Abstract

We show that a linear chain of circular macroscopic resonators coupled in parallel demonstrates the phenomena of “superabsorption” and superradiance. Both the frequency spectrum of the transmitted light through the resonator chain and the decay rate of the resonator chain being prepared in a proper initial state are proportional to the number of resonators in the chain, N, and the intensity of the emitted radiation grows as N 2. The spectral bandwidth, the growth of the decay rate, and the intensity are restricted by the dispersion of the waveguides connecting the resonators.

© 2009 Optical Society of America

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2009 (1)

2008 (2)

F. L. Kien and K. Hakuta, "Cooperative enhancement of channeling of emission from atoms into a nanofiber," Phys. Rev. A 77, 013801 (2008).

S. F. Mingaleev, A. E. Miroshnichenko, and Y. S. Kivshar, "Coupled-resonator-induced reflection in photoniccrystal waveguide structures," Opt. Express 16, 11647-11659 (2008).
[PubMed]

2007 (5)

A. M. Kapitonov and V. N. Astratov, "Observation of nanojet-induced modes with small propagation losses in chains of coupled spherical cavities," Opt. Lett. 32, 409-411 (2007).
[PubMed]

S. Chavez-Cerda, H. M. M. Cessa, and J. R. M. Cessa, "Quantum-like entanglement in classical optics," Opt. Photon. News 12, 38-38 (2007).

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).

L. I. Deych, M. V. Erementchouk, A. A. Lisyansky, E. L. Ivchenko, and M. M. Voronov, "Exciton luminescence in one-dimensional resonant photonic crystals: A phenomenological approach," Phys. Rev. B 76, 075350 (2007).

J. Yao, D. Leuenberger, M.-C. M. Lee, and M. C. Wu, "Silicon microtoroidal resonators with integrated MEMS tunable coupler," IEEE J. Sel. Top. Quantum. Electron. 13, 202-208 (2007).

2006 (3)

2005 (2)

L. Maleki, A. B. Matsko, D. Strekalov, and A. A. Savchenkov, "Photonic media with whispering-gallery modes," Proc. SPIE 5708 180-186 (2005).

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).

2004 (7)

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

D. D. Smith and H. Chang, "Coherence phenomena in coupled optical resonators," J. Mod. Opt. 51, 25032513 (2004).

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

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Interference effects in lossy resonator chains," J. Mod. Opt. 51, 25152522 (2004).

W. Suh, Z. Wang, and S. Fan, "Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities," IEEE J. Quantum Electron. 40, 15111518 (2004).

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).
[PubMed]

L. Pilozzi, A. DAndrea, and K. Cho, "Optical response in multi-quantum wells under Bragg conditions," Phys. Stat. Sol. (C) 1, 14101419 (2004).

2003 (1)

O. Schwelb and I. Frigyes, "A design for a high finesse parallel-coupled microring resonator filter," Microwave Opt. Technol. Lett. 38, 125-129 (2003).

2001 (1)

T. Opatrny and D. G. Welsch, "Coupled cavities for enhancing the cross-phase-modulation in electromagnetically induced transparency," Phys. Rev. A 64, 023805 (2001).

2000 (1)

A. E. Siegman, "Laser beams and resonators: Beyond the 1960s," IEEE J. Sel. Top. Quantum Electron. 6, 1389-1399 (2000).

1999 (2)

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kukubun, "Second-order filter response from parallel coupled glass microring resonators," IEEE Phot. Tech. Lett. 11, 1426-1428 (1999).

M. Hubner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, "Optical lattices achieved by excitons in periodic quantum well structures," Phys. Rev. Lett. 83, 2841-2844 (1999).

1997 (2)

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

S. E. Harris, "Electromagnetically induced transparency," Phys. Today  50, 3642 (1997).

1995 (1)

D. Bouwmeester, N. H. Dekker, F. E. v. Dorsselaer, C. A. Schrama, P. M. Visser, and J. P. Woerdman, "Observation of Landau-Zener dynamics in classical optical systems," Phys. Rev. A 51 646-654 (1995).
[PubMed]

1994 (1)

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, "Bragg reflection of light from quantum-well structures," Phys. Solid State 36, 1156-1161 (1994).

