Abstract

We study the resonant transmission of light in a coupled-resonator optical waveguide interacting with two nearly identical side cavities. We reveal and describe a novel effect of the coupled-resonator-induced reflection (CRIR) characterized by a very high and easily tunable quality factor of the reflection line, for the case of the inter-site coupling between the cavities and the waveguide. This effect differs sharply from the coupled-resonator-induced transparency (CRIT) – an all-optical analogue of the electromagnetically-induced transparency – which has recently been studied theoretically and experimentally for the structures based on micro-ring resonators and photonic crystal cavities. Both CRIR and CRIT effects have the same physical origin which can be attributed to the Fano-Feshbach resonances in the systems exhibiting more than one resonance. We discuss the applicability of the novel CRIR effect to the control of the slow-light propagation and low-threshold all-optical switching.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
    [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. Y. Xu, Y. Li, R. K. Lee, and A. Yariv, "Scattering-theory analysis of waveguide-resonator coupling," Phys. Rev. E 62,7389-7404 (2000).
    [CrossRef]
  4. D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69,063804 (2004).
    [CrossRef]
  5. D. D. Smith and H. Chang, "Coherence phenomena in coupled optical resonators," J. Mod. Opt. 51,2503-2513 (2004).
  6. L. Maleki, A. B. Matsko, A. A. Savchenkov, and V.S. Ilchenko, "Tunable delay line with interacting whisperinggallery- mode resonators," Opt. Lett. 29,626-628 (2004).
    [CrossRef] [PubMed]
  7. A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko and L. Maleki, "Interference effects in lossy resonator chains," J. Mod. Opt. 51,2515-2522 (2004).
    [CrossRef]
  8. 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]
  9. T. Opatrny and D. G. Welsch, "Coupled cavities for enhancing the cross-phase-modulation in electromagnetically induced transparency," Phys. Rev. A 64,23805 (2001).
    [CrossRef]
  10. A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, "Induced transparency and absorption in coupled whispering-gallery microresonators," Phys. Rev. A 71,043804 (2005).
    [CrossRef]
  11. Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency," Phys. Rev. Lett. 96,123901 (2006).
    [CrossRef] [PubMed]
  12. Q. Xu, J. Shakya, and M. Lipson, "Direct measurement of tunable optical delays on chip analogue to electromagnetically induced transparency," Opt. Express 14,6463-6468 (2006).
    [CrossRef] [PubMed]
  13. J. Pan, S. Sandhu, Y. Huo, M. L. Povinelli, M. M. Fejer, S. Fan, and J. S. Harris, "Optical Analogue to Electromagnetically Induced Transparency in Photonic Crystals, Simulation and Experiments," in Slow and Fast Light, OSA Technical Digest (CD) (Optical Society of America, 2007), paper SWB2. http://www.opticsinfobase.org/abstract.cfm?URI=SL-2007-SWB2
  14. R. W. Boyd and D. J. Gauthier, "Transparency on an optical chip," Nature 441,701-702 (2006).
    [CrossRef] [PubMed]
  15. B. Maes, P. Bienstman, and R. Baets, "Switching in coupled nonlinear photonic-crystal resonators," J. Opt. Soc. Am. B 22,1778-1784 (2005).
    [CrossRef]
  16. 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]
  17. S. F. Mingaleev, A. E. Miroshnichenko, and Y. S. Kivshar, "Low-threshold bistability of slow light in photoniccrystal waveguides," Opt. Express 15,12380-12385 (2007).
    [CrossRef] [PubMed]
  18. S. Fan, "Manipulating light with photonic crystals," Physica B 394,221-228 (2007).
    [CrossRef]
  19. S. Fan, "Sharp asymmetric line shapes in side-coupled waveguide-cavity systems," Appl. Phys. Lett. 80,908-910 (2002).
    [CrossRef]
  20. A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Y. S. Kivshar, "Nonlinear Fano resonance and bistable wave transmission," Phys. Rev. E 71,036626 (2005).
    [CrossRef]
  21. M. F. Yanik and S. Fan, "Stopping light all optically", Phys. Rev. Lett. 92,083901 (2004).
    [CrossRef] [PubMed]
  22. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis", Opt. Lett. 24,711 (1999).
    [CrossRef]
  23. 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]
  24. 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]
  25. Q1. H. Feshbach, "Unified theory of nuclear reactions, I," Ann. Phys. (N.Y.) 5, 357 (1958); "A unified theory of nuclear reactions, II," Ann. Phys. (N.Y.) 19,287 (1962).
    [CrossRef]
  26. F. H. Mies, "Configuration interaction theory: effects of overlapping resonances," Phys. Rev. 175, 164-175 (1968);F. H. Mies, "Resonant scattering theory of association reactions and unimolecular decomposition: I. A united theory of radiative and collisional recombination," J. Chem. Phys. 51,787-797 (1969).
    [CrossRef]
  27. A. I. Magunov, I. Rotter, and S. I. Strakhova, "Fano resonances in the overlapping regime," Phys. Rev. B 68,245305 (2003).
    [CrossRef]
  28. M. Raoult and F. H. Mies, "Feshbach resonance in atomic binary collisions in the wigner threshold law regime," Phys. Rev. A 70,012710 (2004).
    [CrossRef]
  29. L. Y. Mario, S. Darmawan, and M. K. Chin, "Asymmetric Fano resonance and bistability for high extinction ratio, large modulation depth, and low power switching," Opt. Express 14,12770-12781 (2006).
    [CrossRef] [PubMed]
  30. 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]
  31. H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides," Phys. Rev. Lett. 94,123901 (2005).
    [CrossRef] [PubMed]
  32. 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]
  33. R. Jacobsen, A. Lavrinenko, L. Frandsen, C. Peucheret, B. Zsigri, G. Moulin, J. Fage-Pedersen, and P. Borel, "Direct experimental and numerical determination of extremely high group indices in photonic crystal waveguides," Opt. Express 13,7861-7871 (2005).
    [CrossRef] [PubMed]
  34. 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]
  35. 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]

