Abstract

We analyze transmission characteristics of two coupled identical cavities, of either standing-wave (SW) or traveling-wave (TW) type, based on temporal coupled mode theory. Mode splitting is observed for both directly (cavity-cavity) and indirectly (cavity-waveguide-cavity) coupled cavity systems. The effects of direct and indirect couplings, if coexisting in one system, can offset each other such that no mode splitting occurs and the original single-cavity resonant frequency is retained. By tuning the configuration of the coupled cavity system, one can obtain different characteristics in transmission spectra, including splitting in transmission, zero transmission, Fano-type transmission, electromagnetically-induced-transparency (EIT)-like transmission, and electromagnetically-induced-absorption (EIA)-like transmission. It is also interesting to notice that a side-coupled SW cavity system performs similarly to an under-coupled TW cavity. The results are useful for the design of cavity-based devices for integration in nanophotonics.

© 2010 Optical Society of America

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    [CrossRef]
  4. S. Xiao, M. H. Khan, H. Shen, and M. Qi, "A highly compact third-order silicon microring add-drop filter with a very large free spectral range, a flat passband and a low delay dispersion," Opt. Express 15, 14765-14771 (2007).
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    [CrossRef]
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    [CrossRef] [PubMed]
  7. T. Sunner, T. Stichel, S. H. Kwon, T.W. Schlereth, S. Hofling, M. Kamp, and A. Forchel, "Photonic crystal cavity based gas sensor," Appl. Phys. Lett. 92, 261112 (2008).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  14. Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, "Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems," Phys. Rev. A 75, 063833 (2007).
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  22. M. Lezama, S. Barreiro, and A. M. Akulshin, "Electromagnetically induced absorption," Phys. Rev. A 59, 4732 (1999).
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  23. X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, "All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities," Phys. Rev. Lett. 102, 173902 (2009).
    [CrossRef] [PubMed]
  24. 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]
  25. S. Manipatruni, P. Dong, Q. Xu, and M. Lipson, "Tunable superluminal propagation on a silicon micro-chip," Opt. Lett. 33, 2928-2930 (2008).
    [CrossRef] [PubMed]

2009 (2)

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, "A picogram- and nanometre-scale photoniccrystal optomechanical cavity," Nature 459, 550-555 (2009).
[CrossRef] [PubMed]

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, "All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities," Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef] [PubMed]

2008 (7)

2007 (4)

S. Xiao, M. H. Khan, H. Shen, and M. Qi, "A highly compact third-order silicon microring add-drop filter with a very large free spectral range, a flat passband and a low delay dispersion," Opt. Express 15, 14765-14771 (2007).
[CrossRef] [PubMed]

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, "Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems," Phys. Rev. A 75, 063833 (2007).
[CrossRef]

K. Totsuka, N. Kobayashi, and M. Tomita, "Slow light in coupled-resonator-induced transparency," Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef] [PubMed]

F. Xia, L. Sekaric, and Y. A. Vlasov, "Ultra-compact optical buffers on a silicon chip," Nature Photon. 1, 65-71 (2007).
[CrossRef]

2006 (2)

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. A. Popovic, C. Manolatou, and M. Watts, "Coupling-induced resonant frequency shifts in coupled dielectric multi-cavity filters," Opt. Express 14, 1208-1222 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

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]

2003 (1)

M. Okano, S. Kako, and S. Noda. "Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal," Phys. Rev. B 68, 235110 (2003).
[CrossRef]

2002 (1)

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

1999 (2)

M. Lezama, S. Barreiro, and A. M. Akulshin, "Electromagnetically induced absorption," Phys. Rev. A 59, 4732 (1999).
[CrossRef]

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

1997 (2)

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

B. E. Little, J. Laine, and S. T. Chu, "Surface-roughness-induced contradirectional coupling in ring and disk resonators," Opt. Lett. 22, 4-6 (1997).
[CrossRef] [PubMed]

1995 (1)

Y. Li and M. Xiao, "Observation of quantum interference between dressed states in electromagnetically induced transparency," Phys. Rev. A 51, 4959-4962 (1995).
[CrossRef] [PubMed]

Akahane, Y.

Akulshin, A. M.

M. Lezama, S. Barreiro, and A. M. Akulshin, "Electromagnetically induced absorption," Phys. Rev. A 59, 4732 (1999).
[CrossRef]

Aoki, K.

