Abstract

We present general aspects of coupling among two or more families of modes with a view to deepen the insight on so-called “dark modes.” We first review the relationship of dark modes, “coherent population trapping,” “rotating wave approximation,” “coupled-mode theory,” and a few related concepts. The approach we emphasize is related either to inhomogeneous light–matter strong coupling or to the variety of multimode coupled systems designed for slowing down light or for filtering light. Some semantic caveats are discussed, notably down to what can be termed “dark” and “bright” in as simple a system as a distributed Bragg reflector case. A generic “NF” classification simply states that whatever the total number N of modes, the key point is the number NF of “prediagonal” families, since the number Nb of bright modes is simply NF leaving Nd=NNF dark modes.

© 2009 Optical Society of America

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2008 (4)

M. Wegener, J. L. Garcia-Pomar, C. M. Soukoulis, N. Meinzer, M. Ruther, and S. Linden, “Toy model for plasmonic metamaterial resonances coupled to two-level system gain,” Opt. Express 16, 19785-19798 (2008).
[CrossRef] [PubMed]

H. C. Liu and A. Yariv, “Grating induced transparency (GIT) and the dark mode in optical waveguides,” in Lasers and Electro-Optics, 2008 OSA Technical Digest Series (Optical Society of America, 2008), paper CMK5.

H. Kurt, H. Benisty, T. Melo, O. Khayam, and C. Cambournac, “Slow-light regime and critical coupling in highly multimode corrugated waveguides,” J. Opt. Soc. Am. B 25, C1-C14 (2008).
[CrossRef]

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

2007 (4)

J. E. Kihm, Y. C. Yoon, D. J. Park, Y. H. Ahn, C. Ropers, C. Lienau, J. Kim, Q. H. Park, and D. S. Kim, “Fabry-Perot tuning of the band-gap polarity in plasmonic crystals,” Phys. Rev. B 75, 035414 (2007).
[CrossRef]

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, H. Brenot, G. H. Duan, and W. Pernice, “In-plane Littrow lasing of broad photonic crystal waveguides,” Appl. Phys. Lett. 91, 041111 (2007).
[CrossRef]

H. Mertens, A. F. Koenderink, and A. Polman, “Plasmon-enhanced luminescence near noble-metal nanospheres: comparison of exact theory and an improved Gersten and Nitzan model,” Phys. Rev. B 76, 115123 (2007).
[CrossRef]

P. Chak, J. K. S. Poon, and A. Yariv, “Optical bright and dark states in side-coupled resonator structures,” Opt. Lett. 32, 1785-1787 (2007).
[CrossRef] [PubMed]

2005 (1)

2003 (3)

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

S. Olivier, H. Benisty, C. Weisbuch, C. J. Smith, T. F. Krauss, and R. Houdré, “Coupled-mode theory and propagation losses in photonic crystal waveguides,” Opt. Express 11, 1490-1496 (2003).
[CrossRef] [PubMed]

A. I. Streltsov, N. V. Dobrodey, and L. S. Cederbaum, “Charge transfer effects in molecule-negative ion complexes induced by core ionization,” J. Chem. Phys. 119, 3051-3062 (2003).
[CrossRef]

2002 (1)

S. Keshavamurthya, N. R. Cerruti, and S. Tomsovic, “Analyzing intramolecular vibrational energy redistribution via the overlap intensity-level velocity correlator,” J. Chem. Phys. 117, 4168-4177 (2002).
[CrossRef]

2001 (1)

1999 (4)

1998 (2)

R. Thissen, P. Lablanquie, R. I. Hall, M. Ukai, and K. Ito, “Photoionization of argon, krypton and xenon clusters in the inner valence shell region,” Eur. Phys. J. D 4, 335-342 (1998).
[CrossRef]

G. C. La Rocca, F. Bassani, and V. M. Agranovich, “Biexcitons and dark states in semiconductor microcavities,” J. Opt. Soc. Am. B 15, 652-660 (1998).
[CrossRef]

1996 (3)

H. Schmidt and A. Imamoglu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936-1938 (1996).
[CrossRef] [PubMed]

R. Houdré, R. P. Stanley, and M. Ilegems, “Strong coupling régime in the presence of inhomogeneous broadening: resolution of an homogeneous linewidth in an inhomogeneously broadened system,” Phys. Rev. A 53, 2711-2715 (1996).
[CrossRef] [PubMed]

E. Arimondo, “Coherent population trapping in laser spectroscopy,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1996), Vol. XXXV, pp. 257-354.
[CrossRef]

1995 (1)

M. Nirmal, D. J. Norris, M. Kuno, M. G. Bawendi, A. L. Efros, and M. Rosen, “Observation of the 'dark exciton' in CdSe quantum dots,” Phys. Rev. Lett. 75, 3728-3731 (1995).
[CrossRef] [PubMed]

1994 (1)

R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, “Measurement of cavity-polaritons dispersion curve from angle resolved photoluminescence experiments,” Phys. Rev. Lett. 73, 2043-2046 (1994).
[CrossRef] [PubMed]

