li, “Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides,” Appl. Phys. Lett. 98, 211104 (2011).
[CrossRef]

Lian, J.

J.-X. Fu, J. Lian, R.-J. Liu, L. Gan, and Z.-Y. Li, “Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides,” Appl. Phys. Lett. 98, 211104 (2011).
[CrossRef]

Liu, R.-J.

J.-X. Fu, J. Lian, R.-J. Liu, L. Gan, and Z.-Y. Li, “Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides,” Appl. Phys. Lett. 98, 211104 (2011).
[CrossRef]

Manolatou, C.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999).
[CrossRef]

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

Marrocco, V.

A. D’Orazio, M. De Sario, V. Marrocco, V. Petruzzelli, and F. Prudenzano, “Photonic crystal drop filter exploiting resonant cavity configuration,” IEEE Trans. Nanotechnol. 7, 10–13 (2008).
[CrossRef]

Meade, R. D.

J. Joannopoulos, R. D. Meade, and J. Winn, Photonic Crystals (Princeton University, 1995).

Min, B. K.

B. K. Min, J. E. Kim, and H. Y. Park, “Channel drop filters using resonant tunneling processes in two-dimensional triangular lattice photonic crystal slabs,” Opt. Commun. 237, 59–63 (2004).
[CrossRef]

Mitsugi, S.

Mohammadnejad, S.

Monifi, F.

M. Djavid, A. Ghaffari, F. Monifi, and M. S. Abrishamian, “Heterostructure photonic crystal channel drop filters using mirror cavities,” J. Opt. A 10, 055203 (2008).
[CrossRef]

Noda, S.

H. Takano, B.-S. Song, T. Aasano, and S. Noda, “Highly effective in-plane channel-drop filters in two-dimensional heterostructure photonic-crystal slab,” Jpn. J. Appl. Phys. 45, 6078–6086 (2006).
[CrossRef]

Y. Akahane, T. Asano, H. Takano, B.-S. Song, Y. Takana, and S. Noda, “Two-dimensional photonic-crystal-slab channel-drop filter with flat-top response,” Opt. Express 13, 2512–2530 (2005).
[CrossRef]

Notomi, M.

Park, H. Y.

B. K. Min, J. E. Kim, and H. Y. Park, “Channel drop filters using resonant tunneling processes in two-dimensional triangular lattice photonic crystal slabs,” Opt. Commun. 237, 59–63 (2004).
[CrossRef]

Petruzzelli, V.

A. D’Orazio, M. De Sario, V. Marrocco, V. Petruzzelli, and F. Prudenzano, “Photonic crystal drop filter exploiting resonant cavity configuration,” IEEE Trans. Nanotechnol. 7, 10–13 (2008).
[CrossRef]

Prudenzano, F.

A. D’Orazio, M. De Sario, V. Marrocco, V. Petruzzelli, and F. Prudenzano, “Photonic crystal drop filter exploiting resonant cavity configuration,” IEEE Trans. Nanotechnol. 7, 10–13 (2008).
[CrossRef]

Qiu, M.

Romero-Vivas, J.

Sadreev, A. F.

E. N. Bulgakov and A. F. Sadreev, “Symmetry breaking in photonic crystal waveguide coupled with the dipole modes of a nonlinear optical cavity,” J. Opt. Soc. Am. B 29, 2924–2928 (2012).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, “All-optical manipulation of light in X- and T-shaped photonic crystal waveguides with a nonlinear dipole defect,” Phys. Rev. B 86, 075125 (2012).
[CrossRef]

Shang, L.

L. Shang, A. Wen, B. Li, and T. Wang, “Coupled spiral-shaped microring resonator-based unidirectional add–drop filters with gapless coupling,” J. Opt. 13, 015503 (2011).
[CrossRef]

Shinya, A.

Soljacic, M.

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

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

Song, B.-S.

H. Takano, B.-S. Song, T. Aasano, and S. Noda, “Highly effective in-plane channel-drop filters in two-dimensional heterostructure photonic-crystal slab,” Jpn. J. Appl. Phys. 45, 6078–6086 (2006).
[CrossRef]

Y. Akahane, T. Asano, H. Takano, B.-S. Song, Y. Takana, and S. Noda, “Two-dimensional photonic-crystal-slab channel-drop filter with flat-top response,” Opt. Express 13, 2512–2530 (2005).
[CrossRef]

Song, G. H.

