Abstract

We theoretically propose and experimentally perform a novel dispersion tuning scheme to realize a tunable Fano resonance in a coupled-resonator-induced transparency (CRIT) structure coupled Mach-Zehnder interferometer. We reveal that the profile of the Fano resonance in the resonator coupled Mach-Zehnder interferometers (RCMZI) is determined not only by the phase shift difference between the two arms of the RCMZI but also by the dispersion (group delay) of the CRIT structure. Furthermore, it is theoretically predicted and experimentally demonstrated that the slope and the asymmetry parameter (q) describing the Fano resonance spectral line shape of the RCMZI experience a sign reversal when the dispersion of the CRIT structure is tuned from abnormal dispersion (fast light) to normal dispersion (slow light). These theoretical and experimental results indicate that the reversible Fano resonance which holds significant implications for some attractive device applications such as highly sensitive biochemical sensors, ultrafast optical switches and routers can be realized by the dispersion tuning scheme in the RCMZI.

© 2013 OSA

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  35. Y. Dumeige, T. K. N. Nguyen, L. Ghisa, S. Trebaol, and P. Feron, “Measurement of the dispersion induced by a slow-light system based on coupled active-resonator-induced transparency,” Phys. Rev. A78(1), 013818 (2008).
    [CrossRef]
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2012 (2)

F. Cheng, H. F. Liu, B. H. Li, J. Han, H. Xiao, X. F. Han, C. Z. Gu, and X. G. Qiu, “Tuning asymmetry parameter of Fano resonance of spoof surface plasmons by modes coupling,” Appl. Phys. Lett.100(13), 131110 (2012).
[CrossRef]

B. B. Li, Y. F. Xiao, C. L. Zou, X. F. Jiang, Y. C. Liu, F. W. Sun, Y. Li, and Q. H. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100(2), 021108 (2012).
[CrossRef]

2011 (2)

B. B. Li, Y. F. Xiao, C. L. Zou, Y. C. Liu, X. F. Jiang, Y. L. Chen, Y. Li, and Q. H. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98(2), 021116 (2011).
[CrossRef]

Y. H. Wen, O. Kuzucu, T. G. Hou, M. Lipson, and A. L. Gaeta, “All-optical switching of a single resonance in silicon ring resonators,” Opt. Lett.36(8), 1413–1415 (2011).
[CrossRef] [PubMed]

2010 (3)

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys.82(3), 2257–2298 (2010).
[CrossRef]

J. Pan, Y. J. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. H. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
[CrossRef]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9(9), 707–715 (2010).
[CrossRef] [PubMed]

2009 (5)

Y. Dumeige, S. Trebaol, and P. Feron, “Intracavity coupled-active-resonator-induced dispersion,” Phys. Rev. A79(1), 013832 (2009).
[CrossRef]

M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O'Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett.94(7), 071101 (2009).
[CrossRef]

T. Tanabe, M. Notomi, H. Taniyama, and E. Kuramochi, “Dynamic release of trapped light from an ultrahigh-Q nanocavity via adiabatic frequency tuning,” Phys. Rev. Lett.102(4), 043907 (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(17), 173902 (2009).
[CrossRef] [PubMed]

M. Terrel, M. J. F. Digonnet, and S. H. Fan, “Ring-coupled Mach-Zehnder interferometer optimized for sensing,” Appl. Opt.48(26), 4874–4879 (2009).
[CrossRef] [PubMed]

2008 (2)

F. Hao, Y. Sonnefraud, P. Van Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

Y. Dumeige, T. K. N. Nguyen, L. Ghisa, S. Trebaol, and P. Feron, “Measurement of the dispersion induced by a slow-light system based on coupled active-resonator-induced transparency,” Phys. Rev. A78(1), 013818 (2008).
[CrossRef]

2007 (7)

L. J. Zhou and A. W. Poon, “Fano resonance-based electrically reconfigurable add-drop filters in silicon microring resonator-coupled Mach-Zehnder interferometers,” Opt. Lett.32(7), 781–783 (2007).
[CrossRef] [PubMed]

S. Sandhu, M. L. Povinelli, and S. H. Fan, “Stopping and time reversing a light pulse using dynamic loss tuning of coupled-resonator delay lines,” Opt. Lett.32(22), 3333–3335 (2007).
[CrossRef] [PubMed]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett.99(13), 133601 (2007).
[CrossRef] [PubMed]