1992 (1)

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69, 3314-3317 (1992).
[CrossRef] [PubMed]

1991 (3)

K. A. Shore, “Control of spontaneous emission in microcavity laser diodes,” Physica B 175, 123-126 (1991).
[CrossRef]

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593-2596 (1991).
[CrossRef] [PubMed]

H. A. Haus and Y. Lai, “Narrow-band distributed feedback reflector design,” J. Lightwave Technol. 9, 754-760 (1991).
[CrossRef]

1990 (2)

1989 (3)

A. Imamoglu and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett. 14, 1344-1346 (1989).
[CrossRef] [PubMed]

S. E. Harris, “Lasers without inversion: interference of lifetime broadened resonances,” Phys. Rev. Lett. 62, 1033-1036 (1989).
[CrossRef] [PubMed]

S. L. Coy, R. Hernandez, and K. K. Lehmann, “Limits on transitions to Gaussian orthogonal ensemble behaviour: saturated radiationless transitions between strongly coupled potential surfaces,” Phys. Rev. A 40, 5935-5949 (1989).
[CrossRef] [PubMed]

1988 (1)

F. T. Hioe and C. E. Carroll, “Coherent population trapping in N-level quantum systems,” Phys. Rev. A 37, 3000-3005 (1988).
[CrossRef] [PubMed]

1987 (1)

S. L. Coy and K. K. Lehmann, “Energy-level statistics for a relaxation Hamiltonian,” Phys. Rev. A 36, 404-407 (1987).
[CrossRef] [PubMed]

1983 (1)

L. Duckhwan and A. C. Albrecht, “On the interaction operator in the optical spectroscopies,” J. Chem. Phys. 78, 3382-3392 (1983).
[CrossRef]

1982 (1)

S. Haroche, “Superradiance: an essay on the theory of collective spontaneous emission,” Phys. Rep. 93, 301-396 (1982).
[CrossRef]

1981 (1)

F. T. Hioe and J. H. Eberly, “N-Level coherence vector and higher conservation laws in quantum optics and quantum mechanics,” Phys. Rev. Lett. 47, 838-841 (1981).
[CrossRef]

1979 (2)

J. R. Ackerhalt, J. H. Eberly, and B. W. Shore, “Statistical broadening and population loss in strongly excited three-level systems,” Phys. Rev. A 19, 248-263 (1979).
[CrossRef]

G. Alzetta, L. Moi, and G. Orriols, “Nonabsorption hyperfine resonances in a sodium vapour irradiated by a multimode dye-laser,” Nuovo Cimento Soc. Ital. Fis., B 52, 209-218 (1979).
[CrossRef]

1978 (1)

1976 (2)

E. Arimondo and G. Orriols, “Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping,” Lett. Nuovo Cimento Soc. Ital. Fis. 17, 333-338 (1976).
[CrossRef]

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of rf transitions and laser beat resonances in oriented Na vapour,” Nuovo Cimento Soc. Ital. Fis., B 36, 5-20 (1976).
[CrossRef]

1973 (1)

A. Yariv, “Coupled mode theory for guided wave optics,” IEEE J. Quantum Electron. 9, 919-933 (1973).
[CrossRef]

1972 (1)

H. Kogelnik and C. V. Shank, “Coupled wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327-2335 (1972).
[CrossRef]

1954 (1)

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99-110 (1954).
[CrossRef]

Ackerhalt, J. R.

J. R. Ackerhalt, J. H. Eberly, and B. W. Shore, “Statistical broadening and population loss in strongly excited three-level systems,” Phys. Rev. A 19, 248-263 (1979).
[CrossRef]

Agranovich, V. M.

Ahn, Y. H.

J. E. Kihm, Y. C. Yoon, D. J. Park, Y. H. Ahn, C. Ropers, C. Lienau, J. Kim, Q. H. Park, and D. S. Kim, “Fabry-Perot tuning of the band-gap polarity in plasmonic crystals,” Phys. Rev. B 75, 035414 (2007).
[CrossRef]

Albrecht, A. C.

L. Duckhwan and A. C. Albrecht, “On the interaction operator in the optical spectroscopies,” J. Chem. Phys. 78, 3382-3392 (1983).
[CrossRef]

Alzetta, G.

G. Alzetta, L. Moi, and G. Orriols, “Nonabsorption hyperfine resonances in a sodium vapour irradiated by a multimode dye-laser,” Nuovo Cimento Soc. Ital. Fis., B 52, 209-218 (1979).
[CrossRef]

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of rf transitions and laser beat resonances in oriented Na vapour,” Nuovo Cimento Soc. Ital. Fis., B 36, 5-20 (1976).
[CrossRef]

Arakawa, Y.

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69, 3314-3317 (1992).
[CrossRef] [PubMed]

Arimondo, E.