Suh, W.

W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40, 1511–1518 (2004).
[CrossRef]

Takana, Y.

Takano, H.

H. Takano, B.-S. Song, T. Aasano, and S. Noda, “Highly effective in-plane channel-drop filters in two-dimensional heterostructure photonic-crystal slab,” Jpn. J. Appl. Phys. 45, 6078–6086 (2006).
[CrossRef]

Y. Akahane, T. Asano, H. Takano, B.-S. Song, Y. Takana, and S. Noda, “Two-dimensional photonic-crystal-slab channel-drop filter with flat-top response,” Opt. Express 13, 2512–2530 (2005).
[CrossRef]

Torres, C. M. S.

Villeneuve, P. R.

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

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3, 4–11 (1998).
[CrossRef]

Wang, T.

L. Shang, A. Wen, B. Li, and T. Wang, “Coupled spiral-shaped microring resonator-based unidirectional add–drop filters with gapless coupling,” J. Opt. 13, 015503 (2011).
[CrossRef]

Wang, X.-H.

Y.-N. Zhao, K.-Z. Li, X.-H. Wang, and C.-J. Jin, “A compact in-plane photonic crystal channel drop filter,” Chin. Phys. B 20, 047210 (2011).
[CrossRef]

Wang, Z.

W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40, 1511–1518 (2004).
[CrossRef]

Wen, A.

L. Shang, A. Wen, B. Li, and T. Wang, “Coupled spiral-shaped microring resonator-based unidirectional add–drop filters with gapless coupling,” J. Opt. 13, 015503 (2011).
[CrossRef]

Winn, J.

J. Joannopoulos, R. D. Meade, and J. Winn, Photonic Crystals (Princeton University, 1995).

Yanik, M. F.

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

Zhang, Z.

Zhao, Y.-N.

Y.-N. Zhao, K.-Z. Li, X.-H. Wang, and C.-J. Jin, “A compact in-plane photonic crystal channel drop filter,” Chin. Phys. B 20, 047210 (2011).
[CrossRef]

Appl. Phys. Lett. (3)

M. Qiu and B. Jaskorzynska, “Design of a channel drop filter in a two-dimensional triangular photonic crystal,” Appl. Phys. Lett. 83, 1074–1076 (2003).
[CrossRef]

J.-X. Fu, J. Lian, R.-J. Liu, L. Gan, and Z.-Y. Li, “Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides,” Appl. Phys. Lett. 98, 211104 (2011).
[CrossRef]

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

Chin. Phys. B (1)

Y.-N. Zhao, K.-Z. Li, X.-H. Wang, and C.-J. Jin, “A compact in-plane photonic crystal channel drop filter,” Chin. Phys. B 20, 047210 (2011).
[CrossRef]

IEEE J. Quantum Electron. (2)

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

W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40, 1511–1518 (2004).
[CrossRef]

IEEE Trans. Nanotechnol. (1)

A. D’Orazio, M. De Sario, V. Marrocco, V. Petruzzelli, and F. Prudenzano, “Photonic crystal drop filter exploiting resonant cavity configuration,” IEEE Trans. Nanotechnol. 7, 10–13 (2008).
[CrossRef]

J. Opt. (1)

L. Shang, A. Wen, B. Li, and T. Wang, “Coupled spiral-shaped microring resonator-based unidirectional add–drop filters with gapless coupling,” J. Opt. 13, 015503 (2011).
[CrossRef]

J. Opt. A (1)

M. Djavid, A. Ghaffari, F. Monifi, and M. S. Abrishamian, “Heterostructure photonic crystal channel drop filters using mirror cavities,” J. Opt. A 10, 055203 (2008).
[CrossRef]

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

Jpn. J. Appl. Phys. (1)

H. Takano, B.-S. Song, T. Aasano, and S. Noda, “Highly effective in-plane channel-drop filters in two-dimensional heterostructure photonic-crystal slab,” Jpn. J. Appl. Phys. 45, 6078–6086 (2006).
[CrossRef]

Opt. Commun. (1)

B. K. Min, J. E. Kim, and H. Y. Park, “Channel drop filters using resonant tunneling processes in two-dimensional triangular lattice photonic crystal slabs,” Opt. Commun. 237, 59–63 (2004).
[CrossRef]

Opt. Express (8)

Phys. Rev. B (2)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, “All-optical manipulation of light in X- and T-shaped photonic crystal waveguides with a nonlinear dipole defect,” Phys. Rev. B 86, 075125 (2012).
[CrossRef]

Phys. Rev. E (1)

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

Other (1)

J. Joannopoulos, R. D. Meade, and J. Winn, Photonic Crystals (Princeton University, 1995).

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Figures (6)

Fig. 1.
Fig. 1.

