Abstract

This paper presents theoretical studies on the ring-bus-ring (RBR) resonator system, which consist of two resonators indirectly coupled through a center waveguide between them. By controlling the intercavity interaction and engineering the phase response through incorporation of RBR with Mach–Zehnder interferometer, we show that it is possible to generate a spectrum resembling electromagnetically induced transparency (EIT), which is qualitatively different compared to other existing EIT schemes. The transparency becomes sharper as the coupling strength between resonators is increased, with the background spectrum significantly reduced as a result of additional phase shift from indirect coupling. In addition, the EIT-like spectrum is generated out of low-finesse resonators, in contrast with existing EIT schemes where the resonator’s finesse is required to be high. Comparisons with finite-difference-time-domain simulation show fairly a good agreement with analytical formulations.

© 2011 Optical Society of America

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  1. J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photonics Technol. Lett. 12, 320-322(2000).
    [CrossRef]
  2. J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12, 90-103 (2004).
    [CrossRef] [PubMed]
  3. S. Darmawan, Y. M. Landobasa, and M. K. Chin, “Pole-zero dynamics of high-order ring resonator filters,” J. Lightwave Technol. 25, 1568-1575 (2007).
    [CrossRef]
  4. V. Van, T. N. Ding, W. N. Herman, and P. T. Ho, “Group delay enhancement in circular arrays of microring resonators,” IEEE Photonics Technol. Lett. 20, 997-999 (2008).
    [CrossRef]
  5. L. Zhang, M. Song, T. Wu, L. Zou, R. G. Beausoleil, and A. E. Willner, “Embedded ring resonators for microphotonic applications,” Opt. Lett. 33, 1978-1980 (2008).
    [CrossRef] [PubMed]
  6. S. Darmawan, Y. M. Landobasa, and M. K. Chin, “Nested ring Mach-Zehnder interferometer,” Opt. Express 15, 437-448(2007).
    [CrossRef] [PubMed]
  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]
  8. L. Maleki, A. B. Matsko, A. A. Savchenkov, and V. S. IIchenko, “Tunable delay line with interacting whispering-gallery-mode resonators,” Opt. Lett. 29, 626-628 (2004).
    [CrossRef] [PubMed]
  9. M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
    [CrossRef] [PubMed]
  10. 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]
  11. 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]
  12. K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98, 213904(2007).
    [CrossRef] [PubMed]
  13. Y. Dumeige, T. K. N. Nguyên, L. Ghişa, S. Trebaol, and P. Féron, “Measurement of the dispersion induced by a slow-light system based on coupled active-resonator-induced transparency,” Phys. Rev. A 78, 013818 (2008).
    [CrossRef]
  14. M. D. Lukin and A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature 413, 273-276(2001).
    [CrossRef] [PubMed]
  15. L. Y. M. Tobing, S. Darmawan, D. R. Lim, M. K. Chin, and T. Mei, “Relaxation of critical coupling condition and characterization of coupling-induced frequency shift in two-ring structures,” IEEE J. Sel. Top. Quantum Electron. 16, 77-84 (2010).
    [CrossRef]
  16. S. Darmawan, Y. M. Landobasa, P. Dumon, R. Baets, and M. K. Chin, “Resonance enhancement in silicon-on-insulator-based two-ring Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett. 20, 1560-1562 (2008).
    [CrossRef]
  17. S. L. Chuang, “Application of the strongly coupled-mode theory to integrated optical device,” IEEE J. Quantum Electron. 23, 499-509 (1987).
    [CrossRef]
  18. 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]
  19. A. M. Prabhu, V. Van, W. N. Herman, and P. T. Ho, “Compact silicon microring-assisted directional couplers for optical signal processing applications,” Opt. Lett. 34, 1249 (2009).
    [CrossRef] [PubMed]
  20. S. Darmawan, L. Y. M. Tobing, and T. Mei, “Coupling induced phase shift in a microring-coupled Mach-Zehnder interferometer,” Opt. Lett. 35, 238 (2010).
    [CrossRef] [PubMed]

2010 (2)

L. Y. M. Tobing, S. Darmawan, D. R. Lim, M. K. Chin, and T. Mei, “Relaxation of critical coupling condition and characterization of coupling-induced frequency shift in two-ring structures,” IEEE J. Sel. Top. Quantum Electron. 16, 77-84 (2010).
[CrossRef]