1992 (2)

C. Pare, L. Gagnon, and P. A. Belanger, "Aspherical laser resonators: An analogy with quantum mechanics," Phys. Rev. A 46, 4150-4160 (1992).
[PubMed]

R. J. C. Spreeuw, M. W. Beijersbergen, and J. P. Woerdman, "Optical ring cavities as tailored four-level systems: An application of the group U(2,2)," Phys. Rev. A 45, 1213-1229 (1992).
[PubMed]

1991 (1)

K. Oda, N. Takato and H. Toba, "A wide-FSR waveguide double-ring resonator for optical FDM transmission systems," J. Lightwave Technol. 9, 728-736 (1991).

1990 (1)

R. J. C. Spreeuw, N. J. van Druten, M. W. Beijersbergen, E. R. Eliel, and J. P. Woerdman, "Classical realization of a strongly driven two-level system," Phys. Rev. Lett. 65 2642-2645 (1990).
[PubMed]

1989 (1)

A. Imamoglu, "Interference of radiatively broadened resonances," Phys. Rev. A 40, 2835 (1989).
[PubMed]

1988 (1)

1975 (1)

R. Bonifacio and L. A. Lugiato, "Cooperative radiation process in two-level systems: Superfluorescence," Phys. Rev. A 11, 1507-1521 (1975).

1954 (1)

R. H. Dicke, "Coherence in spontaneous radiation process," Phys. Rev. 93, 99-110 (1954).

Astratov, V. N.

Beijersbergen, M. W.

R. J. C. Spreeuw, N. J. van Druten, M. W. Beijersbergen, E. R. Eliel, and J. P. Woerdman, "Classical realization of a strongly driven two-level system," Phys. Rev. Lett. 65 2642-2645 (1990).
[PubMed]

Beijersbergen, M.W.

R. J. C. Spreeuw, M. W. Beijersbergen, and J. P. Woerdman, "Optical ring cavities as tailored four-level systems: An application of the group U(2,2)," Phys. Rev. A 45, 1213-1229 (1992).
[PubMed]

Belanger, P. A.

C. Pare, L. Gagnon, and P. A. Belanger, "Aspherical laser resonators: An analogy with quantum mechanics," Phys. Rev. A 46, 4150-4160 (1992).
[PubMed]

Bonifacio, R.

R. Bonifacio and L. A. Lugiato, "Cooperative radiation process in two-level systems: Superfluorescence," Phys. Rev. A 11, 1507-1521 (1975).

Bouwmeester, D.

D. Bouwmeester, N. H. Dekker, F. E. v. Dorsselaer, C. A. Schrama, P. M. Visser, and J. P. Woerdman, "Observation of Landau-Zener dynamics in classical optical systems," Phys. Rev. A 51 646-654 (1995).
[PubMed]

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).

Brick, P.

M. Hubner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, "Optical lattices achieved by excitons in periodic quantum well structures," Phys. Rev. Lett. 83, 2841-2844 (1999).

Cessa, H. M. M.

S. Chavez-Cerda, H. M. M. Cessa, and J. R. M. Cessa, "Quantum-like entanglement in classical optics," Opt. Photon. News 12, 38-38 (2007).

Cessa, J. R. M.

S. Chavez-Cerda, H. M. M. Cessa, and J. R. M. Cessa, "Quantum-like entanglement in classical optics," Opt. Photon. News 12, 38-38 (2007).

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).

D. D. Smith and H. Chang, "Coherence phenomena in coupled optical resonators," J. Mod. Opt. 51, 25032513 (2004).

Chavez-Cerda, S.

S. Chavez-Cerda, H. M. M. Cessa, and J. R. M. Cessa, "Quantum-like entanglement in classical optics," Opt. Photon. News 12, 38-38 (2007).

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).

Chu, S. T.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kukubun, "Second-order filter response from parallel coupled glass microring resonators," IEEE Phot. Tech. Lett. 11, 1426-1428 (1999).

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

Dekker, N. H.