2007 (2)

2006 (7)

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency," Phys. Rev. Lett. 96,123901 (2006).
[CrossRef] [PubMed]

Q. Xu, J. Shakya, and M. Lipson, "Direct measurement of tunable optical delays on chip analogue to electromagnetically induced transparency," Opt. Express 14,6463-6468 (2006).
[CrossRef] [PubMed]

R. W. Boyd and D. J. Gauthier, "Transparency on an optical chip," Nature 441,701-702 (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).
[CrossRef]

L. Y. Mario, S. Darmawan, and M. K. Chin, "Asymmetric Fano resonance and bistability for high extinction ratio, large modulation depth, and low power switching," Opt. Express 14,12770-12781 (2006).
[CrossRef] [PubMed]

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]

2005 (6)

R. Jacobsen, A. Lavrinenko, L. Frandsen, C. Peucheret, B. Zsigri, G. Moulin, J. Fage-Pedersen, and P. 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, "Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides," Phys. Rev. Lett. 94,123901 (2005).
[CrossRef] [PubMed]

B. Maes, P. Bienstman, and R. Baets, "Switching in coupled nonlinear photonic-crystal resonators," J. Opt. Soc. Am. B 22,1778-1784 (2005).
[CrossRef]

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

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, "Induced transparency and absorption in coupled whispering-gallery microresonators," Phys. Rev. A 71,043804 (2005).
[CrossRef]

2004 (7)

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69,063804 (2004).
[CrossRef]

D. D. Smith and H. Chang, "Coherence phenomena in coupled optical resonators," J. Mod. Opt. 51,2503-2513 (2004).

L. Maleki, A. B. Matsko, A. A. Savchenkov, and V.S. Ilchenko, "Tunable delay line with interacting whisperinggallery- mode resonators," Opt. Lett. 29,626-628 (2004).
[CrossRef] [PubMed]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko and L. Maleki, "Interference effects in lossy resonator chains," J. Mod. Opt. 51,2515-2522 (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]

M. F. Yanik and S. Fan, "Stopping light all optically", Phys. Rev. Lett. 92,083901 (2004).
[CrossRef] [PubMed]

M. Raoult and F. H. Mies, "Feshbach resonance in atomic binary collisions in the wigner threshold law regime," Phys. Rev. A 70,012710 (2004).
[CrossRef]

2003 (2)