X. Yang, C. Husko, C. W. Wong, M. B. Yu, and D.-L. Kwong, “Observation of femtojoule optical bistability involving Fano resonances in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett.91(5), 051113 (2007).
[CrossRef]

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett.99(14), 147401 (2007).
[CrossRef] [PubMed]

Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factor in a photonic crystal nanocavity,” Nat. Mater.6(11), 862–865 (2007).
[CrossRef] [PubMed]

Q. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys.3(6), 406–410 (2007).
[CrossRef]

2006 (2)

2005 (3)

Y. Lu, J. Q. Yao, X. F. Li, and P. Wang, “Tunable asymmetrical Fano resonance and bistability in a microcavity-resonator-coupled Mach-Zehnder interferometer,” Opt. Lett.30(22), 3069–3071 (2005).
[CrossRef] [PubMed]

J. T. Shen and S. H. Fan, “Coherent single photon transport in a one-dimensional waveguide coupled with superconducting quantum bits,” Phys. Rev. Lett.95(21), 213001 (2005).
[CrossRef] [PubMed]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005).
[CrossRef] [PubMed]

2004 (3)

G. Shvets and Y. A. Urzhumov, “Engineering the electromagnetic properties of periodic nanostructures using electrostatic resonances,” Phys. Rev. Lett.93(24), 243902 (2004).
[CrossRef] [PubMed]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A69(6), 063804 (2004).
[CrossRef]

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express12(1), 90–103 (2004).
[CrossRef] [PubMed]

2003 (2)

C. Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett.83(8), 1527–1529 (2003).
[CrossRef]

M. F. Yanik, S. H. Fan, and M. Soljačić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett.83(14), 2739–2741 (2003).
[CrossRef]

2002 (2)

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B65(23), 235112 (2002).
[CrossRef]

S. H. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett.80(6), 908–910 (2002).
[CrossRef]

1999 (1)

1961 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev.124(6), 1866–1878 (1961).
[CrossRef]

Andreani, L. C.

M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O'Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett.94(7), 071101 (2009).
[CrossRef]

Asano, T.

Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factor in a photonic crystal nanocavity,” Nat. Mater.6(11), 862–865 (2007).
[CrossRef] [PubMed]

Belotti, M.

M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O'Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett.94(7), 071101 (2009).
[CrossRef]

Boyd, R. W.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A69(6), 063804 (2004).
[CrossRef]

J. E. Heebner and R. W. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt. Lett.24(12), 847–849 (1999).
[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. A69(6), 063804 (2004).
[CrossRef]

Chao, C. Y.

C. Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett.83(8), 1527–1529 (2003).
[CrossRef]

Chen, Y. L.

B. B. Li, Y. F. Xiao, C. L. Zou, Y. C. Liu, X. F. Jiang, Y. L. Chen, Y. Li, and Q. H. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98(2), 021116 (2011).
[CrossRef]

Cheng, F.

F. Cheng, H. F. Liu, B. H. Li, J. Han, H. Xiao, X. F. Han, C. Z. Gu, and X. G. Qiu, “Tuning asymmetry parameter of Fano resonance of spoof surface plasmons by modes coupling,” Appl. Phys. Lett.100(13), 131110 (2012).
[CrossRef]

Chong, C. T.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9(9), 707–715 (2010).
[CrossRef] [PubMed]

Digonnet, M. J. F.

Dong, P.

Q. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys.3(6), 406–410 (2007).
[CrossRef]

Dumeige, Y.

Y. Dumeige, S. Trebaol, and P. Feron, “Intracavity coupled-active-resonator-induced dispersion,” Phys. Rev. A79(1), 013832 (2009).
[CrossRef]

Y. Dumeige, T. K. N. Nguyen, L. Ghisa, S. Trebaol, and P. Feron, “Measurement of the dispersion induced by a slow-light system based on coupled active-resonator-induced transparency,” Phys. Rev. A78(1), 013818 (2008).
[CrossRef]

Fan, S.

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B65(23), 235112 (2002).
[CrossRef]

Fan, S. H.