Microcavity eigenmodes (space profiles of the electric field directed parallel to the rods) in the two-dimensional square lattice PhC consisting of GaAs dielectric rods with radius 0.18a and dielectric constant ϵ=11.56, where a=0.5μm is the lattice unit [20]. The rods are shown as open gray circles. The defect, shown as the open white circle, has (a), (b) ϵd=6.5 and the radius rd=0.4a in the case of dipole modes with eigenfrequency 0.368 and (c), (d) ϵd=11.9 and rd=0.6a in the case of hexapole modes with eigenfrequency 0.384. Two rows of rods, shown as dashed open circles, are assumed to be removed to fabricate two parallel waveguides.

Fig. 2.
Fig. 2.

Four-port system with a nonlinear cavity between two waveguides. γ11/2 and γ21/2 are the coupling constants between waveguides and eigenmodes.

Fig. 3.
Fig. 3.

Transmission spectrum via the dipole modes of a linear microcavity. The defect rod with dielectric constant ϵd=6.5 has a circular cross section with radius 0.4a.

Fig. 4.
Fig. 4.

Transmission spectra into ports 3 and 4 via the dipole modes of the defect cavity. The defect rod with dielectric constant ϵd=6.5 has an elliptic cross section with major and minor semiaxes 0.43a and 0.4a. (a) Linear defect; (b), (c) nonlinear defect with n2=2×1013cm2/W for P0=0.35W/a. (d) The transmission from port 1 into port 3 versus the intensity of injected light for ω=ωc=0.3621. Open circles mark the stable solution, and asterisks mark the unstable solution of Eqs. (6). The dashed curves show the solution of the nonlinear Maxwell equations.

Fig. 5.
Fig. 5.

Real part of the scattering wave function (electric field) in the PhC, which holds two parallel waveguides and one nonlinear cavity with two (a) dipole and (b) hexapole eigenmodes. Injected power and frequency obey the conditions for 100% channel dropping. Pink curves are optical streamlines.

Fig. 6.
Fig. 6.

Transmission spectra via two hexapole modes of a defect cavity. The defect rod with dielectric constant ϵd=11.9 has a circular cross section with radius 0.6a but is shifted by ±0.03a. (a) Linear defect. (b) Nonlinear defect with n2=2×1013cm2/W modes for P0=0.4W/a. Dashed curves show the solution of the nonlinear Maxwell equations, and open circles mark the stable solution, while asterisks mark the unstable solution of the CMT equation [Eq. (6)].

Equations (12)

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iω|A=(iΩ^+Γ^)|AK^T|S+,
|S=C^|S++K^|A,
K^+K^=2Γ^,C^K^*=K^.
C^=(0100100000010010),Γ^=(2γ1002γ2).
K^=(iγ1γ2iγ1γ2iγ1γ2iγ1γ2).
[ωω1+λ11|A1|2+λ12|A2|2+2iγ1]A1+2λ12Re(A1*A2)A2=γ1S1+,2λ12Re(A1*A2)A1+[ωω2+λ22|A2|2+λ12|A1|2+2iγ2]A2=iγ2S1+,
λmn=c2n22a2Em2(x,y)En2(x,y)dxdy,
cn2a2εPhCEm(x,y)En(x,y)dxdy=δmn,
S1=iγ1A1γ2A2,S2=S1++iγ1A1+γ2A2,σ1=iγ1A1γ2A2,σ2=iγ1A1+γ2A2.
iγ1A1=γ2A2=12S1+;
|S1+|2=4γ1γ2(ω2ω1)(λ11λ12)(γ1γ2)
ω=ω1(ω2ω1)(λ11γ2+λ12γ1)(λ11λ12)(γ1γ2),

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