A. I. Magunov, I. Rotter, and S. I. Strakhova, "Fano resonances in the overlapping regime," Phys. Rev. B 68,245305 (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 (1)

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

2001 (3)

T. Opatrny and D. G. Welsch, "Coupled cavities for enhancing the cross-phase-modulation in electromagnetically induced transparency," Phys. Rev. A 64,23805 (2001).
[CrossRef]

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]

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]

2000 (1)

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, "Scattering-theory analysis of waveguide-resonator coupling," Phys. Rev. E 62,7389-7404 (2000).
[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]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis", Opt. Lett. 24,711 (1999).
[CrossRef]

1997 (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

1968 (1)

F. H. Mies, "Configuration interaction theory: effects of overlapping resonances," Phys. Rev. 175, 164-175 (1968);F. H. Mies, "Resonant scattering theory of association reactions and unimolecular decomposition: I. A united theory of radiative and collisional recombination," J. Chem. Phys. 51,787-797 (1969).
[CrossRef]

F. H. Mies, "Configuration interaction theory: effects of overlapping resonances," Phys. Rev. 175, 164-175 (1968);F. H. Mies, "Resonant scattering theory of association reactions and unimolecular decomposition: I. A united theory of radiative and collisional recombination," J. Chem. Phys. 51,787-797 (1969).
[CrossRef]

1962 (1)

Q1. H. Feshbach, "Unified theory of nuclear reactions, I," Ann. Phys. (N.Y.) 5, 357 (1958); "A unified theory of nuclear reactions, II," Ann. Phys. (N.Y.) 19,287 (1962).
[CrossRef]

Assefa, S.

Baets, R.

Bienstman, P.

Bogaerts, W.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides," Phys. Rev. Lett. 94,123901 (2005).
[CrossRef] [PubMed]

Borel, P.

Boyd, R. W.

R. W. Boyd and D. J. Gauthier, "Transparency on an optical chip," Nature 441,701-702 (2006).
[CrossRef] [PubMed]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69,063804 (2004).
[CrossRef]

Busch, K.

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]

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]

Chang, H.

D. D. Smith and H. Chang, "Coherence phenomena in coupled optical resonators," J. Mod. Opt. 51,2503-2513 (2004).

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69,063804 (2004).
[CrossRef]

Chin, M. K.

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Darmawan, S.

Engelen, R. J. P.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides," Phys. Rev. Lett. 94,123901 (2005).
[CrossRef] [PubMed]

Fage-Pedersen, J.

Fan, S.

S. Fan, "Manipulating light with photonic crystals," Physica B 394,221-228 (2007).
[CrossRef]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency," Phys. Rev. Lett. 96,123901 (2006).
[CrossRef] [PubMed]

M. F. Yanik and S. Fan, "Stopping light all optically", Phys. Rev. Lett. 92,083901 (2004).
[CrossRef] [PubMed]

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]

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

Farca, G.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, "Induced transparency and absorption in coupled whispering-gallery microresonators," Phys. Rev. A 71,043804 (2005).
[CrossRef]

Feshbach, H.

Q1. H. Feshbach, "Unified theory of nuclear reactions, I," Ann. Phys. (N.Y.) 5, 357 (1958); "A unified theory of nuclear reactions, II," Ann. Phys. (N.Y.) 19,287 (1962).
[CrossRef]

Flach, S.

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

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Frandsen, L.

Fuller, K. A.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69,063804 (2004).
[CrossRef]

Garcia-Martin, A.

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]

Gauthier, D. J.

R. W. Boyd and D. J. Gauthier, "Transparency on an optical chip," Nature 441,701-702 (2006).
[CrossRef] [PubMed]

Gersen, H.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides," Phys. Rev. Lett. 94,123901 (2005).
[CrossRef] [PubMed]

Hamann, H. F.

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]

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]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Hermann, D.

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]

Ilchenko, V. S.

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko and L. Maleki, "Interference effects in lossy resonator chains," J. Mod. Opt. 51,2515-2522 (2004).
[CrossRef]

Ilchenko, V.S.

Jacobsen, R.

Joannopoulos, J. D.

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]

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]

Johnson, S. G.