J. Pan, Y. J. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. H. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
[CrossRef]

M. Terrel, M. J. F. Digonnet, and S. H. Fan, “Ring-coupled Mach-Zehnder interferometer optimized for sensing,” Appl. Opt.48(26), 4874–4879 (2009).
[CrossRef] [PubMed]

S. Sandhu, M. L. Povinelli, and S. H. Fan, “Stopping and time reversing a light pulse using dynamic loss tuning of coupled-resonator delay lines,” Opt. Lett.32(22), 3333–3335 (2007).
[CrossRef] [PubMed]

J. T. Shen and S. H. Fan, “Coherent single photon transport in a one-dimensional waveguide coupled with superconducting quantum bits,” Phys. Rev. Lett.95(21), 213001 (2005).
[CrossRef] [PubMed]

M. F. Yanik, S. H. Fan, and M. Soljačić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett.83(14), 2739–2741 (2003).
[CrossRef]

S. H. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett.80(6), 908–910 (2002).
[CrossRef]

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev.124(6), 1866–1878 (1961).
[CrossRef]

Fedotov, V. A.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett.99(14), 147401 (2007).
[CrossRef] [PubMed]

Fejer, M. M.

J. Pan, Y. J. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. H. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
[CrossRef]

Feron, P.

Y. Dumeige, S. Trebaol, and P. Feron, “Intracavity coupled-active-resonator-induced dispersion,” Phys. Rev. A79(1), 013832 (2009).
[CrossRef]

Y. Dumeige, T. K. N. Nguyen, L. Ghisa, S. Trebaol, and P. Feron, “Measurement of the dispersion induced by a slow-light system based on coupled active-resonator-induced transparency,” Phys. Rev. A78(1), 013818 (2008).
[CrossRef]

Flach, S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys.82(3), 2257–2298 (2010).
[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. A69(6), 063804 (2004).
[CrossRef]

Gaeta, A. L.

Galli, M.

M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O'Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett.94(7), 071101 (2009).
[CrossRef]

Ghisa, L.

Y. Dumeige, T. K. N. Nguyen, L. Ghisa, S. Trebaol, and P. Feron, “Measurement of the dispersion induced by a slow-light system based on coupled active-resonator-induced transparency,” Phys. Rev. A78(1), 013818 (2008).
[CrossRef]

Giessen, H.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9(9), 707–715 (2010).
[CrossRef] [PubMed]

Gong, Q. H.

B. B. Li, Y. F. Xiao, C. L. Zou, X. F. Jiang, Y. C. Liu, F. W. Sun, Y. Li, and Q. H. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100(2), 021108 (2012).
[CrossRef]

B. B. Li, Y. F. Xiao, C. L. Zou, Y. C. Liu, X. F. Jiang, Y. L. Chen, Y. Li, and Q. H. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98(2), 021116 (2011).
[CrossRef]

Gu, C. Z.

F. Cheng, H. F. Liu, B. H. Li, J. Han, H. Xiao, X. F. Han, C. Z. Gu, and X. G. Qiu, “Tuning asymmetry parameter of Fano resonance of spoof surface plasmons by modes coupling,” Appl. Phys. Lett.100(13), 131110 (2012).
[CrossRef]

Guo, L. J.

C. Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett.83(8), 1527–1529 (2003).
[CrossRef]

Halas, N. J.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9(9), 707–715 (2010).
[CrossRef] [PubMed]

F. Hao, Y. Sonnefraud, P. Van Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

Han, J.

F. Cheng, H. F. Liu, B. H. Li, J. Han, H. Xiao, X. F. Han, C. Z. Gu, and X. G. Qiu, “Tuning asymmetry parameter of Fano resonance of spoof surface plasmons by modes coupling,” Appl. Phys. Lett.100(13), 131110 (2012).
[CrossRef]

Han, X. F.

F. Cheng, H. F. Liu, B. H. Li, J. Han, H. Xiao, X. F. Han, C. Z. Gu, and X. G. Qiu, “Tuning asymmetry parameter of Fano resonance of spoof surface plasmons by modes coupling,” Appl. Phys. Lett.100(13), 131110 (2012).
[CrossRef]

Hao, F.

F. Hao, Y. Sonnefraud, P. Van Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

Harris, J. S.

J. Pan, Y. J. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. H. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
[CrossRef]

Heebner, J. E.

Hou, T. G.

Huang, Y. Y.

Huo, Y. J.

J. Pan, Y. J. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. H. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
[CrossRef]

Husko, C.

X. Yang, C. Husko, C. W. Wong, M. B. Yu, and D.-L. Kwong, “Observation of femtojoule optical bistability involving Fano resonances in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett.91(5), 051113 (2007).
[CrossRef]

Jiang, X. F.