S. Darmawan, L. Y. M. Tobing, and T. Mei, “Coupling induced phase shift in a microring-coupled Mach-Zehnder interferometer,” Opt. Lett. 35, 238 (2010).
[CrossRef] [PubMed]

2009 (1)

2008 (4)

S. Darmawan, Y. M. Landobasa, P. Dumon, R. Baets, and M. K. Chin, “Resonance enhancement in silicon-on-insulator-based two-ring Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett. 20, 1560-1562 (2008).
[CrossRef]

Y. Dumeige, T. K. N. Nguyên, L. Ghişa, S. Trebaol, and P. Féron, “Measurement of the dispersion induced by a slow-light system based on coupled active-resonator-induced transparency,” Phys. Rev. A 78, 013818 (2008).
[CrossRef]

V. Van, T. N. Ding, W. N. Herman, and P. T. Ho, “Group delay enhancement in circular arrays of microring resonators,” IEEE Photonics Technol. Lett. 20, 997-999 (2008).
[CrossRef]

L. Zhang, M. Song, T. Wu, L. Zou, R. G. Beausoleil, and A. E. Willner, “Embedded ring resonators for microphotonic applications,” Opt. Lett. 33, 1978-1980 (2008).
[CrossRef] [PubMed]

2007 (3)

2006 (2)

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]

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]

2005 (1)

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 (4)

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12, 90-103 (2004).
[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]

L. Maleki, A. B. Matsko, A. A. Savchenkov, and V. S. IIchenko, “Tunable delay line with interacting whispering-gallery-mode resonators,” Opt. Lett. 29, 626-628 (2004).
[CrossRef] [PubMed]

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef] [PubMed]

2001 (1)

M. D. Lukin and A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature 413, 273-276(2001).
[CrossRef] [PubMed]

2000 (1)

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photonics Technol. Lett. 12, 320-322(2000).
[CrossRef]

1987 (1)

S. L. Chuang, “Application of the strongly coupled-mode theory to integrated optical device,” IEEE J. Quantum Electron. 23, 499-509 (1987).
[CrossRef]

Absil, P. P.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photonics Technol. Lett. 12, 320-322(2000).
[CrossRef]

Baets, R.

S. Darmawan, Y. M. Landobasa, P. Dumon, R. Baets, and M. K. Chin, “Resonance enhancement in silicon-on-insulator-based two-ring Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett. 20, 1560-1562 (2008).
[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]

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]

Chin, M. K.

L. Y. M. Tobing, S. Darmawan, D. R. Lim, M. K. Chin, and T. Mei, “Relaxation of critical coupling condition and characterization of coupling-induced frequency shift in two-ring structures,” IEEE J. Sel. Top. Quantum Electron. 16, 77-84 (2010).
[CrossRef]

S. Darmawan, Y. M. Landobasa, P. Dumon, R. Baets, and M. K. Chin, “Resonance enhancement in silicon-on-insulator-based two-ring Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett. 20, 1560-1562 (2008).
[CrossRef]

S. Darmawan, Y. M. Landobasa, and M. K. Chin, “Nested ring Mach-Zehnder interferometer,” Opt. Express 15, 437-448(2007).
[CrossRef] [PubMed]

S. Darmawan, Y. M. Landobasa, and M. K. Chin, “Pole-zero dynamics of high-order ring resonator filters,” J. Lightwave Technol. 25, 1568-1575 (2007).
[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]

Chuang, S. L.

S. L. Chuang, “Application of the strongly coupled-mode theory to integrated optical device,” IEEE J. Quantum Electron. 23, 499-509 (1987).
[CrossRef]

Darmawan, S.

Ding, T. N.

V. Van, T. N. Ding, W. N. Herman, and P. T. Ho, “Group delay enhancement in circular arrays of microring resonators,” IEEE Photonics Technol. Lett. 20, 997-999 (2008).
[CrossRef]

Dumeige, Y.

Y. Dumeige, T. K. N. Nguyên, L. Ghişa, S. Trebaol, and P. Féron, “Measurement of the dispersion induced by a slow-light system based on coupled active-resonator-induced transparency,” Phys. Rev. A 78, 013818 (2008).
[CrossRef]

Dumon, P.

S. Darmawan, Y. M. Landobasa, P. Dumon, R. Baets, and M. K. Chin, “Resonance enhancement in silicon-on-insulator-based two-ring Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett. 20, 1560-1562 (2008).
[CrossRef]

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]

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef] [PubMed]

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]

Féron, P.