D. Bouwmeester, N. H. Dekker, F. E. v. Dorsselaer, C. A. Schrama, P. M. Visser, and J. P. Woerdman, "Observation of Landau-Zener dynamics in classical optical systems," Phys. Rev. A 51 646-654 (1995).
[PubMed]

DeRose, G. A.

Deych, L. I.

L. I. Deych, M. V. Erementchouk, A. A. Lisyansky, E. L. Ivchenko, and M. M. Voronov, "Exciton luminescence in one-dimensional resonant photonic crystals: A phenomenological approach," Phys. Rev. B 76, 075350 (2007).

Dicke, R. H.

R. H. Dicke, "Coherence in spontaneous radiation process," Phys. Rev. 93, 99-110 (1954).

Dragoman, D.

Eliel, E. R.

R. J. C. Spreeuw, N. J. van Druten, M. W. Beijersbergen, E. R. Eliel, and J. P. Woerdman, "Classical realization of a strongly driven two-level system," Phys. Rev. Lett. 65 2642-2645 (1990).
[PubMed]

Ell, C.

M. Hubner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, "Optical lattices achieved by excitons in periodic quantum well structures," Phys. Rev. Lett. 83, 2841-2844 (1999).

Erementchouk, M. V.

L. I. Deych, M. V. Erementchouk, A. A. Lisyansky, E. L. Ivchenko, and M. M. Voronov, "Exciton luminescence in one-dimensional resonant photonic crystals: A phenomenological approach," Phys. Rev. B 76, 075350 (2007).

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).
[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).
[PubMed]

W. Suh, Z. Wang, and S. Fan, "Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities," IEEE J. Quantum Electron. 40, 15111518 (2004).

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).

Foresi, J.

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

Frigyes, I.

O. Schwelb and I. Frigyes, "A design for a high finesse parallel-coupled microring resonator filter," Microwave Opt. Technol. Lett. 38, 125-129 (2003).

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).

Gagnon, L.

C. Pare, L. Gagnon, and P. A. Belanger, "Aspherical laser resonators: An analogy with quantum mechanics," Phys. Rev. A 46, 4150-4160 (1992).
[PubMed]

Gibbs, H. M.

M. Hubner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, "Optical lattices achieved by excitons in periodic quantum well structures," Phys. Rev. Lett. 83, 2841-2844 (1999).

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).

Hakuta, K.

F. L. Kien and K. Hakuta, "Cooperative enhancement of channeling of emission from atoms into a nanofiber," Phys. Rev. A 77, 013801 (2008).

Harris, S. E.

S. E. Harris, "Electromagnetically induced transparency," Phys. Today  50, 3642 (1997).

Haus, H. A.

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

Hubner, M.

M. Hubner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, "Optical lattices achieved by excitons in periodic quantum well structures," Phys. Rev. Lett. 83, 2841-2844 (1999).

Ilchenko, V. S.

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

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Interference effects in lossy resonator chains," J. Mod. Opt. 51, 25152522 (2004).

Imamoglu, A.

A. Imamoglu, "Interference of radiatively broadened resonances," Phys. Rev. A 40, 2835 (1989).
[PubMed]

Ivchenko, E. L.

L. I. Deych, M. V. Erementchouk, A. A. Lisyansky, E. L. Ivchenko, and M. M. Voronov, "Exciton luminescence in one-dimensional resonant photonic crystals: A phenomenological approach," Phys. Rev. B 76, 075350 (2007).

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, "Bragg reflection of light from quantum-well structures," Phys. Solid State 36, 1156-1161 (1994).

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).

Jorda, S.

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, "Bragg reflection of light from quantum-well structures," Phys. Solid State 36, 1156-1161 (1994).

Kaneko, T.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kukubun, "Second-order filter response from parallel coupled glass microring resonators," IEEE Phot. Tech. Lett. 11, 1426-1428 (1999).

Kapitonov, A. M.

Khitrova, G.

M. Hubner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, "Optical lattices achieved by excitons in periodic quantum well structures," Phys. Rev. Lett. 83, 2841-2844 (1999).