B. B. Li, Y. F. Xiao, C. L. Zou, X. F. Jiang, Y. C. Liu, F. W. Sun, Y. Li, and Q. H. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100(2), 021108 (2012).
[CrossRef]

B. B. Li, Y. F. Xiao, C. L. Zou, Y. C. Liu, X. F. Jiang, Y. L. Chen, Y. Li, and Q. H. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98(2), 021116 (2011).
[CrossRef]

Joannopoulos, J. D.

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B65(23), 235112 (2002).
[CrossRef]

Kivshar, Y. S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys.82(3), 2257–2298 (2010).
[CrossRef]

Krauss, T. F.

M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O'Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett.94(7), 071101 (2009).
[CrossRef]

Kuramochi, E.

T. Tanabe, M. Notomi, H. Taniyama, and E. Kuramochi, “Dynamic release of trapped light from an ultrahigh-Q nanocavity via adiabatic frequency tuning,” Phys. Rev. Lett.102(4), 043907 (2009).
[CrossRef] [PubMed]

Kuzucu, O.

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(17), 173902 (2009).
[CrossRef] [PubMed]

X. Yang, C. Husko, C. W. Wong, M. B. Yu, and D.-L. Kwong, “Observation of femtojoule optical bistability involving Fano resonances in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett.91(5), 051113 (2007).
[CrossRef]

Li, B. B.

B. B. Li, Y. F. Xiao, C. L. Zou, X. F. Jiang, Y. C. Liu, F. W. Sun, Y. Li, and Q. H. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100(2), 021108 (2012).
[CrossRef]

B. B. Li, Y. F. Xiao, C. L. Zou, Y. C. Liu, X. F. Jiang, Y. L. Chen, Y. Li, and Q. H. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98(2), 021116 (2011).
[CrossRef]

Li, B. H.

F. Cheng, H. F. Liu, B. H. Li, J. Han, H. Xiao, X. F. Han, C. Z. Gu, and X. G. Qiu, “Tuning asymmetry parameter of Fano resonance of spoof surface plasmons by modes coupling,” Appl. Phys. Lett.100(13), 131110 (2012).
[CrossRef]

Li, X. F.

Li, Y.

B. B. Li, Y. F. Xiao, C. L. Zou, X. F. Jiang, Y. C. Liu, F. W. Sun, Y. Li, and Q. H. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100(2), 021108 (2012).
[CrossRef]

B. B. Li, Y. F. Xiao, C. L. Zou, Y. C. Liu, X. F. Jiang, Y. L. Chen, Y. Li, and Q. H. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98(2), 021116 (2011).
[CrossRef]

Liang, W.

Lipson, M.

Y. H. Wen, O. Kuzucu, T. G. Hou, M. Lipson, and A. L. Gaeta, “All-optical switching of a single resonance in silicon ring resonators,” Opt. Lett.36(8), 1413–1415 (2011).
[CrossRef] [PubMed]

Q. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys.3(6), 406–410 (2007).
[CrossRef]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Liu, H. F.

F. Cheng, H. F. Liu, B. H. Li, J. Han, H. Xiao, X. F. Han, C. Z. Gu, and X. G. Qiu, “Tuning asymmetry parameter of Fano resonance of spoof surface plasmons by modes coupling,” Appl. Phys. Lett.100(13), 131110 (2012).
[CrossRef]

Liu, Y. C.

B. B. Li, Y. F. Xiao, C. L. Zou, X. F. Jiang, Y. C. Liu, F. W. Sun, Y. Li, and Q. H. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100(2), 021108 (2012).
[CrossRef]

B. B. Li, Y. F. Xiao, C. L. Zou, Y. C. Liu, X. F. Jiang, Y. L. Chen, Y. Li, and Q. H. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98(2), 021116 (2011).
[CrossRef]

Lu, Y.

Luk’yanchuk, B.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9(9), 707–715 (2010).
[CrossRef] [PubMed]

Maier, S. A.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9(9), 707–715 (2010).
[CrossRef] [PubMed]

F. Hao, Y. Sonnefraud, P. Van Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

Miroshnichenko, A. E.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys.82(3), 2257–2298 (2010).
[CrossRef]

Mookherjea, S.

Nagashima, T.

Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factor in a photonic crystal nanocavity,” Nat. Mater.6(11), 862–865 (2007).
[CrossRef] [PubMed]

Nguyen, T. K. N.