E. Arimondo, “Coherent population trapping in laser spectroscopy,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1996), Vol. XXXV, pp. 257-354.
[CrossRef]

E. Arimondo and G. Orriols, “Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping,” Lett. Nuovo Cimento Soc. Ital. Fis. 17, 333-338 (1976).
[CrossRef]

Ayre, M.

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, H. Brenot, G. H. Duan, and W. Pernice, “In-plane Littrow lasing of broad photonic crystal waveguides,” Appl. Phys. Lett. 91, 041111 (2007).
[CrossRef]

Bassani, F.

Bawendi, M. G.

M. Nirmal, D. J. Norris, M. Kuno, M. G. Bawendi, A. L. Efros, and M. Rosen, “Observation of the 'dark exciton' in CdSe quantum dots,” Phys. Rev. Lett. 75, 3728-3731 (1995).
[CrossRef] [PubMed]

Beausoleil, R. G.

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

Benisty, H.

Bergman, D. J.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

Boller, K. J.

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593-2596 (1991).
[CrossRef] [PubMed]

Brenot, H.

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, H. Brenot, G. H. Duan, and W. Pernice, “In-plane Littrow lasing of broad photonic crystal waveguides,” Appl. Phys. Lett. 91, 041111 (2007).
[CrossRef]

Budker, D.

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yaschuk, “Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxation,” Phys. Rev. Lett. 83, 1767-1770 (1999).
[CrossRef]

Cambournac, C.

H. Kurt, H. Benisty, T. Melo, O. Khayam, and C. Cambournac, “Slow-light regime and critical coupling in highly multimode corrugated waveguides,” J. Opt. Soc. Am. B 25, C1-C14 (2008).
[CrossRef]

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, H. Brenot, G. H. Duan, and W. Pernice, “In-plane Littrow lasing of broad photonic crystal waveguides,” Appl. Phys. Lett. 91, 041111 (2007).
[CrossRef]

Carroll, C. E.

F. T. Hioe and C. E. Carroll, “Coherent population trapping in N-level quantum systems,” Phys. Rev. A 37, 3000-3005 (1988).
[CrossRef] [PubMed]

Cassagne, D.

Cederbaum, L. S.

A. I. Streltsov, N. V. Dobrodey, and L. S. Cederbaum, “Charge transfer effects in molecule-negative ion complexes induced by core ionization,” J. Chem. Phys. 119, 3051-3062 (2003).
[CrossRef]

Cerruti, N. R.

S. Keshavamurthya, N. R. Cerruti, and S. Tomsovic, “Analyzing intramolecular vibrational energy redistribution via the overlap intensity-level velocity correlator,” J. Chem. Phys. 117, 4168-4177 (2002).
[CrossRef]

Chak, P.

Coy, S. L.

S. L. Coy, R. Hernandez, and K. K. Lehmann, “Limits on transitions to Gaussian orthogonal ensemble behaviour: saturated radiationless transitions between strongly coupled potential surfaces,” Phys. Rev. A 40, 5935-5949 (1989).
[CrossRef] [PubMed]

S. L. Coy and K. K. Lehmann, “Energy-level statistics for a relaxation Hamiltonian,” Phys. Rev. A 36, 404-407 (1987).
[CrossRef] [PubMed]

Davis, J.

DeLaRue, R. M.

Dicke, R. H.

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99-110 (1954).
[CrossRef]

Dobrodey, N. V.

A. I. Streltsov, N. V. Dobrodey, and L. S. Cederbaum, “Charge transfer effects in molecule-negative ion complexes induced by core ionization,” J. Chem. Phys. 119, 3051-3062 (2003).
[CrossRef]

Duan, G. H.

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, H. Brenot, G. H. Duan, and W. Pernice, “In-plane Littrow lasing of broad photonic crystal waveguides,” Appl. Phys. Lett. 91, 041111 (2007).
[CrossRef]

Duckhwan, L.

L. Duckhwan and A. C. Albrecht, “On the interaction operator in the optical spectroscopies,” J. Chem. Phys. 78, 3382-3392 (1983).
[CrossRef]

Eberly, J. H.

F. T. Hioe and J. H. Eberly, “N-Level coherence vector and higher conservation laws in quantum optics and quantum mechanics,” Phys. Rev. Lett. 47, 838-841 (1981).
[CrossRef]

J. R. Ackerhalt, J. H. Eberly, and B. W. Shore, “Statistical broadening and population loss in strongly excited three-level systems,” Phys. Rev. A 19, 248-263 (1979).
[CrossRef]

Efros, A. L.

M. Nirmal, D. J. Norris, M. Kuno, M. G. Bawendi, A. L. Efros, and M. Rosen, “Observation of the 'dark exciton' in CdSe quantum dots,” Phys. Rev. Lett. 75, 3728-3731 (1995).
[CrossRef] [PubMed]

Federov, M. V.

Fellow, L.

Garcia-Pomar, J. L.

Gozzini, A.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of rf transitions and laser beat resonances in oriented Na vapour,” Nuovo Cimento Soc. Ital. Fis., B 36, 5-20 (1976).
[CrossRef]

Gray, H. R.

Hall, R. I.