Y. Dumeige, T. K. N. Nguyên, L. Ghişa, S. Trebaol, and P. Féron, “Measurement of the dispersion induced by a slow-light system based on coupled active-resonator-induced transparency,” Phys. Rev. A 78, 013818 (2008).
[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]

Ghisa, L.

Y. Dumeige, T. K. N. Nguyên, L. Ghişa, S. Trebaol, and P. Féron, “Measurement of the dispersion induced by a slow-light system based on coupled active-resonator-induced transparency,” Phys. Rev. A 78, 013818 (2008).
[CrossRef]

Herman, W. N.

A. M. Prabhu, V. Van, W. N. Herman, and P. T. Ho, “Compact silicon microring-assisted directional couplers for optical signal processing applications,” Opt. Lett. 34, 1249 (2009).
[CrossRef] [PubMed]

V. Van, T. N. Ding, W. N. Herman, and P. T. Ho, “Group delay enhancement in circular arrays of microring resonators,” IEEE Photonics Technol. Lett. 20, 997-999 (2008).
[CrossRef]

Ho, P. T.

A. M. Prabhu, V. Van, W. N. Herman, and P. T. Ho, “Compact silicon microring-assisted directional couplers for optical signal processing applications,” Opt. Lett. 34, 1249 (2009).
[CrossRef] [PubMed]

V. Van, T. N. Ding, W. N. Herman, and P. T. Ho, “Group delay enhancement in circular arrays of microring resonators,” IEEE Photonics Technol. Lett. 20, 997-999 (2008).
[CrossRef]

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photonics Technol. Lett. 12, 320-322(2000).
[CrossRef]

Hryniewicz, J. V.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photonics Technol. Lett. 12, 320-322(2000).
[CrossRef]

Huang, Y.

IIchenko, V. S.

Imamoglu, A.

M. D. Lukin and A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature 413, 273-276(2001).
[CrossRef] [PubMed]

Kobayashi, N.

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

Landobasa, Y. M.

Lim, D. R.

L. Y. M. Tobing, S. Darmawan, D. R. Lim, M. K. Chin, and T. Mei, “Relaxation of critical coupling condition and characterization of coupling-induced frequency shift in two-ring structures,” IEEE J. Sel. Top. Quantum Electron. 16, 77-84 (2010).
[CrossRef]

Lipson, M.

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.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photonics Technol. Lett. 12, 320-322(2000).
[CrossRef]

Lukin, M. D.

M. D. Lukin and A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature 413, 273-276(2001).
[CrossRef] [PubMed]

Maleki, L.

Mario, L. Y.

Matsko, A. B.

Mei, T.

L. Y. M. Tobing, S. Darmawan, D. R. Lim, M. K. Chin, and T. Mei, “Relaxation of critical coupling condition and characterization of coupling-induced frequency shift in two-ring structures,” IEEE J. Sel. Top. Quantum Electron. 16, 77-84 (2010).
[CrossRef]

S. Darmawan, L. Y. M. Tobing, and T. Mei, “Coupling induced phase shift in a microring-coupled Mach-Zehnder interferometer,” Opt. Lett. 35, 238 (2010).
[CrossRef] [PubMed]

Mookherjea, S.

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]

Nguyên, T. K. N.

Y. Dumeige, T. K. N. Nguyên, L. Ghişa, S. Trebaol, and P. Féron, “Measurement of the dispersion induced by a slow-light system based on coupled active-resonator-induced transparency,” Phys. Rev. A 78, 013818 (2008).
[CrossRef]

Paloczi, G. T.

Poon, J. K. S.

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]

Prabhu, A. M.

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]

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.

Scheuer, J.

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]

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]

Song, M.

Suh, W.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef] [PubMed]

Tobing, L. Y. M.

L. Y. M. Tobing, S. Darmawan, D. R. Lim, M. K. Chin, and T. Mei, “Relaxation of critical coupling condition and characterization of coupling-induced frequency shift in two-ring structures,” IEEE J. Sel. Top. Quantum Electron. 16, 77-84 (2010).
[CrossRef]

S. Darmawan, L. Y. M. Tobing, and T. Mei, “Coupling induced phase shift in a microring-coupled Mach-Zehnder interferometer,” Opt. Lett. 35, 238 (2010).
[CrossRef] [PubMed]

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]

Trebaol, S.