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, "Coupling of quantum-dot light emission with a three-dimensional photonic-crystal nanocavity," Nature Photonics 2, 688-692 (2008).
[CrossRef]

Arakawa, Y.

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, "Coupling of quantum-dot light emission with a three-dimensional photonic-crystal nanocavity," Nature Photonics 2, 688-692 (2008).
[CrossRef]

Asano, T.

Barreiro, S.

M. Lezama, S. Barreiro, and A. M. Akulshin, "Electromagnetically induced absorption," Phys. Rev. A 59, 4732 (1999).
[CrossRef]

Beausoleil, R. G.

Boyd, R. W.

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]

Camacho, R.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, "A picogram- and nanometre-scale photoniccrystal optomechanical cavity," Nature 459, 550-555 (2009).
[CrossRef] [PubMed]

Chan, J.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, "A picogram- and nanometre-scale photoniccrystal optomechanical cavity," Nature 459, 550-555 (2009).
[CrossRef] [PubMed]

Chang, H.

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]

Chen, Y. L.

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, "Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems," Phys. Rev. A 75, 063833 (2007).
[CrossRef]

Chu, S. T.

B. E. Little, J. Laine, and S. T. Chu, "Surface-roughness-induced contradirectional coupling in ring and disk resonators," Opt. Lett. 22, 4-6 (1997).
[CrossRef] [PubMed]

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

Dainese, M.

Dong, P.

Eichenfield, M.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, "A picogram- and nanometre-scale photoniccrystal optomechanical cavity," Nature 459, 550-555 (2009).
[CrossRef] [PubMed]

Fan, 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]

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

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

Forchel, A.

T. Sunner, T. Stichel, S. H. Kwon, T.W. Schlereth, S. Hofling, M. Kamp, and A. Forchel, "Photonic crystal cavity based gas sensor," Appl. Phys. Lett. 92, 261112 (2008).
[CrossRef]

Foresi, J.

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

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]

Guimard, D.

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, "Coupling of quantum-dot light emission with a three-dimensional photonic-crystal nanocavity," Nature Photonics 2, 688-692 (2008).
[CrossRef]

Guo, G. C.

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, "Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems," Phys. Rev. A 75, 063833 (2007).
[CrossRef]

Haus, H. A.

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

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

Hofling, S.

T. Sunner, T. Stichel, S. H. Kwon, T.W. Schlereth, S. Hofling, M. Kamp, and A. Forchel, "Photonic crystal cavity based gas sensor," Appl. Phys. Lett. 92, 261112 (2008).
[CrossRef]

Iwamoto, S.

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, "Coupling of quantum-dot light emission with a three-dimensional photonic-crystal nanocavity," Nature Photonics 2, 688-692 (2008).
[CrossRef]

Jiang, W.

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, "Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems," Phys. Rev. A 75, 063833 (2007).
[CrossRef]

Joannopoulos, J. D.

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

Kako, S.

M. Okano, S. Kako, and S. Noda. "Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal," Phys. Rev. B 68, 235110 (2003).
[CrossRef]

Kamp, M.

T. Sunner, T. Stichel, S. H. Kwon, T.W. Schlereth, S. Hofling, M. Kamp, and A. Forchel, "Photonic crystal cavity based gas sensor," Appl. Phys. Lett. 92, 261112 (2008).
[CrossRef]

Khan, M. H.

Khan, M. J.

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

Kobayashi, N.

K. Totsuka, N. Kobayashi, and M. Tomita, "Slow light in coupled-resonator-induced transparency," Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef] [PubMed]

Kuramochi, E.

M. Notomi, E. Kuramochi, and T. Tanabe, "Large-scale arrays of ultrahigh-Q coupled nanocavities," Nature Photon. 2, 741-747 (2008).
[CrossRef]

Kwon, S. H.

T. Sunner, T. Stichel, S. H. Kwon, T.W. Schlereth, S. Hofling, M. Kamp, and A. Forchel, "Photonic crystal cavity based gas sensor," Appl. Phys. Lett. 92, 261112 (2008).
[CrossRef]

Kwong, D. L.

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, "All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities," Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef] [PubMed]

Laine, J.

Laine, J. P.

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

Lezama, M.

M. Lezama, S. Barreiro, and A. M. Akulshin, "Electromagnetically induced absorption," Phys. Rev. A 59, 4732 (1999).
[CrossRef]

Li, Q.