Kien, F. L.

F. L. Kien and K. Hakuta, "Cooperative enhancement of channeling of emission from atoms into a nanofiber," Phys. Rev. A 77, 013801 (2008).

Kivshar, Y. S.

Koch, S. W.

M. Hubner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, "Optical lattices achieved by excitons in periodic quantum well structures," Phys. Rev. Lett. 83, 2841-2844 (1999).

Kukubun, Y.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kukubun, "Second-order filter response from parallel coupled glass microring resonators," IEEE Phot. Tech. Lett. 11, 1426-1428 (1999).

Laine, J. P.

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

Lee, E. S.

M. Hubner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, "Optical lattices achieved by excitons in periodic quantum well structures," Phys. Rev. Lett. 83, 2841-2844 (1999).

Lee, M.-C. M.

J. Yao, D. Leuenberger, M.-C. M. Lee, and M. C. Wu, "Silicon microtoroidal resonators with integrated MEMS tunable coupler," IEEE J. Sel. Top. Quantum. Electron. 13, 202-208 (2007).

Leuenberger, D.

J. Yao, D. Leuenberger, M.-C. M. Lee, and M. C. Wu, "Silicon microtoroidal resonators with integrated MEMS tunable coupler," IEEE J. Sel. Top. Quantum. Electron. 13, 202-208 (2007).

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).
[PubMed]

Q. Xu, J. Shakya, and M. Lipson, "Direct measurement of tunable optical delays on chip analogue to electromagnetically induced transparency," Opt. Express 14, 63-68 (2006).

Lisyansky, A. A.

L. I. Deych, M. V. Erementchouk, A. A. Lisyansky, E. L. Ivchenko, and M. M. Voronov, "Exciton luminescence in one-dimensional resonant photonic crystals: A phenomenological approach," Phys. Rev. B 76, 075350 (2007).

Little, B. E.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kukubun, "Second-order filter response from parallel coupled glass microring resonators," IEEE Phot. Tech. Lett. 11, 1426-1428 (1999).

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

Lugiato, L. A.

R. Bonifacio and L. A. Lugiato, "Cooperative radiation process in two-level systems: Superfluorescence," Phys. Rev. A 11, 1507-1521 (1975).

Maleki, L.

L. Maleki, A. B. Matsko, D. Strekalov, and A. A. Savchenkov, "Photonic media with whispering-gallery modes," Proc. SPIE 5708 180-186 (2005).

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

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Interference effects in lossy resonator chains," J. Mod. Opt. 51, 25152522 (2004).

Matsko, A. B.

L. Maleki, A. B. Matsko, D. Strekalov, and A. A. Savchenkov, "Photonic media with whispering-gallery modes," Proc. SPIE 5708 180-186 (2005).

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

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Interference effects in lossy resonator chains," J. Mod. Opt. 51, 25152522 (2004).

Mingaleev, S. F.

Miroshnichenko, A. E.

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).

Nesvizhskii, A. I.

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, "Bragg reflection of light from quantum-well structures," Phys. Solid State 36, 1156-1161 (1994).

Oda, K.

K. Oda, N. Takato and H. Toba, "A wide-FSR waveguide double-ring resonator for optical FDM transmission systems," J. Lightwave Technol. 9, 728-736 (1991).

Opatrny, T.

T. Opatrny and D. G. Welsch, "Coupled cavities for enhancing the cross-phase-modulation in electromagnetically induced transparency," Phys. Rev. A 64, 023805 (2001).

Pan, W.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kukubun, "Second-order filter response from parallel coupled glass microring resonators," IEEE Phot. Tech. Lett. 11, 1426-1428 (1999).

Pare, C.

C. Pare, L. Gagnon, and P. A. Belanger, "Aspherical laser resonators: An analogy with quantum mechanics," Phys. Rev. A 46, 4150-4160 (1992).
[PubMed]

Pilozzi, L.

L. Pilozzi, A. DAndrea, and K. Cho, "Optical response in multi-quantum wells under Bragg conditions," Phys. Stat. Sol. (C) 1, 14101419 (2004).