R. Thissen, P. Lablanquie, R. I. Hall, M. Ukai, and K. Ito, “Photoionization of argon, krypton and xenon clusters in the inner valence shell region,” Eur. Phys. J. D 4, 335-342 (1998).
[CrossRef]

Haroche, S.

S. Haroche, “Superradiance: an essay on the theory of collective spontaneous emission,” Phys. Rep. 93, 301-396 (1982).
[CrossRef]

Harris, S. E.

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593-2596 (1991).
[CrossRef] [PubMed]

A. Imamoglu and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett. 14, 1344-1346 (1989).
[CrossRef] [PubMed]

S. E. Harris, “Lasers without inversion: interference of lifetime broadened resonances,” Phys. Rev. Lett. 62, 1033-1036 (1989).
[CrossRef] [PubMed]

Haus, H. A.

H. A. Haus and Y. Lai, “Narrow-band distributed feedback reflector design,” J. Lightwave Technol. 9, 754-760 (1991).
[CrossRef]

Hernandez, R.

S. L. Coy, R. Hernandez, and K. K. Lehmann, “Limits on transitions to Gaussian orthogonal ensemble behaviour: saturated radiationless transitions between strongly coupled potential surfaces,” Phys. Rev. A 40, 5935-5949 (1989).
[CrossRef] [PubMed]

Hioe, F. T.

F. T. Hioe and C. E. Carroll, “Coherent population trapping in N-level quantum systems,” Phys. Rev. A 37, 3000-3005 (1988).
[CrossRef] [PubMed]

F. T. Hioe and J. H. Eberly, “N-Level coherence vector and higher conservation laws in quantum optics and quantum mechanics,” Phys. Rev. Lett. 47, 838-841 (1981).
[CrossRef]

Houdré, R.

S. Olivier, H. Benisty, C. Weisbuch, C. J. Smith, T. F. Krauss, and R. Houdré, “Coupled-mode theory and propagation losses in photonic crystal waveguides,” Opt. Express 11, 1490-1496 (2003).
[CrossRef] [PubMed]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. DeLaRue, R. Houdré, U. Oesterle, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063-2077 (1999).
[CrossRef]

R. Houdré, R. P. Stanley, and M. Ilegems, “Strong coupling régime in the presence of inhomogeneous broadening: resolution of an homogeneous linewidth in an inhomogeneously broadened system,” Phys. Rev. A 53, 2711-2715 (1996).
[CrossRef] [PubMed]

R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, “Measurement of cavity-polaritons dispersion curve from angle resolved photoluminescence experiments,” Phys. Rev. Lett. 73, 2043-2046 (1994).
[CrossRef] [PubMed]

Ilegems, M.

R. Houdré, R. P. Stanley, and M. Ilegems, “Strong coupling régime in the presence of inhomogeneous broadening: resolution of an homogeneous linewidth in an inhomogeneously broadened system,” Phys. Rev. A 53, 2711-2715 (1996).
[CrossRef] [PubMed]

R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, “Measurement of cavity-polaritons dispersion curve from angle resolved photoluminescence experiments,” Phys. Rev. Lett. 73, 2043-2046 (1994).
[CrossRef] [PubMed]

Imamoglu, A.

Ishikawa, A.

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69, 3314-3317 (1992).
[CrossRef] [PubMed]

Ito, K.

R. Thissen, P. Lablanquie, R. I. Hall, M. Ukai, and K. Ito, “Photoionization of argon, krypton and xenon clusters in the inner valence shell region,” Eur. Phys. J. D 4, 335-342 (1998).
[CrossRef]

Ivanov, M. Y.

Johnson, M.

Keshavamurthya, S.

S. Keshavamurthya, N. R. Cerruti, and S. Tomsovic, “Analyzing intramolecular vibrational energy redistribution via the overlap intensity-level velocity correlator,” J. Chem. Phys. 117, 4168-4177 (2002).
[CrossRef]

Khayam, O.

H. Kurt, H. Benisty, T. Melo, O. Khayam, and C. Cambournac, “Slow-light regime and critical coupling in highly multimode corrugated waveguides,” J. Opt. Soc. Am. B 25, C1-C14 (2008).
[CrossRef]

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, H. Brenot, G. H. Duan, and W. Pernice, “In-plane Littrow lasing of broad photonic crystal waveguides,” Appl. Phys. Lett. 91, 041111 (2007).
[CrossRef]

Kihm, J. E.

J. E. Kihm, Y. C. Yoon, D. J. Park, Y. H. Ahn, C. Ropers, C. Lienau, J. Kim, Q. H. Park, and D. S. Kim, “Fabry-Perot tuning of the band-gap polarity in plasmonic crystals,” Phys. Rev. B 75, 035414 (2007).
[CrossRef]

Kim, D. S.

J. E. Kihm, Y. C. Yoon, D. J. Park, Y. H. Ahn, C. Ropers, C. Lienau, J. Kim, Q. H. Park, and D. S. Kim, “Fabry-Perot tuning of the band-gap polarity in plasmonic crystals,” Phys. Rev. B 75, 035414 (2007).
[CrossRef]

Kim, J.