Y. Dumeige, T. K. N. Nguyên, L. Ghişa, S. Trebaol, and P. Féron, “Measurement of the dispersion induced by a slow-light system based on coupled active-resonator-induced transparency,” Phys. Rev. A 78, 013818 (2008).
[CrossRef]

Van, V.

A. M. Prabhu, V. Van, W. N. Herman, and P. T. Ho, “Compact silicon microring-assisted directional couplers for optical signal processing applications,” Opt. Lett. 34, 1249 (2009).
[CrossRef] [PubMed]

V. Van, T. N. Ding, W. N. Herman, and P. T. Ho, “Group delay enhancement in circular arrays of microring resonators,” IEEE Photonics Technol. Lett. 20, 997-999 (2008).
[CrossRef]

Wang, Z.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef] [PubMed]

Willner, A. E.

Wilson, R. A.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photonics Technol. Lett. 12, 320-322(2000).
[CrossRef]

Wu, T.

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]

Yanik, M. F.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef] [PubMed]

Yariv, A.

Zhang, L.

Zou, L.

IEEE J. Quantum Electron. (1)

S. L. Chuang, “Application of the strongly coupled-mode theory to integrated optical device,” IEEE J. Quantum Electron. 23, 499-509 (1987).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

L. Y. M. Tobing, S. Darmawan, D. R. Lim, M. K. Chin, and T. Mei, “Relaxation of critical coupling condition and characterization of coupling-induced frequency shift in two-ring structures,” IEEE J. Sel. Top. Quantum Electron. 16, 77-84 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

S. Darmawan, Y. M. Landobasa, P. Dumon, R. Baets, and M. K. Chin, “Resonance enhancement in silicon-on-insulator-based two-ring Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett. 20, 1560-1562 (2008).
[CrossRef]

IEEE Photonics Technol. Lett. (2)

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photonics Technol. Lett. 12, 320-322(2000).
[CrossRef]

V. Van, T. N. Ding, W. N. Herman, and P. T. Ho, “Group delay enhancement in circular arrays of microring resonators,” IEEE Photonics Technol. Lett. 20, 997-999 (2008).
[CrossRef]

J. Lightwave Technol. (1)

Nature (1)

M. D. Lukin and A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature 413, 273-276(2001).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (4)

Phys. Rev. A (3)

Y. Dumeige, T. K. N. Nguyên, L. Ghişa, S. Trebaol, and P. Féron, “Measurement of the dispersion induced by a slow-light system based on coupled active-resonator-induced transparency,” Phys. Rev. A 78, 013818 (2008).
[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. Lett. (3)

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[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]

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

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Figures (8)

Fig. 1
Fig. 1

(a) RBR device. (b) Proposed RBRMZI structure with the third optical pathway (P3) in the MZI. The dashed box indicates the tricoupler. (c) Two possible optical pathways (P1 and P2) excited in the RBR structure.

Fig. 2
Fig. 2

(a) Transmission spectrum and (b) buildup factors for different values of γ. (c) Fields distribution for γ = 1 , γ = 1.05 ( B 1 and B 2 maximum, and B 1 = B 2 ), and γ = 2 as calculated using the 2D-FDTD simulations.

Fig. 3
Fig. 3

(a) Buildup ratio B 21 = B 2 / B 1 of RBR for detuned cavity resonance. (b) Phase response of RBR, which can be decomposed of R1 and R2, respectively. The resonance order of 120 was chosen to reflect the typical dimensions of fabricated ring resonator ( γ = 1.05 ).

Fig. 4
Fig. 4

(a) Characteristics of EIT-like amplitude and phase spectrum. Various realizations of EIT-like spectrum in (b) mutually coupled resonators, (c) cascade of two indirectly coupled resonators, and (d) RBRMZI.

Fig. 5
Fig. 5

(a) Transmission of lossless and balanced RBRMZI ( T MZI ) for different r 0 . (b) Plot of B 1 and B 2 for corresponding r 0 values. The dashed lines indicate the resonance locations of the two resonators.

Fig. 6
Fig. 6

(a) Calculated finesse, finesse enhancement, and ER of RBRMZI (blue) and DRMZI (red) for a typical loss coefficient ( a 1 0.995 ) as a function of the coupling coefficient ( r 1 ). (b) Comparison of transmission spectrum of RBRMZI (blue) and DRMZI (red) for the same finesse ( 200 ). It can be seen that the envelope effect in DRMZI is much more serious compared to that in RBRMZI. The γ = 1.05 in RBR was chosen for illustration.