Y. Dumeige, T. K. N. Nguyen, L. Ghisa, S. Trebaol, and P. Feron, “Measurement of the dispersion induced by a slow-light system based on coupled active-resonator-induced transparency,” Phys. Rev. A78(1), 013818 (2008).
[CrossRef]

Noda, S.

Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factor in a photonic crystal nanocavity,” Nat. Mater.6(11), 862–865 (2007).
[CrossRef] [PubMed]

Nordlander, P.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9(9), 707–715 (2010).
[CrossRef] [PubMed]

F. Hao, Y. Sonnefraud, P. Van Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

Notomi, M.

T. Tanabe, M. Notomi, H. Taniyama, and E. Kuramochi, “Dynamic release of trapped light from an ultrahigh-Q nanocavity via adiabatic frequency tuning,” Phys. Rev. Lett.102(4), 043907 (2009).
[CrossRef] [PubMed]

O'Faolain, L.

M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O'Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett.94(7), 071101 (2009).
[CrossRef]

Paloczi, G. T.

Pan, J.

J. Pan, Y. J. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. H. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
[CrossRef]

Papasimakis, N.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett.99(14), 147401 (2007).
[CrossRef] [PubMed]

Pati, G. S.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett.99(13), 133601 (2007).
[CrossRef] [PubMed]

Poon, A. W.

Poon, J. K. S.

Portalupi, S. L.

M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O'Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett.94(7), 071101 (2009).
[CrossRef]

Povinelli, M. L.

J. Pan, Y. J. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. H. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
[CrossRef]

S. Sandhu, M. L. Povinelli, and S. H. Fan, “Stopping and time reversing a light pulse using dynamic loss tuning of coupled-resonator delay lines,” Opt. Lett.32(22), 3333–3335 (2007).
[CrossRef] [PubMed]

Pradhan, S.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Prosvirnin, S. L.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett.99(14), 147401 (2007).
[CrossRef] [PubMed]

Qiu, X. G.

F. Cheng, H. F. Liu, B. H. Li, J. Han, H. Xiao, X. F. Han, C. Z. Gu, and X. G. Qiu, “Tuning asymmetry parameter of Fano resonance of spoof surface plasmons by modes coupling,” Appl. Phys. Lett.100(13), 131110 (2012).
[CrossRef]

Rose, M.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett.99(14), 147401 (2007).
[CrossRef] [PubMed]

Rosenberger, A. T.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A69(6), 063804 (2004).
[CrossRef]

Salit, K.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett.99(13), 133601 (2007).
[CrossRef] [PubMed]

Salit, M.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett.99(13), 133601 (2007).
[CrossRef] [PubMed]

Sandhu, S.

J. Pan, Y. J. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. H. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
[CrossRef]

S. Sandhu, M. L. Povinelli, and S. H. Fan, “Stopping and time reversing a light pulse using dynamic loss tuning of coupled-resonator delay lines,” Opt. Lett.32(22), 3333–3335 (2007).
[CrossRef] [PubMed]

Scheuer, J.

Schmidt, B.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Shahriar, M. S.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett.99(13), 133601 (2007).
[CrossRef] [PubMed]

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J. T. Shen and S. H. Fan, “Coherent single photon transport in a one-dimensional waveguide coupled with superconducting quantum bits,” Phys. Rev. Lett.95(21), 213001 (2005).
[CrossRef] [PubMed]

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G. Shvets and Y. A. Urzhumov, “Engineering the electromagnetic properties of periodic nanostructures using electrostatic resonances,” Phys. Rev. Lett.93(24), 243902 (2004).
[CrossRef] [PubMed]

Smith, D. D.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A69(6), 063804 (2004).
[CrossRef]

Soljacic, M.

M. F. Yanik, S. H. Fan, and M. Soljačić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett.83(14), 2739–2741 (2003).
[CrossRef]

Sonnefraud, Y.

F. Hao, Y. Sonnefraud, P. Van Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

Stuhrmann, N.

J. Pan, Y. J. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. H. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
[CrossRef]

Sugiya, T.

Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factor in a photonic crystal nanocavity,” Nat. Mater.6(11), 862–865 (2007).
[CrossRef] [PubMed]

Sun, F. W.

B. B. Li, Y. F. Xiao, C. L. Zou, X. F. Jiang, Y. C. Liu, F. W. Sun, Y. Li, and Q. H. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100(2), 021108 (2012).
[CrossRef]

Tanabe, T.