Karle, T. J.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides," Phys. Rev. Lett. 94,123901 (2005).
[CrossRef] [PubMed]

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]

Kivshar, Y. S.

S. F. Mingaleev, A. E. Miroshnichenko, and Y. S. Kivshar, "Low-threshold bistability of slow light in photoniccrystal waveguides," Opt. Express 15,12380-12385 (2007).
[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).
[CrossRef]

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

Korterik, J. P.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides," Phys. Rev. Lett. 94,123901 (2005).
[CrossRef] [PubMed]

Krauss, T. F.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides," Phys. Rev. Lett. 94,123901 (2005).
[CrossRef] [PubMed]

Kuipers, L.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides," Phys. Rev. Lett. 94,123901 (2005).
[CrossRef] [PubMed]

Laine, J.-P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Lavrinenko, A.

Lee, R. K.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, "Scattering-theory analysis of waveguide-resonator coupling," Phys. Rev. E 62,7389-7404 (2000).
[CrossRef]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis", Opt. Lett. 24,711 (1999).
[CrossRef]

Li, Y.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, "Scattering-theory analysis of waveguide-resonator coupling," Phys. Rev. E 62,7389-7404 (2000).
[CrossRef]

Lipson, M.

Q. Xu, J. Shakya, and M. Lipson, "Direct measurement of tunable optical delays on chip analogue to electromagnetically induced transparency," Opt. Express 14,6463-6468 (2006).
[CrossRef] [PubMed]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency," Phys. Rev. Lett. 96,123901 (2006).
[CrossRef] [PubMed]

Little, B. E.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Maes, B.

Magunov, A. I.

A. I. Magunov, I. Rotter, and S. I. Strakhova, "Fano resonances in the overlapping regime," Phys. Rev. B 68,245305 (2003).
[CrossRef]

Maleki, L.

L. Maleki, A. B. Matsko, A. A. Savchenkov, and V.S. Ilchenko, "Tunable delay line with interacting whisperinggallery- mode resonators," Opt. Lett. 29,626-628 (2004).
[CrossRef] [PubMed]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko and L. Maleki, "Interference effects in lossy resonator chains," J. Mod. Opt. 51,2515-2522 (2004).
[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]

Mario, L. Y.

Matsko, A. B.

L. Maleki, A. B. Matsko, A. A. Savchenkov, and V.S. Ilchenko, "Tunable delay line with interacting whisperinggallery- mode resonators," Opt. Lett. 29,626-628 (2004).
[CrossRef] [PubMed]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko and L. Maleki, "Interference effects in lossy resonator chains," J. Mod. Opt. 51,2515-2522 (2004).
[CrossRef]

McNab, S. J.

Mies, F. H.

M. Raoult and F. H. Mies, "Feshbach resonance in atomic binary collisions in the wigner threshold law regime," Phys. Rev. A 70,012710 (2004).
[CrossRef]

F. H. Mies, "Configuration interaction theory: effects of overlapping resonances," Phys. Rev. 175, 164-175 (1968);F. H. Mies, "Resonant scattering theory of association reactions and unimolecular decomposition: I. A united theory of radiative and collisional recombination," J. Chem. Phys. 51,787-797 (1969).
[CrossRef]

F. H. Mies, "Configuration interaction theory: effects of overlapping resonances," Phys. Rev. 175, 164-175 (1968);F. H. Mies, "Resonant scattering theory of association reactions and unimolecular decomposition: I. A united theory of radiative and collisional recombination," J. Chem. Phys. 51,787-797 (1969).
[CrossRef]

Mingaleev, S. F.

S. F. Mingaleev, A. E. Miroshnichenko, and Y. S. Kivshar, "Low-threshold bistability of slow light in photoniccrystal waveguides," Opt. Express 15,12380-12385 (2007).
[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).
[CrossRef]

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

Miroshnichenko, A. E.

S. F. Mingaleev, A. E. Miroshnichenko, and Y. S. Kivshar, "Low-threshold bistability of slow light in photoniccrystal waveguides," Opt. Express 15,12380-12385 (2007).
[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).
[CrossRef]

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

Moulin, G.

Naweed, A.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, "Induced transparency and absorption in coupled whispering-gallery microresonators," Phys. Rev. A 71,043804 (2005).
[CrossRef]

Notomi, M.