Li, Y.

Y. Li and M. Xiao, "Observation of quantum interference between dressed states in electromagnetically induced transparency," Phys. Rev. A 51, 4959-4962 (1995).
[CrossRef] [PubMed]

Lipson, M.

S. Manipatruni, P. Dong, Q. Xu, and M. Lipson, "Tunable superluminal propagation on a silicon micro-chip," Opt. Lett. 33, 2928-2930 (2008).
[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, J. Laine, and S. T. Chu, "Surface-roughness-induced contradirectional coupling in ring and disk resonators," Opt. Lett. 22, 4-6 (1997).
[CrossRef] [PubMed]

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

Liu, F. F.

Manipatruni, S.

Manolatou, C.

M. A. Popovic, C. Manolatou, and M. Watts, "Coupling-induced resonant frequency shifts in coupled dielectric multi-cavity filters," Opt. Express 14, 1208-1222 (2006).
[CrossRef] [PubMed]

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

Nishioka, M.

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, "Coupling of quantum-dot light emission with a three-dimensional photonic-crystal nanocavity," Nature Photonics 2, 688-692 (2008).
[CrossRef]

Noda, S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt. Express 13, 1202-1214 (2005).
[CrossRef] [PubMed]

M. Okano, S. Kako, and S. Noda. "Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal," Phys. Rev. B 68, 235110 (2003).
[CrossRef]

Nomura, M.

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, "Coupling of quantum-dot light emission with a three-dimensional photonic-crystal nanocavity," Nature Photonics 2, 688-692 (2008).
[CrossRef]

Notomi, M.

M. Notomi, E. Kuramochi, and T. Tanabe, "Large-scale arrays of ultrahigh-Q coupled nanocavities," Nature Photon. 2, 741-747 (2008).
[CrossRef]

Okano, M.

M. Okano, S. Kako, and S. Noda. "Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal," Phys. Rev. B 68, 235110 (2003).
[CrossRef]

Painter, O.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, "A picogram- and nanometre-scale photoniccrystal optomechanical cavity," Nature 459, 550-555 (2009).
[CrossRef] [PubMed]

Popovic, M. A.

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]

Qi, M.

Qiu, M.

Rosenberger, A. T.

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]

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]

Schlereth, T.W.

T. Sunner, T. Stichel, S. H. Kwon, T.W. Schlereth, S. Hofling, M. Kamp, and A. Forchel, "Photonic crystal cavity based gas sensor," Appl. Phys. Lett. 92, 261112 (2008).
[CrossRef]

Sekaric, L.

F. Xia, L. Sekaric, and Y. A. Vlasov, "Ultra-compact optical buffers on a silicon chip," Nature Photon. 1, 65-71 (2007).
[CrossRef]

Shakya, J.

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]

Shen, H.

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]

Song, B. S.

Song, M.

Stichel, T.

T. Sunner, T. Stichel, S. H. Kwon, T.W. Schlereth, S. Hofling, M. Kamp, and A. Forchel, "Photonic crystal cavity based gas sensor," Appl. Phys. Lett. 92, 261112 (2008).
[CrossRef]

Su, Y. K.

Sunner, T.

T. Sunner, T. Stichel, S. H. Kwon, T.W. Schlereth, S. Hofling, M. Kamp, and A. Forchel, "Photonic crystal cavity based gas sensor," Appl. Phys. Lett. 92, 261112 (2008).
[CrossRef]

Tanabe, T.

M. Notomi, E. Kuramochi, and T. Tanabe, "Large-scale arrays of ultrahigh-Q coupled nanocavities," Nature Photon. 2, 741-747 (2008).
[CrossRef]

Tomita, M.

K. Totsuka, N. Kobayashi, and M. Tomita, "Slow light in coupled-resonator-induced transparency," Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef] [PubMed]

Totsuka, K.

K. Totsuka, N. Kobayashi, and M. Tomita, "Slow light in coupled-resonator-induced transparency," Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef] [PubMed]

Vahala, K. J.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, "A picogram- and nanometre-scale photoniccrystal optomechanical cavity," Nature 459, 550-555 (2009).
[CrossRef] [PubMed]

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 resonance channel add-drop filters," IEEE J. Quantum Electron. 35, 1322-1331 (1999).
[CrossRef]

Vlasov, Y. A.