T. Tanabe, M. Notomi, H. Taniyama, and E. Kuramochi, “Dynamic release of trapped light from an ultrahigh-Q nanocavity via adiabatic frequency tuning,” Phys. Rev. Lett.102(4), 043907 (2009).
[CrossRef] [PubMed]

Tanaka, Y.

Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factor in a photonic crystal nanocavity,” Nat. Mater.6(11), 862–865 (2007).
[CrossRef] [PubMed]

Taniyama, H.

T. Tanabe, M. Notomi, H. Taniyama, and E. Kuramochi, “Dynamic release of trapped light from an ultrahigh-Q nanocavity via adiabatic frequency tuning,” Phys. Rev. Lett.102(4), 043907 (2009).
[CrossRef] [PubMed]

Terrel, M.

Trebaol, S.

Y. Dumeige, S. Trebaol, and P. Feron, “Intracavity coupled-active-resonator-induced dispersion,” Phys. Rev. A79(1), 013832 (2009).
[CrossRef]

Y. Dumeige, T. K. N. Nguyen, L. Ghisa, S. Trebaol, and P. Feron, “Measurement of the dispersion induced by a slow-light system based on coupled active-resonator-induced transparency,” Phys. Rev. A78(1), 013818 (2008).
[CrossRef]

Upham, J.

Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factor in a photonic crystal nanocavity,” Nat. Mater.6(11), 862–865 (2007).
[CrossRef] [PubMed]

Urzhumov, Y. A.

G. Shvets and Y. A. Urzhumov, “Engineering the electromagnetic properties of periodic nanostructures using electrostatic resonances,” Phys. Rev. Lett.93(24), 243902 (2004).
[CrossRef] [PubMed]

Vahala, K. J.

Van Dorpe, P.

F. Hao, Y. Sonnefraud, P. Van Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

Wang, P.

Wen, Y. H.

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(17), 173902 (2009).
[CrossRef] [PubMed]

X. Yang, C. Husko, C. W. Wong, M. B. Yu, and D.-L. Kwong, “Observation of femtojoule optical bistability involving Fano resonances in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett.91(5), 051113 (2007).
[CrossRef]

Xiao, H.

F. Cheng, H. F. Liu, B. H. Li, J. Han, H. Xiao, X. F. Han, C. Z. Gu, and X. G. Qiu, “Tuning asymmetry parameter of Fano resonance of spoof surface plasmons by modes coupling,” Appl. Phys. Lett.100(13), 131110 (2012).
[CrossRef]

Xiao, Y. F.

B. B. Li, Y. F. Xiao, C. L. Zou, X. F. Jiang, Y. C. Liu, F. W. Sun, Y. Li, and Q. H. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100(2), 021108 (2012).
[CrossRef]

B. B. Li, Y. F. Xiao, C. L. Zou, Y. C. Liu, X. F. Jiang, Y. L. Chen, Y. Li, and Q. H. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98(2), 021116 (2011).
[CrossRef]

Xu, Q.

Q. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys.3(6), 406–410 (2007).
[CrossRef]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Yang, L.

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(17), 173902 (2009).
[CrossRef] [PubMed]

X. Yang, C. Husko, C. W. Wong, M. B. Yu, and D.-L. Kwong, “Observation of femtojoule optical bistability involving Fano resonances in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett.91(5), 051113 (2007).
[CrossRef]

Yanik, M. F.

M. F. Yanik, S. H. Fan, and M. Soljačić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett.83(14), 2739–2741 (2003).
[CrossRef]

Yao, J. Q.

Yariv, A.

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(17), 173902 (2009).
[CrossRef] [PubMed]

Yu, M. B.

X. Yang, C. Husko, C. W. Wong, M. B. Yu, and D.-L. Kwong, “Observation of femtojoule optical bistability involving Fano resonances in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett.91(5), 051113 (2007).
[CrossRef]

Zheludev, N. I.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9(9), 707–715 (2010).
[CrossRef] [PubMed]

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett.99(14), 147401 (2007).
[CrossRef] [PubMed]

Zhou, L. J.

Zou, C. L.