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]

O??Boyle, M.

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]

Opatrny, T.

T. Opatrny and D. G. Welsch, "Coupled cavities for enhancing the cross-phase-modulation in electromagnetically induced transparency," Phys. Rev. A 64,23805 (2001).
[CrossRef]

Peucheret, C.

Povinelli, M. L.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency," Phys. Rev. Lett. 96,123901 (2006).
[CrossRef] [PubMed]

Raoult, M.

M. Raoult and F. H. Mies, "Feshbach resonance in atomic binary collisions in the wigner threshold law regime," Phys. Rev. A 70,012710 (2004).
[CrossRef]

Rosenberger, A. T.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, "Induced transparency and absorption in coupled whispering-gallery microresonators," Phys. Rev. A 71,043804 (2005).
[CrossRef]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69,063804 (2004).
[CrossRef]

Rotter, I.

A. I. Magunov, I. Rotter, and S. I. Strakhova, "Fano resonances in the overlapping regime," Phys. Rev. B 68,245305 (2003).
[CrossRef]

Sandhu, S.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency," Phys. Rev. Lett. 96,123901 (2006).
[CrossRef] [PubMed]

Savchenkov, A. A.

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko and L. Maleki, "Interference effects in lossy resonator chains," J. Mod. Opt. 51,2515-2522 (2004).
[CrossRef]

L. Maleki, A. B. Matsko, A. A. Savchenkov, and V.S. Ilchenko, "Tunable delay line with interacting whisperinggallery- mode resonators," Opt. Lett. 29,626-628 (2004).
[CrossRef] [PubMed]

Scherer, A.

Schillinger, M.

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]

Shakya, J.

Q. Xu, J. Shakya, and M. Lipson, "Direct measurement of tunable optical delays on chip analogue to electromagnetically induced transparency," Opt. Express 14,6463-6468 (2006).
[CrossRef] [PubMed]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency," Phys. Rev. Lett. 96,123901 (2006).
[CrossRef] [PubMed]

Shinya, A.

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]

Shopova, S. I.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, "Induced transparency and absorption in coupled whispering-gallery microresonators," Phys. Rev. A 71,043804 (2005).
[CrossRef]

Smith, D. D.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69,063804 (2004).
[CrossRef]

D. D. Smith and H. Chang, "Coherence phenomena in coupled optical resonators," J. Mod. Opt. 51,2503-2513 (2004).

Strakhova, S. I.

A. I. Magunov, I. Rotter, and S. I. Strakhova, "Fano resonances in the overlapping regime," Phys. Rev. B 68,245305 (2003).
[CrossRef]

Strekalov, D.

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko and L. Maleki, "Interference effects in lossy resonator chains," J. Mod. Opt. 51,2515-2522 (2004).
[CrossRef]

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]

Takahashi, C.

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]

Takahashi, J.

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]

van Hulst, N. F.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides," Phys. Rev. Lett. 94,123901 (2005).
[CrossRef] [PubMed]

Villeneuve, P. R.

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]

Vlasov, Y. A.

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]

Welsch, D. G.

T. Opatrny and D. G. Welsch, "Coupled cavities for enhancing the cross-phase-modulation in electromagnetically induced transparency," Phys. Rev. A 64,23805 (2001).
[CrossRef]

Xu, Q.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency," Phys. Rev. Lett. 96,123901 (2006).
[CrossRef] [PubMed]

Q. Xu, J. Shakya, and M. Lipson, "Direct measurement of tunable optical delays on chip analogue to electromagnetically induced transparency," Opt. Express 14,6463-6468 (2006).
[CrossRef] [PubMed]

Xu, Y.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, "Scattering-theory analysis of waveguide-resonator coupling," Phys. Rev. E 62,7389-7404 (2000).
[CrossRef]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis", Opt. Lett. 24,711 (1999).
[CrossRef]

Yamada, K.

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]

Yanik, M. F.

M. F. Yanik and S. Fan, "Stopping light all optically", Phys. Rev. Lett. 92,083901 (2004).
[CrossRef] [PubMed]

Yariv, A.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, "Scattering-theory analysis of waveguide-resonator coupling," Phys. Rev. E 62,7389-7404 (2000).
[CrossRef]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis", Opt. Lett. 24,711 (1999).
[CrossRef]

Yokohama, I.