Poon, J. K.

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).
[PubMed]

Prineas, J. P.

M. Hubner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, "Optical lattices achieved by excitons in periodic quantum well structures," Phys. Rev. Lett. 83, 2841-2844 (1999).

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).

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).

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).
[PubMed]

Savchenkov, A. A.

L. Maleki, A. B. Matsko, D. Strekalov, and A. A. Savchenkov, "Photonic media with whispering-gallery modes," Proc. SPIE 5708 180-186 (2005).

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

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Interference effects in lossy resonator chains," J. Mod. Opt. 51, 25152522 (2004).

Schwelb, O.

O. Schwelb and I. Frigyes, "A design for a high finesse parallel-coupled microring resonator filter," Microwave Opt. Technol. Lett. 38, 125-129 (2003).

Shakya, J.

Q. Xu, J. Shakya, and M. Lipson, "Direct measurement of tunable optical delays on chip analogue to electromagnetically induced transparency," Opt. Express 14, 63-68 (2006).

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).
[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).

Siegman, A. E.

A. E. Siegman, "Laser beams and resonators: Beyond the 1960s," IEEE J. Sel. Top. Quantum Electron. 6, 1389-1399 (2000).

Smith, D. D.

D. D. Smith and H. Chang, "Coherence phenomena in coupled optical resonators," J. Mod. Opt. 51, 25032513 (2004).

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

Spreeuw, R. J. C.

R. J. C. Spreeuw, M. W. Beijersbergen, and J. P. Woerdman, "Optical ring cavities as tailored four-level systems: An application of the group U(2,2)," Phys. Rev. A 45, 1213-1229 (1992).
[PubMed]

R. J. C. Spreeuw, N. J. van Druten, M. W. Beijersbergen, E. R. Eliel, and J. P. Woerdman, "Classical realization of a strongly driven two-level system," Phys. Rev. Lett. 65 2642-2645 (1990).
[PubMed]

Strekalov, D.

L. Maleki, A. B. Matsko, D. Strekalov, and A. A. Savchenkov, "Photonic media with whispering-gallery modes," Proc. SPIE 5708 180-186 (2005).

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Interference effects in lossy resonator chains," J. Mod. Opt. 51, 25152522 (2004).

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).
[PubMed]

W. Suh, Z. Wang, and S. Fan, "Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities," IEEE J. Quantum Electron. 40, 15111518 (2004).

Takato, N.

K. Oda, N. Takato and H. Toba, "A wide-FSR waveguide double-ring resonator for optical FDM transmission systems," J. Lightwave Technol. 9, 728-736 (1991).

Toba, H.

K. Oda, N. Takato and H. Toba, "A wide-FSR waveguide double-ring resonator for optical FDM transmission systems," J. Lightwave Technol. 9, 728-736 (1991).

Urquhart, P.

van Druten, N. J.

R. J. C. Spreeuw, N. J. van Druten, M. W. Beijersbergen, E. R. Eliel, and J. P. Woerdman, "Classical realization of a strongly driven two-level system," Phys. Rev. Lett. 65 2642-2645 (1990).
[PubMed]

Voronov, M. M.

L. I. Deych, M. V. Erementchouk, A. A. Lisyansky, E. L. Ivchenko, and M. M. Voronov, "Exciton luminescence in one-dimensional resonant photonic crystals: A phenomenological approach," Phys. Rev. B 76, 075350 (2007).

Wang, Z.

W. Suh, Z. Wang, and S. Fan, "Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities," IEEE J. Quantum Electron. 40, 15111518 (2004).

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).
[PubMed]

Welsch, D. G.

T. Opatrny and D. G. Welsch, "Coupled cavities for enhancing the cross-phase-modulation in electromagnetically induced transparency," Phys. Rev. A 64, 023805 (2001).

Woerdman, J. P.