J. E. Kihm, Y. C. Yoon, D. J. Park, Y. H. Ahn, C. Ropers, C. Lienau, J. Kim, Q. H. Park, and D. S. Kim, “Fabry-Perot tuning of the band-gap polarity in plasmonic crystals,” Phys. Rev. B 75, 035414 (2007).
[CrossRef]

Kimball, D. F.

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yaschuk, “Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxation,” Phys. Rev. Lett. 83, 1767-1770 (1999).
[CrossRef]

Koenderink, A. F.

H. Mertens, A. F. Koenderink, and A. Polman, “Plasmon-enhanced luminescence near noble-metal nanospheres: comparison of exact theory and an improved Gersten and Nitzan model,” Phys. Rev. B 76, 115123 (2007).
[CrossRef]

Kogelnik, H.

H. Kogelnik and C. V. Shank, “Coupled wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327-2335 (1972).
[CrossRef]

Krauss, T. F.

Kulander, K. C.

Kuno, M.

M. Nirmal, D. J. Norris, M. Kuno, M. G. Bawendi, A. L. Efros, and M. Rosen, “Observation of the 'dark exciton' in CdSe quantum dots,” Phys. Rev. Lett. 75, 3728-3731 (1995).
[CrossRef] [PubMed]

Kurt, H.

La Rocca, G. C.

Labilloy, D.

Lablanquie, P.

R. Thissen, P. Lablanquie, R. I. Hall, M. Ukai, and K. Ito, “Photoionization of argon, krypton and xenon clusters in the inner valence shell region,” Eur. Phys. J. D 4, 335-342 (1998).
[CrossRef]

Lai, Y.

H. A. Haus and Y. Lai, “Narrow-band distributed feedback reflector design,” J. Lightwave Technol. 9, 754-760 (1991).
[CrossRef]

Lee, R. K.

Lehmann, K. K.

S. L. Coy, R. Hernandez, and K. K. Lehmann, “Limits on transitions to Gaussian orthogonal ensemble behaviour: saturated radiationless transitions between strongly coupled potential surfaces,” Phys. Rev. A 40, 5935-5949 (1989).
[CrossRef] [PubMed]

S. L. Coy and K. K. Lehmann, “Energy-level statistics for a relaxation Hamiltonian,” Phys. Rev. A 36, 404-407 (1987).
[CrossRef] [PubMed]

Lienau, C.

J. E. Kihm, Y. C. Yoon, D. J. Park, Y. H. Ahn, C. Ropers, C. Lienau, J. Kim, Q. H. Park, and D. S. Kim, “Fabry-Perot tuning of the band-gap polarity in plasmonic crystals,” Phys. Rev. B 75, 035414 (2007).
[CrossRef]

Linden, S.

Liu, H. C.

H. C. Liu and A. Yariv, “Grating induced transparency (GIT) and the dark mode in optical waveguides,” in Lasers and Electro-Optics, 2008 OSA Technical Digest Series (Optical Society of America, 2008), paper CMK5.

Meinzer, N.

Melo, T.

Mertens, H.

H. Mertens, A. F. Koenderink, and A. Polman, “Plasmon-enhanced luminescence near noble-metal nanospheres: comparison of exact theory and an improved Gersten and Nitzan model,” Phys. Rev. B 76, 115123 (2007).
[CrossRef]

Moi, L.

G. Alzetta, L. Moi, and G. Orriols, “Nonabsorption hyperfine resonances in a sodium vapour irradiated by a multimode dye-laser,” Nuovo Cimento Soc. Ital. Fis., B 52, 209-218 (1979).
[CrossRef]

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of rf transitions and laser beat resonances in oriented Na vapour,” Nuovo Cimento Soc. Ital. Fis., B 36, 5-20 (1976).
[CrossRef]

Nirmal, M.

M. Nirmal, D. J. Norris, M. Kuno, M. G. Bawendi, A. L. Efros, and M. Rosen, “Observation of the 'dark exciton' in CdSe quantum dots,” Phys. Rev. Lett. 75, 3728-3731 (1995).
[CrossRef] [PubMed]

Nishioka, M.

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69, 3314-3317 (1992).
[CrossRef] [PubMed]

Norris, D. J.

M. Nirmal, D. J. Norris, M. Kuno, M. G. Bawendi, A. L. Efros, and M. Rosen, “Observation of the 'dark exciton' in CdSe quantum dots,” Phys. Rev. Lett. 75, 3728-3731 (1995).
[CrossRef] [PubMed]

Oesterle, U.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. DeLaRue, R. Houdré, U. Oesterle, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063-2077 (1999).
[CrossRef]

R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, “Measurement of cavity-polaritons dispersion curve from angle resolved photoluminescence experiments,” Phys. Rev. Lett. 73, 2043-2046 (1994).
[CrossRef] [PubMed]

Olivier, S.

Orriols, G.