Fig. 7
Fig. 7

(a) Comparison between the 2D-FDTD calculations (thick faded) and the analytical method (thin bold) for RBR and RBRMZI. (b) Intensity distributions (in dB scale) of RBRMZI for two situations indicated in the spectrum. The fitted loss and size detuning are a 1 0.99 and γ 1.0497 , respectively.

Fig. 8
Fig. 8

Transmission of RBRMZI and the (a) associated buildup factors with (b) different coupling gaps (g; in microns).

Equations (24)

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[ b 1 b 0 b 2 ] = [ r 1 i t 1 t 12 i t 1 r 0 i t 2 t 21 i t 2 r 2 ] [ s 1 s 0 s 2 ] .
s 1 = ( i t 1 s 0 + t 12 s 2 ) A 1 / ( 1 r 1 A 1 ) , s 2 = ( i t 2 s 0 + t 21 s 1 ) A 2 / ( 1 r 2 A 2 ) , b 0 = r 0 s 0 + i t 1 s 1 + i t 2 s 2 ,
t RBR b 0 s 0 = r 0 r 2 A 1 r 1 A 2 + A 1 A 2 1 r 1 A 1 r 2 A 2 + r 0 A 1 A 2 ,
φ RBR = tan 1 [ a 1 r 2 sin δ 1 + a 2 r 1 sin δ 2 a 1 a 2 sin ( δ 1 + δ 2 ) r 0 ( a 1 r 2 cos δ 1 + a 2 r 1 cos δ 2 a 1 a 2 cos ( δ 1 + δ 2 ) ) ] + tan 1 [ a 1 r 1 sin δ 1 + a 2 r 2 sin δ 2 r 0 a 1 a 2 sin ( δ 1 + δ 2 ) 1 ( a 1 r 1 cos δ 1 + a 2 r 2 cos δ 2 r 0 a 1 a 2 cos ( δ 1 + δ 2 ) ) ] .
B 1 = | s 1 s 0 | 2 = | i t 1 ( 1 A 2 ) A 1 1 r 1 A 1 r 2 A 2 + r 0 A 1 A 2 | 2 , B 2 = | s 2 s 0 | 2 = | i t 2 ( 1 A 1 ) A 2 1 r 1 A 1 r 2 A 2 + r 0 A 1 A 2 | 2 ,
B 21 = B 2 B 1 = | i t 2 A 2 ( 1 A 1 ) i t 1 A 1 ( 1 A 2 ) | 2 a 1 , 2 1 ( t 2 t 1 ) 2 [ sin ( δ 1 / 2 ) sin ( δ 2 / 2 ) ] 2 .
γ δ 2 / δ 1 = L 2 / L 1 .
B 1 , 2 = | t 1 , 2 A 1 1 r 0 A 1 | 2 , T RBR | t RBR | 2 = | r 0 A 1 1 r 0 A 1 | 2 , B 21 = ( t 2 t 1 ) 2 .
t MZI | t MZI | exp ( i φ MZI ) = ( i 2 ) [ | t RBR | exp ( i φ RBR ) + exp ( i φ B ) ] = 1 2 exp ( i φ RBR + φ B + π 2 ) { | t RBR | exp [ i ( φ RBR φ B 2 ) ] + exp [ i ( φ RBR φ B 2 ) ] } ,
T MZI | t MZI | 2 = cos 2 ( φ RBR / 2 ) , φ MZI = ( φ RBR + π ) / 2 + arg [ cos ( φ RBR / 2 ) ] .
η = F CRIT / F one-ring ,
ER = T MZI ( δ CRIT ) / T MZI ( δ CRIT ± Δ δ ) ,
Ω β + K = ( β + κ 11 κ 1 0 κ 1 β + κ 00 κ 2 0 κ 2 β + κ 22 ) ( β ˜ 1 κ 1 0 κ 1 β ˜ 0 κ 2 0 κ 2 β ˜ 2 ) ,