R. J. C. Spreeuw, M. W. Beijersbergen, and J. P. Woerdman, "Optical ring cavities as tailored four-level systems: An application of the group U(2,2)," Phys. Rev. A 45, 1213-1229 (1992).
[PubMed]

R. J. C. Spreeuw, N. J. van Druten, M. W. Beijersbergen, E. R. Eliel, and J. P. Woerdman, "Classical realization of a strongly driven two-level system," Phys. Rev. Lett. 65 2642-2645 (1990).
[PubMed]

Wu, M. C.

J. Yao, D. Leuenberger, M.-C. M. Lee, and M. C. Wu, "Silicon microtoroidal resonators with integrated MEMS tunable coupler," IEEE J. Sel. Top. Quantum. Electron. 13, 202-208 (2007).

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).

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).
[PubMed]

Q. Xu, J. Shakya, and M. Lipson, "Direct measurement of tunable optical delays on chip analogue to electromagnetically induced transparency," Opt. Express 14, 63-68 (2006).

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).
[PubMed]

Yao, J.

J. Yao, D. Leuenberger, M.-C. M. Lee, and M. C. Wu, "Silicon microtoroidal resonators with integrated MEMS tunable coupler," IEEE J. Sel. Top. Quantum. Electron. 13, 202-208 (2007).

Yariv, A.

Zhu, 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).

IEEE J. Quantum Electron. (1)

W. Suh, Z. Wang, and S. Fan, "Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities," IEEE J. Quantum Electron. 40, 15111518 (2004).

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

A. E. Siegman, "Laser beams and resonators: Beyond the 1960s," IEEE J. Sel. Top. Quantum Electron. 6, 1389-1399 (2000).

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

J. Yao, D. Leuenberger, M.-C. M. Lee, and M. C. Wu, "Silicon microtoroidal resonators with integrated MEMS tunable coupler," IEEE J. Sel. Top. Quantum. Electron. 13, 202-208 (2007).

IEEE Phot. Tech. Lett. (1)

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kukubun, "Second-order filter response from parallel coupled glass microring resonators," IEEE Phot. Tech. Lett. 11, 1426-1428 (1999).

J. Lightwave Technol. (2)

K. Oda, N. Takato and H. Toba, "A wide-FSR waveguide double-ring resonator for optical FDM transmission systems," J. Lightwave Technol. 9, 728-736 (1991).

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

J. Mod. Opt. (2)

D. D. Smith and H. Chang, "Coherence phenomena in coupled optical resonators," J. Mod. Opt. 51, 25032513 (2004).

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Interference effects in lossy resonator chains," J. Mod. Opt. 51, 25152522 (2004).

J. Opt. Soc. Am. A (2)

Microwave Opt. Technol. Lett. (1)

O. Schwelb and I. Frigyes, "A design for a high finesse parallel-coupled microring resonator filter," Microwave Opt. Technol. Lett. 38, 125-129 (2003).

Opt. Express (2)

Opt. Lett. (3)

Opt. Photon. News (1)

S. Chavez-Cerda, H. M. M. Cessa, and J. R. M. Cessa, "Quantum-like entanglement in classical optics," Opt. Photon. News 12, 38-38 (2007).

Phys. Rev. (1)

R. H. Dicke, "Coherence in spontaneous radiation process," Phys. Rev. 93, 99-110 (1954).

Phys. Rev. A (10)

R. Bonifacio and L. A. Lugiato, "Cooperative radiation process in two-level systems: Superfluorescence," Phys. Rev. A 11, 1507-1521 (1975).

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).

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).

A. Imamoglu, "Interference of radiatively broadened resonances," Phys. Rev. A 40, 2835 (1989).
[PubMed]

T. Opatrny and D. G. Welsch, "Coupled cavities for enhancing the cross-phase-modulation in electromagnetically induced transparency," Phys. Rev. A 64, 023805 (2001).

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).

C. Pare, L. Gagnon, and P. A. Belanger, "Aspherical laser resonators: An analogy with quantum mechanics," Phys. Rev. A 46, 4150-4160 (1992).
[PubMed]

R. J. C. Spreeuw, M. W. Beijersbergen, and J. P. Woerdman, "Optical ring cavities as tailored four-level systems: An application of the group U(2,2)," Phys. Rev. A 45, 1213-1229 (1992).
[PubMed]

D. Bouwmeester, N. H. Dekker, F. E. v. Dorsselaer, C. A. Schrama, P. M. Visser, and J. P. Woerdman, "Observation of Landau-Zener dynamics in classical optical systems," Phys. Rev. A 51 646-654 (1995).
[PubMed]

F. L. Kien and K. Hakuta, "Cooperative enhancement of channeling of emission from atoms into a nanofiber," Phys. Rev. A 77, 013801 (2008).