G. Alzetta, L. Moi, and G. Orriols, “Nonabsorption hyperfine resonances in a sodium vapour irradiated by a multimode dye-laser,” Nuovo Cimento Soc. Ital. Fis., B 52, 209-218 (1979).
[CrossRef]

E. Arimondo and G. Orriols, “Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping,” Lett. Nuovo Cimento Soc. Ital. Fis. 17, 333-338 (1976).
[CrossRef]

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of rf transitions and laser beat resonances in oriented Na vapour,” Nuovo Cimento Soc. Ital. Fis., B 36, 5-20 (1976).
[CrossRef]

Park, D. J.

J. E. Kihm, Y. C. Yoon, D. J. Park, Y. H. Ahn, C. Ropers, C. Lienau, J. Kim, Q. H. Park, and D. S. Kim, “Fabry-Perot tuning of the band-gap polarity in plasmonic crystals,” Phys. Rev. B 75, 035414 (2007).
[CrossRef]

Park, Q. H.

J. E. Kihm, Y. C. Yoon, D. J. Park, Y. H. Ahn, C. Ropers, C. Lienau, J. Kim, Q. H. Park, and D. S. Kim, “Fabry-Perot tuning of the band-gap polarity in plasmonic crystals,” Phys. Rev. B 75, 035414 (2007).
[CrossRef]

Pellandini, P.

R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, “Measurement of cavity-polaritons dispersion curve from angle resolved photoluminescence experiments,” Phys. Rev. Lett. 73, 2043-2046 (1994).
[CrossRef] [PubMed]

Peral, E.

Pernice, W.

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, H. Brenot, G. H. Duan, and W. Pernice, “In-plane Littrow lasing of broad photonic crystal waveguides,” Appl. Phys. Lett. 91, 041111 (2007).
[CrossRef]

Polman, A.

H. Mertens, A. F. Koenderink, and A. Polman, “Plasmon-enhanced luminescence near noble-metal nanospheres: comparison of exact theory and an improved Gersten and Nitzan model,” Phys. Rev. B 76, 115123 (2007).
[CrossRef]

Poon, J. K. S.

Rattier, M.

Rochester, S. M.

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yaschuk, “Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxation,” Phys. Rev. Lett. 83, 1767-1770 (1999).
[CrossRef]

Ropers, C.

J. E. Kihm, Y. C. Yoon, D. J. Park, Y. H. Ahn, C. Ropers, C. Lienau, J. Kim, Q. H. Park, and D. S. Kim, “Fabry-Perot tuning of the band-gap polarity in plasmonic crystals,” Phys. Rev. B 75, 035414 (2007).
[CrossRef]

Rosen, M.

M. Nirmal, D. J. Norris, M. Kuno, M. G. Bawendi, A. L. Efros, and M. Rosen, “Observation of the 'dark exciton' in CdSe quantum dots,” Phys. Rev. Lett. 75, 3728-3731 (1995).
[CrossRef] [PubMed]

Ruther, M.

Scherer, A.

Schmidt, H.

Shank, C. V.

H. Kogelnik and C. V. Shank, “Coupled wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327-2335 (1972).
[CrossRef]

Shore, B.

Shore, B. W.

J. R. Ackerhalt, J. H. Eberly, and B. W. Shore, “Statistical broadening and population loss in strongly excited three-level systems,” Phys. Rev. A 19, 248-263 (1979).
[CrossRef]

Shore, K. A.

K. A. Shore, “Control of spontaneous emission in microcavity laser diodes,” Physica B 175, 123-126 (1991).
[CrossRef]

Smith, C. J.

Smith, C. J. M.

Song, M.

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

Soukoulis, C. M.

Stanley, R. P.

R. Houdré, R. P. Stanley, and M. Ilegems, “Strong coupling régime in the presence of inhomogeneous broadening: resolution of an homogeneous linewidth in an inhomogeneously broadened system,” Phys. Rev. A 53, 2711-2715 (1996).
[CrossRef] [PubMed]

R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, “Measurement of cavity-polaritons dispersion curve from angle resolved photoluminescence experiments,” Phys. Rev. Lett. 73, 2043-2046 (1994).
[CrossRef] [PubMed]

Stockman, M. I.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

Streltsov, A. I.

A. I. Streltsov, N. V. Dobrodey, and L. S. Cederbaum, “Charge transfer effects in molecule-negative ion complexes induced by core ionization,” J. Chem. Phys. 119, 3051-3062 (2003).
[CrossRef]

Stroud, C. R.

Tamir, T.

T. Tamir, “Guided wave optoelectronics,” in Springer Series in Electronics and Photonics (Springer, 1990).
[CrossRef]

Thissen, R.

R. Thissen, P. Lablanquie, R. I. Hall, M. Ukai, and K. Ito, “Photoionization of argon, krypton and xenon clusters in the inner valence shell region,” Eur. Phys. J. D 4, 335-342 (1998).
[CrossRef]

Tomsovic, S.