B. B. Li, Y. F. Xiao, C. L. Zou, X. F. Jiang, Y. C. Liu, F. W. Sun, Y. Li, and Q. H. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100(2), 021108 (2012).
[CrossRef]

B. B. Li, Y. F. Xiao, C. L. Zou, Y. C. Liu, X. F. Jiang, Y. L. Chen, Y. Li, and Q. H. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98(2), 021116 (2011).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (9)

X. Yang, C. Husko, C. W. Wong, M. B. Yu, and D.-L. Kwong, “Observation of femtojoule optical bistability involving Fano resonances in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett.91(5), 051113 (2007).
[CrossRef]

B. B. Li, Y. F. Xiao, C. L. Zou, X. F. Jiang, Y. C. Liu, F. W. Sun, Y. Li, and Q. H. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100(2), 021108 (2012).
[CrossRef]

M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O'Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett.94(7), 071101 (2009).
[CrossRef]

S. H. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett.80(6), 908–910 (2002).
[CrossRef]

C. Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett.83(8), 1527–1529 (2003).
[CrossRef]

J. Pan, Y. J. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. H. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
[CrossRef]

F. Cheng, H. F. Liu, B. H. Li, J. Han, H. Xiao, X. F. Han, C. Z. Gu, and X. G. Qiu, “Tuning asymmetry parameter of Fano resonance of spoof surface plasmons by modes coupling,” Appl. Phys. Lett.100(13), 131110 (2012).
[CrossRef]

B. B. Li, Y. F. Xiao, C. L. Zou, Y. C. Liu, X. F. Jiang, Y. L. Chen, Y. Li, and Q. H. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98(2), 021116 (2011).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic of a CRIT structure coupled Mach-Zehnder interferometer.

Fig. 2
Fig. 2

(a) Dependence of the asymmetry parameter q (solid curve) and the slope S( ω 0 ) (dashed curve) of the Fano resonance of the RCMZI on the loss parameter a 1 for different δϕ . (b) Dependence of the asymmetry parameter q (solid curve) and the slope S( ω 0 ) (dashed curve) of the Fano resonance of the RCMZI on the loss parameter a 1 for δϕ=0 and different ρ 2 . (c) Dependence of the asymmetry parameter q (solid curve) and the slope S( ω 0 ) (dashed curve) of the Fano resonance of the RCMZI on the loss parameter a 1 for δϕ=0 and different ρ 1 . In (a), or (b), or (c), the solid and dashed curves that are of same color are the results with the identical parameters. The other system parameters are ρ 1 =0.938 , ρ 2 =0.755 , a 2 =0.79 , τ 1 =15.2ns , and τ 2 =18.5ns .

Fig. 3
Fig. 3

The asymmetry parameter q (solid curve) of the Fano resonance of the RCMZI, the slope S( ω 0 ) (dashed curve) of the Fano resonance of the RCMZI, and the group delay τ g20 (dotted curve) of the CRIT structure depending on the loss parameter a 1 . The corresponding system parameters are ρ 1 =0.938 , ρ 2 =0.755 , a 2 =0.79 , a 1 =0.720 , τ 1 =15.2ns , and τ 2 =18.5ns .

Fig. 4
Fig. 4

Experiment setup. WDM: wavelength division multiplexer. Red and blue lines represent 1550 nm and 980 nm channels of WDMs; DET: InGaAs photodetector; OSC: digital oscilloscope; Input coupler and Output coupler: 3 dB coupler; Coupler A and Coupler B: 3 dB coupler. The configuration in the dashed box is a nearly balanced RCMZI that is implemented by coupling a CRIT structure to an arm of a fiber Mach–Zehnder interferometer.

Fig. 5
Fig. 5

The experimental (a) and theoretical (b) transmission spectra T 2 (Δ) of the CRIT structure depending on frequency detuning Δ= (ω ω 0 ) / 2π for the five different loss parameter a 1 values. In Fig. 5(a), the red, orange, yellow, green, and blue curves are measured under the 980 nm pump powers of 0 mW, 2.01 mW, 2.73 mW, 7.49 mW, and 12.4 mW, respectively. The corresponding inferred loss parameter a 1 values are 0.58 (red), 0.73 (orange), 0.75 (yellow), 0.82 (green), and 0.84 (blue). In Fig. 5(b), each dashed curve is produced by the experiment parameters of the solid curve of same color in Fig. 5(a).

Fig. 6
Fig. 6

The experimental (a) and theoretical (b) group delay τ g2 (Δ) curves of the CRIT structure depending on frequency detuning Δ= (ω ω 0 ) / 2π for the five different loss parameter a 1 values shown in Fig. 5. The solid curves in Figs. 5(a) and 6(a) that are of same color are simultaneously measured results with the identical loss parameter a 1 . In Fig. 6(b), each dashed curve is the corresponding theoretical simulation result of the solid curve of same color in Fig. 6(a).