κ p q = k 0 2 2 β q E p * ( r ) E q ( r ) [ ϵ ( r ) ϵ p ( r ) ] d r ,
σ 1 , 3 β ¯ ± δ = ( β ˜ 1 + β ˜ 0 ) 2 ± Δ β ˜ 2 + κ 2 , σ 2 = β ˜ 1 , ν 1 , 3 = [ 1 Δ β ˜ ± δ κ 1 κ 2 κ 1 ] T , ν 2 = [ 1 0 κ 1 κ 2 ] T .
[ b 1 b 0 b 2 ] = [ exp ( i σ 1 z ) exp ( i σ 2 z ) exp ( i σ 3 z ) ( δ Δ β ˜ κ 1 ) exp ( i σ 1 z ) 0 ( δ + Δ β ˜ κ 1 ) exp ( i σ 3 z ) ( κ 2 / κ 1 ) exp ( i σ 1 z ) ( κ 1 / κ 2 ) exp ( i σ 2 z ) ( κ 2 / κ 1 ) exp ( i σ 3 z ) ] [ c 1 c 0 c 2 ] ,
[ c 1 c 0 c 2 ] = [ κ 1 2 κ 2 ( δ + Δ β ˜ 2 δ ) κ 1 2 δ κ 1 κ 2 κ 2 ( δ + Δ β ˜ 2 δ ) κ 2 2 κ 2 0 κ 1 κ 2 κ 2 κ 1 2 κ 2 ( δ Δ β ˜ 2 δ ) κ 1 2 δ κ 1 κ 2 κ 2 ( δ Δ β ˜ 2 δ ) ] [ s 1 s 0 s 2 ] .
M 11 = ( κ 1 κ ) 2 [ cos ( δ z ) + i ( Δ β ˜ δ ) sin ( δ z ) ] exp ( i β ¯ z ) + ( κ 2 κ ) 2 exp ( i β ˜ 1 z ) , M 22 = [ cos ( δ z ) i ( Δ β ˜ δ ) sin ( δ z ) ] exp ( i β ¯ z ) , M 33 = ( κ 2 κ ) 2 [ cos ( δ z ) + i ( Δ β ˜ δ ) sin ( δ z ) ] exp ( i β ¯ z ) + ( κ 1 κ ) 2 exp ( i β ˜ 1 z ) , M 12 = M 21 = i ( κ 1 δ ) sin ( δ z ) exp ( i β ¯ z ) , M 23 = M 32 = i ( κ 2 δ ) sin ( δ z ) exp ( i β ¯ z ) , M 13 = M 31 = ( κ 1 κ 2 κ 2 ) [ cos ( δ z ) + i ( Δ β ˜ δ ) sin ( δ z ) ] exp ( i β ¯ z ) ( κ 1 κ 2 κ 2 ) exp ( i β ˜ 1 z ) .
[ b 1 b 0 b 2 ] = exp ( i β ¯ z ) [ r 1 exp ( i φ 1 ) i t 1 t 12 exp ( i φ 12 ) i t 1 r 0 exp ( i φ 0 ) i t 2 t 21 exp ( i φ 21 ) i t 2 r 2 exp ( i φ 2 ) ] [ s 1 s 0 s 2 ] .
r 0 = cos ( κ z ) , r 1 = ( κ 1 2 cos ( κ z ) + κ 2 2 ) / κ 2 , r 2 = ( κ 1 2 + κ 2 2 cos ( κ z ) ) / κ 2 , t 1 = ( κ 1 / κ ) sin ( κ z ) , t 2 = ( κ 2 / κ ) sin ( κ z ) , t 12 = t 21 = ( κ 1 κ 2 / κ 2 ) [ cos ( κ z ) 1 ] ,
t 1 , 2 = sin ( κ z ) 2 , r 1 , 2 = 1 + cos ( κ z ) 2 , r 0 = cos ( κ z ) , t 12 = t 21 = 1 cos ( κ z ) 2 .
r 2 + r 1 = κ 1 2 cos ( κ z ) + κ 2 2 κ 2 + κ 2 2 cos ( κ z ) + κ 1 2 κ 2 = ( κ 1 2 + κ 2 2 ) cos ( κ z ) + ( κ 1 2 + κ 2 2 ) κ 2 .
r 1 + r 2 = 1 + r 0 .
t 1 r 2 t 2 t 21 = t 1 , t 2 r 1 t 1 t 12 = t 2 , r 1 r 2 t 12 t 21 = r 0 , r 1 r 0 + t 1 2 = r 2 , r 0 r 2 + t 2 2 = r 1 , r 0 2 + t 1 2 + t 2 2 = 1 .

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