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]

Zsigri, B.

Ann. Phys. (N.Y.) (1)

Q1. H. Feshbach, "Unified theory of nuclear reactions, I," Ann. Phys. (N.Y.) 5, 357 (1958); "A unified theory of nuclear reactions, II," Ann. Phys. (N.Y.) 19,287 (1962).
[CrossRef]

Appl. Phys. Lett. (1)

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

IEEE J. Quantum Electron. (1)

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]

J. Lightwave Technol. (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

J. Mod. Opt. (2)

D. D. Smith and H. Chang, "Coherence phenomena in coupled optical resonators," J. Mod. Opt. 51,2503-2513 (2004).

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko and L. Maleki, "Interference effects in lossy resonator chains," J. Mod. Opt. 51,2515-2522 (2004).
[CrossRef]

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

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]

Nature (2)

R. W. Boyd and D. J. Gauthier, "Transparency on an optical chip," Nature 441,701-702 (2006).
[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 (5)

Opt. Lett. (4)

Phys. Rev. (1)

F. H. Mies, "Configuration interaction theory: effects of overlapping resonances," Phys. Rev. 175, 164-175 (1968);F. H. Mies, "Resonant scattering theory of association reactions and unimolecular decomposition: I. A united theory of radiative and collisional recombination," J. Chem. Phys. 51,787-797 (1969).
[CrossRef]

Phys. Rev. A (4)

M. Raoult and F. H. Mies, "Feshbach resonance in atomic binary collisions in the wigner threshold law regime," Phys. Rev. A 70,012710 (2004).
[CrossRef]

T. Opatrny and D. G. Welsch, "Coupled cavities for enhancing the cross-phase-modulation in electromagnetically induced transparency," Phys. Rev. A 64,23805 (2001).
[CrossRef]

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, "Induced transparency and absorption in coupled whispering-gallery microresonators," Phys. Rev. A 71,043804 (2005).
[CrossRef]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69,063804 (2004).
[CrossRef]

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]

A. I. Magunov, I. Rotter, and S. I. Strakhova, "Fano resonances in the overlapping regime," Phys. Rev. B 68,245305 (2003).
[CrossRef]

Phys. Rev. E (3)

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

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, "Scattering-theory analysis of waveguide-resonator coupling," Phys. Rev. E 62,7389-7404 (2000).
[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)

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency," Phys. Rev. Lett. 96,123901 (2006).
[CrossRef] [PubMed]

M. F. Yanik and S. Fan, "Stopping light all optically", Phys. Rev. Lett. 92,083901 (2004).
[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, "Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides," Phys. Rev. Lett. 94,123901 (2005).
[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]

Physica B (1)

S. Fan, "Manipulating light with photonic crystals," Physica B 394,221-228 (2007).
[CrossRef]

Other (1)

J. Pan, S. Sandhu, Y. Huo, M. L. Povinelli, M. M. Fejer, S. Fan, and J. S. Harris, "Optical Analogue to Electromagnetically Induced Transparency in Photonic Crystals, Simulation and Experiments," in Slow and Fast Light, OSA Technical Digest (CD) (Optical Society of America, 2007), paper SWB2. http://www.opticsinfobase.org/abstract.cfm?URI=SL-2007-SWB2

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

Three types of the geometries of a straight photonic-crystal waveguide side coupled to two nonlinear optical resonators, α and β. Standard coupled-mode theory is based on the geometry (a) which does not account for discreteness-induced effects in the photonic-crystal waveguides. For instance, light transmission and bistability are qualitatively different for (b) on-site and (c) inter-site locations of the resonator along waveguide and this cannot be distinguished within the conceptual framework of structure of type (a).

Fig. 2.
Fig. 2.

Typical transmission curves for four different cases (a) two identical side-coupled defects ωα = ωβ (solid). For reference we also put transmission for single side-coupled cavity (dashed); (b) two side-coupled cavities with larger detuned eigenfrequencies |ωα ωβ | ≫ 1; (c) and (d) correspond to two side-coupled cavities with slightly detuned eigenfrequencies |ωα ωβ |≪1 for two geometries: (c) on-site coupling shown in Fig. 1(b) and (d) inter-site coupling shown in Fig. 1(c).