F. Xia, L. Sekaric, and Y. A. Vlasov, "Ultra-compact optical buffers on a silicon chip," Nature Photon. 1, 65-71 (2007).
[CrossRef]

Watts, M.

Willner, A. E.

Wong, C. W.

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, "All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities," Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef] [PubMed]

Wosinski, L.

Wu, T.

Xia, F.

F. Xia, L. Sekaric, and Y. A. Vlasov, "Ultra-compact optical buffers on a silicon chip," Nature Photon. 1, 65-71 (2007).
[CrossRef]

Xiao, M.

Y. Li and M. Xiao, "Observation of quantum interference between dressed states in electromagnetically induced transparency," Phys. Rev. A 51, 4959-4962 (1995).
[CrossRef] [PubMed]

Xiao, S.

Xiao, Y. F.

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, "Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems," Phys. Rev. A 75, 063833 (2007).
[CrossRef]

Xu, Q.

S. Manipatruni, P. Dong, Q. Xu, and M. Lipson, "Tunable superluminal propagation on a silicon micro-chip," Opt. Lett. 33, 2928-2930 (2008).
[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]

Yang, X.

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, "All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities," Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef] [PubMed]

Yu, M.

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, "All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities," Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef] [PubMed]

Zhang, L.

Zhang, Z.

Zhang, Z. Y.

Zou, L.

Zou, X. B.

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, "Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems," Phys. Rev. A 75, 063833 (2007).
[CrossRef]

Appl. Phys. Lett. (2)

T. Sunner, T. Stichel, S. H. Kwon, T.W. Schlereth, S. Hofling, M. Kamp, and A. Forchel, "Photonic crystal cavity based gas sensor," Appl. Phys. Lett. 92, 261112 (2008).
[CrossRef]

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

IEEE J. Lightwave Technol. (1)

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

IEEE J. Quantum Electron. (1)

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

J. Lightwave Technol. (1)

Nature (1)

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, "A picogram- and nanometre-scale photoniccrystal optomechanical cavity," Nature 459, 550-555 (2009).
[CrossRef] [PubMed]

Nature Photon. (2)

F. Xia, L. Sekaric, and Y. A. Vlasov, "Ultra-compact optical buffers on a silicon chip," Nature Photon. 1, 65-71 (2007).
[CrossRef]

M. Notomi, E. Kuramochi, and T. Tanabe, "Large-scale arrays of ultrahigh-Q coupled nanocavities," Nature Photon. 2, 741-747 (2008).
[CrossRef]

Nature Photonics (1)

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, "Coupling of quantum-dot light emission with a three-dimensional photonic-crystal nanocavity," Nature Photonics 2, 688-692 (2008).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. A (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]

Y. Li and M. Xiao, "Observation of quantum interference between dressed states in electromagnetically induced transparency," Phys. Rev. A 51, 4959-4962 (1995).
[CrossRef] [PubMed]

M. Lezama, S. Barreiro, and A. M. Akulshin, "Electromagnetically induced absorption," Phys. Rev. A 59, 4732 (1999).
[CrossRef]

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, "Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems," Phys. Rev. A 75, 063833 (2007).
[CrossRef]

Phys. Rev. B (1)

M. Okano, S. Kako, and S. Noda. "Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal," Phys. Rev. B 68, 235110 (2003).
[CrossRef]

Phys. Rev. Lett. (3)

K. Totsuka, N. Kobayashi, and M. Tomita, "Slow light in coupled-resonator-induced transparency," Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef] [PubMed]

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, "All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities," Phys. Rev. Lett. 102, 173902 (2009).
[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]

Other (1)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: molding the flow of light (second edition) (Princeton University Press, Princeton, 2008).

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Figures (14)

Fig. 1.
Fig. 1.

Schematics of single cavities. (a) and (b) are SW cavities with side-coupling and shoulder-coupling configuration denoted as S1 and S2, respectively. (c) is a TW cavity denoted as T1.

Fig. 2.
Fig. 2.

Transmission, phase shift and group delay of single SW and TW cavity. For S1 and S2, Qi=16×104, Qw=2×104. For over-coupled T1, Qi=4×104, Qw=3.2×104. For under-coupled T1, Qw=4×104, Qi=3.2×104. We assume λ0=1550 nm here and in the following figures.