S. Keshavamurthya, N. R. Cerruti, and S. Tomsovic, “Analyzing intramolecular vibrational energy redistribution via the overlap intensity-level velocity correlator,” J. Chem. Phys. 117, 4168-4177 (2002).
[CrossRef]

Ukai, M.

R. Thissen, P. Lablanquie, R. I. Hall, M. Ukai, and K. Ito, “Photoionization of argon, krypton and xenon clusters in the inner valence shell region,” Eur. Phys. J. D 4, 335-342 (1998).
[CrossRef]

Vuckovic, J.

Waks, E.

Wegener, M.

Weisbuch, C.

S. Olivier, H. Benisty, C. Weisbuch, C. J. Smith, T. F. Krauss, and R. Houdré, “Coupled-mode theory and propagation losses in photonic crystal waveguides,” Opt. Express 11, 1490-1496 (2003).
[CrossRef] [PubMed]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. DeLaRue, R. Houdré, U. Oesterle, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063-2077 (1999).
[CrossRef]

R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, “Measurement of cavity-polaritons dispersion curve from angle resolved photoluminescence experiments,” Phys. Rev. Lett. 73, 2043-2046 (1994).
[CrossRef] [PubMed]

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69, 3314-3317 (1992).
[CrossRef] [PubMed]

Whitley, R. M.

Willner, A. E.

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

Wu, T.

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

Xu, Y.

Yariv, A.

Yaschuk, V. V.

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yaschuk, “Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxation,” Phys. Rev. Lett. 83, 1767-1770 (1999).
[CrossRef]

Yoon, Y. C.

J. E. Kihm, Y. C. Yoon, D. J. Park, Y. H. Ahn, C. Ropers, C. Lienau, J. Kim, Q. H. Park, and D. S. Kim, “Fabry-Perot tuning of the band-gap polarity in plasmonic crystals,” Phys. Rev. B 75, 035414 (2007).
[CrossRef]

Zhang, L.

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

Zou, L.

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

Appl. Phys. Lett. (1)

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, H. Brenot, G. H. Duan, and W. Pernice, “In-plane Littrow lasing of broad photonic crystal waveguides,” Appl. Phys. Lett. 91, 041111 (2007).
[CrossRef]

Embedded ring resonators for microphotonics applications (1)

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

Eur. Phys. J. D (1)

R. Thissen, P. Lablanquie, R. I. Hall, M. Ukai, and K. Ito, “Photoionization of argon, krypton and xenon clusters in the inner valence shell region,” Eur. Phys. J. D 4, 335-342 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Yariv, “Coupled mode theory for guided wave optics,” IEEE J. Quantum Electron. 9, 919-933 (1973).
[CrossRef]

J. Appl. Phys. (1)

H. Kogelnik and C. V. Shank, “Coupled wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327-2335 (1972).
[CrossRef]

J. Chem. Phys. (3)

L. Duckhwan and A. C. Albrecht, “On the interaction operator in the optical spectroscopies,” J. Chem. Phys. 78, 3382-3392 (1983).
[CrossRef]

A. I. Streltsov, N. V. Dobrodey, and L. S. Cederbaum, “Charge transfer effects in molecule-negative ion complexes induced by core ionization,” J. Chem. Phys. 119, 3051-3062 (2003).
[CrossRef]

S. Keshavamurthya, N. R. Cerruti, and S. Tomsovic, “Analyzing intramolecular vibrational energy redistribution via the overlap intensity-level velocity correlator,” J. Chem. Phys. 117, 4168-4177 (2002).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. B (3)

Lett. Nuovo Cimento Soc. Ital. Fis. (1)

E. Arimondo and G. Orriols, “Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping,” Lett. Nuovo Cimento Soc. Ital. Fis. 17, 333-338 (1976).
[CrossRef]

Nuovo Cimento Soc. Ital. Fis., B (2)

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of rf transitions and laser beat resonances in oriented Na vapour,” Nuovo Cimento Soc. Ital. Fis., B 36, 5-20 (1976).
[CrossRef]

G. Alzetta, L. Moi, and G. Orriols, “Nonabsorption hyperfine resonances in a sodium vapour irradiated by a multimode dye-laser,” Nuovo Cimento Soc. Ital. Fis., B 52, 209-218 (1979).
[CrossRef]

Opt. Express (4)

Opt. Lett. (5)

Phys. Rep. (1)

S. Haroche, “Superradiance: an essay on the theory of collective spontaneous emission,” Phys. Rep. 93, 301-396 (1982).
[CrossRef]

Phys. Rev. (1)

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99-110 (1954).
[CrossRef]

Phys. Rev. A (5)

S. L. Coy, R. Hernandez, and K. K. Lehmann, “Limits on transitions to Gaussian orthogonal ensemble behaviour: saturated radiationless transitions between strongly coupled potential surfaces,” Phys. Rev. A 40, 5935-5949 (1989).
[CrossRef] [PubMed]

S. L. Coy and K. K. Lehmann, “Energy-level statistics for a relaxation Hamiltonian,” Phys. Rev. A 36, 404-407 (1987).
[CrossRef] [PubMed]