Fig. 3.
Fig. 3.

Frequencies of localized cavity modes created by changing the radius r def of (a) a single rod [with the electric field profile of the mode shown in (d)], and (b) two neighboring rods [with the electric field profiles of two modes shown in (e) and (f)] 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 [with the electric field profile of the slow-light guided mode at the propagation band edge k = 0 shown in (g)]. Results are calculated with eleven maximally localized Wannier functions[23] (blue lines) in an excellent agreement with the supercell plane-waves method [24] (red circles).

Fig. 4.
Fig. 4.

(a) Schematic structure of a photonic-crystal waveguide coupled to two side cavities. (b) Linear transmission coefficient of the photonic-crystal waveguide for: (i) single side-coupled cavity with εα = 12. (dotted); (ii) two identical side-coupled cavities with εα = εβ = 12. (dashed); (iii) two side-coupled cavities with different permittivities εα = 12. and εβ = 12.001 (solid).

Fig. 5.
Fig. 5.

Width of the asymmetric Fano-Feshbach resonance vs. the permittivity detuning of two cavities. In all cases εα = 12., and (a) εβ = 12.005, (b) εβ = 12.004, (c) εβ = 12.003, (d) εβ = 12.002, (e) εβ = 12.001,.

Fig. 6.
Fig. 6.

Nonlinear transmission for the parameters used in Fig. 4. We assume that one cavity is nonlinear, such that λα = 3.903 ∙ 107χ(3) α and λβ = 0. The light frequency is ω = 0.3170418(2πc/a).

Equations (21)

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

T ( ω ) = σ 2 ( ω ) σ 2 ( ω ) + 1 , R ( ω ) = 1 σ 2 ( ω ) + 1 ,
σ ( ω ) ( ω α ω ) γ α ,
σ ( ω ) ( ω α ω ) ( ω β ω ) Γ ( ω t ω ) ,
ω t = γ α ω β + γ β ω α γ α + γ β ,
Γ t = δ ω 2 8 γ α .
ρ ( ω ) ψ n = ψ n + 1 + ψ n 1 + μ = α , β η n , μ ψ μ ,
( ω ω μ ) γ μ ( 0 ) ψ μ = n = η n , μ ψ n + λ μ ψ μ 2 ψ μ .
σ ( ω ) ( ω̃ α ± ω ) γ α ± ,
σ ( ω ) ( ω r 1 ± ω ) ( ω r 2 ± ω ) Γ ± ( ω t ω ) ,
ω r 1 ± = ω α + ω β 2 γ α ( 0 ) + γ β ( 0 ) 2
+ 1 2 ( ω α ω β γ α ( 0 ) ± γ β ( 0 ) ) 2 + 4 γ α ( 0 ) γ β ( 0 ) ,
ω r 2 ± = ω α + ω β 2 γ α ( 0 ) + γ β ( 0 ) 2
1 2 ( ω α ω β γ α ( 0 ) γ β ( 0 ) ) 2 + 4 γ α ( 0 ) γ β ( 0 ) ,
Γ r ± = [ tan ( k ( ω t ) s 2 ) ] 1 γ α ( 0 ) ( 1 1 1 + ( δω 2 γ α ( 0 ) ) 2 )
[ tan ( k ( ω t ) s 2 ) ] 1 δ ω 2 8 γ α ( 0 ) ,
σ ( ω ) ( ω r + ω ) ( ω r ω ) γ α ( ω t ω ) ,
ω r ± = ω α + ω β 2 ± 1 2 ( ω α ω β ) 2 + 4 γ α , β 2 ,
ω r + = ω α + γ α , β ω α ω β , ω r = ω β γ α , β ω α ω β ,
ω α , β [ 0.317045 + 6.83 · 10 3 ( ε α , β 12 ) ] ( 2 π c a ) ,
γ α , β ( 0 ) ± ( 4.3 · 10 6 ) ( 2 π c a ) ,
ω ( k ) [ 0.31680 + 0.89626 ( ka 2 π ) 2 ] ( 2 π c a ) .

Metrics