Fig. 3.
Fig. 3.

Schematics of two identical coupled cavity modes with symmetric waveguide coupling. (a)-(c) consist of two SW cavities but with different waveguide coupling configurations (S3-S5). (d) consists of two TW cavities (T2).

Fig. 4.
Fig. 4.

The transmission, phase shift and group delay for different Qc for S3 (a-c), S4 (d-f) and S5 (g-i). Qi=10×104, Qw=4×104.

Fig. 5.
Fig. 5.

The transmission, phase shift and group delay for different Qc for T2. Qi=10×104 and Qw=4×104.

Fig. 6.
Fig. 6.

Schematics of two identical coupled cavity modes with asymmetric waveguide coupling. (a) and (b) consist of two SW cavities with different waveguide-coupling configurations, denoted by S6 and S7, respectively. (c) consists of two TW cavities denoted by T3.

Fig. 7.
Fig. 7.

Illustration of the transmission, phase shift and group delay of cavities for S6 (a-c) and S7 (d-f). Qi1=10×104, Qw=4×104 and Qi2=10×105.

Fig. 8.
Fig. 8.

Illustration of the transmission, phase shift and group delay of cavities for T3. Qi1=10×104, Qw=4×104 and Qi2=10×105.

Fig. 9.
Fig. 9.

Schematics of two coupled cavity modes through waveguide. (a) and (b) are two SW cavity modes indirectly coupled through one waveguide (S8 and S9). (c) is two TW cavity modes indirectly coupled by two waveguides (T4).

Fig. 10.
Fig. 10.

The transmission, phase shift and group delay for S8 system. The black and red lines are for the transmitted port and reflected port, respectively. Qi=2×105 and Qw=4×104. The phase shift induced by the waveguide is ϕ=0.785 rad.

Fig. 11.
Fig. 11.

The transmission, phase shift and group delay for S9 system. The black line and red line are for the transmitted port and reflected port, respectively. Qi=8×105 and Qw=8×104. ϕ = −0.2 rad for (a)-(c) and ϕ = 1.57 rad for (d)-(f).

Fig. 12.
Fig. 12.

Schematic of two coupled cavity modes with direct and indirect couplings. (a) two SW cavity modes coupled by one waveguide (S10). (b) and (c) are two TW cavity modes coupled by one waveguide (T5) and two waveguides (T6), respectively.

Fig. 13.
Fig. 13.

The transmission, phase shift and group delay of S10. The black line (t) and red line (r) denote the transmission for the transmitted port and reflected port, respectively. Qw = 4×104, Qi = 2×105, Qc = 4.0067×105, ϕ= -0.1 rad.

Fig. 14.
Fig. 14.

The transmission, phase shift and group delay of T5 when the direct coupling is offset by the indirect coupling through waveguide in resonant frequency. Qc = 2 × 104, ϕ = -1.57 rad. Qw = 4×104 and Qi = 2×105 for two under-coupled TW cavities and Qw = 2×105 and Qi = 4×104 for two over-coupled TW cavities.

Tables (3)

Tables Icon

Table 1. Comparisons between single SW and TW cavities.

Tables Icon

Table 2. Mode-splitting characteristic for S6 for different coupling strengths.

Tables Icon

Table 3. Mode-splitting characteristic for S8 for different f introduced by waveguide.

Equations (25)