Phys. Rev. B (1)

L. I. Deych, M. V. Erementchouk, A. A. Lisyansky, E. L. Ivchenko, and M. M. Voronov, "Exciton luminescence in one-dimensional resonant photonic crystals: A phenomenological approach," Phys. Rev. B 76, 075350 (2007).

Phys. Rev. Lett. (4)

M. Hubner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, "Optical lattices achieved by excitons in periodic quantum well structures," Phys. Rev. Lett. 83, 2841-2844 (1999).

R. J. C. Spreeuw, N. J. van Druten, M. W. Beijersbergen, E. R. Eliel, and J. P. Woerdman, "Classical realization of a strongly driven two-level system," Phys. Rev. Lett. 65 2642-2645 (1990).
[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).
[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).
[PubMed]

Phys. Solid State (1)

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, "Bragg reflection of light from quantum-well structures," Phys. Solid State 36, 1156-1161 (1994).

Phys. Stat. Sol. (C) (1)

L. Pilozzi, A. DAndrea, and K. Cho, "Optical response in multi-quantum wells under Bragg conditions," Phys. Stat. Sol. (C) 1, 14101419 (2004).

Phys. Today (1)

S. E. Harris, "Electromagnetically induced transparency," Phys. Today  50, 3642 (1997).

Proc. SPIE (1)

L. Maleki, A. B. Matsko, D. Strekalov, and A. A. Savchenkov, "Photonic media with whispering-gallery modes," Proc. SPIE 5708 180-186 (2005).

Other (5)

J. Heebner, R. Grover, and T. A. Ibrahim, Optical Microresonators: Theory, Fabrication, and Applications (Springer-Verlag, London, 2008).

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, "Fano resonance in nanoscale structures," arXiv.org > condmat > arXiv:0902.3014

A. E. Siegman, Lasers (University Science Books, Mill Valley, California, 1986).

F. Xia, L. Sekaric, and Y. Vlasov, "Resonantly enhanced all optical buffers on a silicon chip," IEEE Proceedings of Photonics in Switching Symposium, pp. 7-8 (2007).

D. Dragoman and M. Dragoman, Quantum-Classical Analogies (Springer, 2004).

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Figures (2)

Fig. 1.
Fig. 1.

(a) A chain of circular resonators in parallel configuration. (b) The resonators are connected to the external environment through single mode waveguides and, due to the interference of the decays, interact with each other. Such an interaction leads to the superradiance phenomenon in the resonator chain.

Fig. 2.
Fig. 2.

Stop-band formed by one (solid line), two (dashed line), three (dotted line), five (dash-dotted line), and eight (dash-dot-dotted line) resonators in the parallel configuration with (a) L=0 and (b) L=2πa. The individual resonator has finesse F=27, so that Nmax =4 Eq. (6). The lineshape for the first three lines is given by Eq. (3).

Equations (7)

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

(b1b2)=(1T2iTiT1T2)(α1eiπk(ω)αα2),
(b3(j+1)α2(j+1))=([1T2e2iπk(ω)α]eik(ω)L(1e2iπk(ω)α)1T2eiπk(ω)αT2(1e2iπk(ω)α)1T2eiπk(ω)αT2(1e2iπk(ω)α1T2)[1+(1+T2)e2iπk(ω)α]eik(ω)L(1e2iπk(ω)α1T2))(b3(j)α2(j)),
t (ωω0)2N2γ2+(ωω0)2 ,
r N2γ2N2γ2+(ωω0)2 ,
vj+1=Ujvj=(eikL00eikL)vj,
Nmax<2Fπ,
e˙j+γΣl=1l=Nel=0 ,

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