R. Houdré, R. P. Stanley, and M. Ilegems, “Strong coupling régime in the presence of inhomogeneous broadening: resolution of an homogeneous linewidth in an inhomogeneously broadened system,” Phys. Rev. A 53, 2711-2715 (1996).
[CrossRef] [PubMed]

F. T. Hioe and C. E. Carroll, “Coherent population trapping in N-level quantum systems,” Phys. Rev. A 37, 3000-3005 (1988).
[CrossRef] [PubMed]

J. R. Ackerhalt, J. H. Eberly, and B. W. Shore, “Statistical broadening and population loss in strongly excited three-level systems,” Phys. Rev. A 19, 248-263 (1979).
[CrossRef]

Phys. Rev. B (2)

H. Mertens, A. F. Koenderink, and A. Polman, “Plasmon-enhanced luminescence near noble-metal nanospheres: comparison of exact theory and an improved Gersten and Nitzan model,” Phys. Rev. B 76, 115123 (2007).
[CrossRef]

J. E. Kihm, Y. C. Yoon, D. J. Park, Y. H. Ahn, C. Ropers, C. Lienau, J. Kim, Q. H. Park, and D. S. Kim, “Fabry-Perot tuning of the band-gap polarity in plasmonic crystals,” Phys. Rev. B 75, 035414 (2007).
[CrossRef]

Phys. Rev. Lett. (8)

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

F. T. Hioe and J. H. Eberly, “N-Level coherence vector and higher conservation laws in quantum optics and quantum mechanics,” Phys. Rev. Lett. 47, 838-841 (1981).
[CrossRef]

S. E. Harris, “Lasers without inversion: interference of lifetime broadened resonances,” Phys. Rev. Lett. 62, 1033-1036 (1989).
[CrossRef] [PubMed]

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yaschuk, “Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxation,” Phys. Rev. Lett. 83, 1767-1770 (1999).
[CrossRef]

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593-2596 (1991).
[CrossRef] [PubMed]

M. Nirmal, D. J. Norris, M. Kuno, M. G. Bawendi, A. L. Efros, and M. Rosen, “Observation of the 'dark exciton' in CdSe quantum dots,” Phys. Rev. Lett. 75, 3728-3731 (1995).
[CrossRef] [PubMed]

R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, “Measurement of cavity-polaritons dispersion curve from angle resolved photoluminescence experiments,” Phys. Rev. Lett. 73, 2043-2046 (1994).
[CrossRef] [PubMed]

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69, 3314-3317 (1992).
[CrossRef] [PubMed]

Physica B (1)

K. A. Shore, “Control of spontaneous emission in microcavity laser diodes,” Physica B 175, 123-126 (1991).
[CrossRef]

Other (3)

E. Arimondo, “Coherent population trapping in laser spectroscopy,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1996), Vol. XXXV, pp. 257-354.
[CrossRef]

T. Tamir, “Guided wave optoelectronics,” in Springer Series in Electronics and Photonics (Springer, 1990).
[CrossRef]

H. C. Liu and A. Yariv, “Grating induced transparency (GIT) and the dark mode in optical waveguides,” in Lasers and Electro-Optics, 2008 OSA Technical Digest Series (Optical Society of America, 2008), paper CMK5.

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Figures (4)

Fig. 1
Fig. 1

Graphical solution of Eq. (2). The contributing homographic functions are thinner continuous dark gray lines, and each represents the response of a single oscillator. Solutions associated to bright and dark states are shown for a small E o value (dashed line) and for a more detuned value (dashed-dotted line).

Fig. 2
Fig. 2

Dispersion relation for one mode coupled to a manifold of { q } modes; (a) the single mode { p = 1 } is dispersionless; (b) the single mode { p = 1 } has backward dispersion; The ellipse-shaped line is the sum of real and imaginary wave vectors as is classical in the CMT approach.

Fig. 3
Fig. 3

Dispersion relation for a general case between { p } and { q } modes; (a) { p } modes are dispersionless; (b) { p } modes have backward dispersion; (c) and (d) are magnifications of the indicated regions of (a) and (b) showing the local advent of slow light flatbands.

Fig. 4
Fig. 4

(a) Dispersion of an ideal straight broad waveguide (hyperbolic branches); (b) same with folding at Brillouin zone edge; (c), (d) dispersion for 5 + 5 modes, with the indicated coupling. The closed curves, more intricate in (d), are again the sum of real plus imaginary parts of wave vectors in the coupled mode (CMT) approach. Case (d) shows maximal light slowdown in the indicated region.

Tables (1)

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Table 1 Uses of the Dark State Terminology: Domain, Relevant References, Comment

Equations (3)

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M = ( P G p q G q p Q ) , P = ( E 1 0 0 E n ) ,
Q = ( E p + 1 0 0 E p + q ) .
S ( λ ) = k = 1 q g k 2 ( E k λ ) 1 ( E o λ ) = 0 .

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