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d dt a 1 = ( j ω 0 1 τ i 1 τ w ) a 1 1 τ w s i a 2
d dt a 2 = ( j ω 0 1 τ i 1 τ w ) a 2 a 1
t S 3 = 1 1 2 Q w ( 1 j ( 2 δ + 1 / Q c ) + 1 / Q i + 1 / Q w + 1 j ( 2 δ 1 / Q c ) + 1 / Q i + 1 / Q w )
t S 4 = 1 2 Q w ( 1 j ( 2 δ + 1 / Q c ) + 1 / Q i + 1 / Q w + 1 j ( 2 δ 1 / Q c ) + 1 / Q i + 1 / Q w )
t S 5 = 1 Q w ( 1 j ( 2 δ + 1 / Q c ) + 1 / Q i + 1 / Q w 1 j ( 2 δ 1 / Q c ) + 1 / Q i + 1 / Q w )
t T 2 = 1 1 Q w ( 1 j ( 2 δ + 1 / Q c ) + 1 / Q i + 1 / Q w + 1 j ( 2 δ 1 / Q c ) + 1 / Q i + 1 / Q w )
d dt a 1 = ( j ω 0 1 τ i 1 1 τ w ) a 1 + 1 τ w s i a 2
d dt a 2 = ( j ω 0 1 τ i 2 ) a 2 a 1
t S 6 = 1 1 Q w j 2 δ + 1 Q i 2 ( j 2 δ + 1 2 Q i 2 + 1 2 Q i 1 + 1 2 Q w ) 2 + ( 1 Q c ) 2 ( 1 2 Q i 1 1 2 Q i 2 + 1 2 Q w ) 2
t S 7 = 1 Q w j 2 δ + 1 Q i 2 ( j 2 δ + 1 2 Q i 2 + 1 2 Q i 1 + 1 2 Q w ) 2 + ( 1 Q c ) 2 ( 1 2 Q i 1 1 2 Q i 2 + 1 2 Q w ) 2
t T 3 = 1 2 Q w j 2 δ + 1 Q i 2 ( j 2 δ + 1 2 Q i 2 + 1 2 Q i 1 + 1 2 Q w ) 2 + ( 1 Q c ) 2 ( 1 2 Q i 1 1 2 Q i 2 + 1 2 Q w ) 2
T S 6 = 1 δ 2 ( 2 / ( Q i 1 Q w ) + 1 / Q w 2 ) δ 2 ( 1 / Q i 1 + 1 / Q w ) 2 + 4 ( δ 2 1 / ( 4 Q c 2 ) ) 2
T S 7 = δ 2 / Q w 2 δ 2 ( 1 / Q i 1 + 1 / Q w ) 2 + 4 ( δ 2 1 / ( 4 Q c 2 ) ) 2
T T 3 = 1 4 δ 2 / ( Q i 1 Q w ) δ 2 ( 1 / Q i 1 + 1 / Q w ) 2 + 4 ( δ 2 1 / ( 4 Q c 2 ) ) 2
d dt a 1 = ( j ω 0 1 τ i 1 τ w ) a 1 + 1 τ w s i + 1 τ w ( e 1 τ w a 2 )
d dt a 2 = ( j ω 0 1 τ i 1 τ w ) a 2 + 1 τ w e ( s i 1 τ w a 1 )
t S 8 = e ( 1 γ 0 ) 2 1 γ 0 2 e j 2 ϕ
r S 8 = γ 0 γ 0 e j 2 ϕ + 2 γ 0 2 e j 2 ϕ 1 γ 0 2 e j 2 ϕ
t S 8 = e ( 1 1 Q w ( 1 + e ) 2 2 e j ( 2 δ + sin ϕ Q w ) + 1 Q i + 1 + cos ϕ Q w + 1 Q w ( 1 e ) 2 2 e j ( 2 δ sin ϕ Q w ) + 1 Q i + 1 cos ϕ Q w )
t S 9 = γ 1 γ 2 e 1 ( 1 + γ 1 ) ( 1 + γ 2 ) e j 2 ϕ
r S 9 = ( 1 + γ 1 ) + ( 1 + 2 γ 1 ) ( 1 + γ 2 ) e 1 ( 1 + γ 1 ) ( 1 + γ 2 ) e j 2 ϕ
t S 9 = 1 / ( 8 Q w 2 sin ϕ ) [ j ( δ + cot ( ϕ / 2 ) / 4 Q w ) + 1 / ( 2 Q i ) + 1 / ( 4 Q w ) ] [ j ( δ tan ( ϕ / 2 ) / 4 Q w ) + 1 / ( 2 Q i ) + 1 / ( 4 Q w ) ]
t S 10 = e 1 + γ 1 + γ 2 + γ 1 γ 2 ( e + j Q w / Q c ) ( e j Q w / Q c ) 1 γ 1 γ 2 ( e + j Q w / Q c ) 2
r S 10 = γ 1 + γ 2 e j 2 ϕ + 2 γ 1 γ 2 e ( e + j Q w / Q c ) 1 γ 1 γ 2 ( e + j Q w / Q c ) 2
t T 5 = e 1 2 γ 1 2 γ 2 + ( 4 + j 2 Q w Q c e + Q w Q c Q w Q c ) γ 1 γ 2 1 j Q w Q c ( 2 e + j Q w Q c ) γ 1 γ 2

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