Fig. 7
Fig. 7

The experimental (a) and theoretical (b) interference transmission spectra T out (Δ) of the RCMZI versus frequency detuning Δ= (ω ω 0 ) / 2π . (c) The experimental (solid curves) and fitting (dashed curves) interference transmission spectra T out (ε) of the RCMZI versus the reduced frequency detuning ε . The solid curves in Figs. 5(a), 6(a), and 7(a) that are of same color are simultaneously measured results with the identical loss parameter a 1 . In Fig. 7(a), for the five different loss parameter a 1 values, the phase shift difference Δϕ is 1.67(red), 1.62(orange), 1.61(yellow), 1.61(green), and 1.60(blue), respectively. In Fig. 7(b), each dashed curve is the corresponding theoretical simulation result of the solid curve of same color in Fig. 7(a).The theoretical (dashed curves in Fig. 7(b)) and fitting (dashed curves in Fig. 7(c)) interference transmission spectra are achieved by using Eqs. (1) and (3), respectively. In Fig. 7(c), each solid curve is obtained from the one of identical color in Fig. 7(a) by transforming the horizontal axis.

Tables (1)

Tables Icon

Table 1 The experimental results of q and S( ω 0 ) .

Equations (18)

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T out (ω)= | E out (ω) / E in (ω) | 2 = | t 2 (ω)exp(iΔϕ) | 2 /8 ,
S( ω 0 )= 1 τ 2 ( T out ω | ω 0 )= τ g20 | t 20 |sin( θ 20 Δϕ) 4 τ 2 ,
T out (ε)= (1+ ρ 2 2 2 ρ 2 δϕ) (ε+q) 2 8 ρ 2 2 ( ε 2 +1) + (1+ t 20 2 2 t 20 δϕ) 8( ε 2 +1) + (1 ρ 2 2 ) 2 8( ε 2 +1) (1 ρ 2 a 2 t 10 ) 2 (1+ ρ 2 2 2 ρ 2 δϕ) ,
q= (1 ρ 2 2 ) ρ 2 | τ g20 ( a 2 | t 10 | ρ 2 ) | [(1+ ρ 2 2 2 ρ 2 δϕ)(1 ρ 2 a 2 t 10 ) τ g20 ( a 2 | t 10 | ρ 2 )] .
τ g20 = (1 ρ 2 2 ) a 2 | t 10 |( τ g10 + τ 2 ) ( a 2 | t 10 | ρ 2 )(1 ρ 2 a 2 | t 10 |) ,
0= τ 2 τ 1 + a 1 (1 ρ 1 2 ) ( a 1 ρ 1 )(1 ρ 1 a 1 ) ,
a 1 = ( ρ 1 a 2 ± ρ 2 ) ( a 2 ± ρ 1 ρ 2 ) ,
a 1 = ρ 1 .
V 1 = η 1 I 1 ,
V 2 = η 2 I 2 = η 2 I 1 (1 ρ A 2 ) ρ out 2 a A / ρ A 2 ,
V 2 = η 2 I 2 = η 2 I 3 ρ B 2 (1 ρ out 2 ) a B / (1 ρ B 2 ) ,
V 3 = η 3 I 3 ,
χ A = η 2 (1 ρ A 2 ) ρ out 2 a A / ( η 1 ρ A 2 ) ,
χ B = η 2 ρ B 2 (1 ρ out 2 ) a B / [ η 3 (1 ρ B 2 )] .
V 1 = η 1 I 1 = η 1 I 0 ρ in 2 T 2 (ω) ρ A 2 a tr ,
V 2 = η 2 I 2 = η 2 I 1 (1 ρ A 2 ) ρ out 2 a A ρ A 2 + η 2 I 3 ρ B 2 (1 ρ out 2 ) a B (1 ρ B 2 ) +2 η 2 I 1 I 3 (1 ρ A 2 ) ρ out 2 a A ρ B 2 (1 ρ out 2 ) a B ρ A 2 (1 ρ B 2 ) ×cos( θ 2 Δϕ),
V 3 = η 3 I 3 = η 3 I 0 (1 ρ in 2 )(1 ρ B 2 ) a B / a ref .
θ 2 (ω)=Δϕ+arccos[ ( V 2 χ A V 1 χ B V 3 ) 2 χ A V 1 χ B V 3 ].

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