Abstract

We investigate the electromagnetically induced transparency (EIT) and nonlinear pulse propagation in a Λ-type three-level atomic gas filled in a slot waveguide, in which electric field is strongly confined inside the slot of the waveguide due to the discontinuity of dielectric constant. We find that EIT effect can be greatly enhanced due to the reduction of optical-field mode volume contributed by waveguide geometry. Comparing with the atomic gases in free space, the EIT transparency window in the slot waveguide system can be much wider and deeper, and the Kerr nonlinearity of probe laser field can be much stronger. We also prove that using slot waveguide ultraslow optical solitons can be produced efficiently with extremely low generation power.

© 2013 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Electromagnetically induced transparency and nonlinear pulse propagation in an atomic medium confined in a waveguide

Liang Li, Chengjie Zhu, L. Deng, and Guoxiang Huang
J. Opt. Soc. Am. B 30(1) 197-204 (2013)

Ultraslow optical solitons in atomic media with spontaneously generated coherence

Chao Hang and Guoxiang Huang
J. Opt. Soc. Am. B 29(8) 2009-2015 (2012)

Stern–Gerlach effect of multi-component ultraslow optical solitons via electromagnetically induced transparency

Zhiming Chen and Guoxiang Huang
J. Opt. Soc. Am. B 30(8) 2248-2256 (2013)

More Recommended Articles

References

  • View by:
  • Article Order
  • |
  • Year
  • |
  • Author
  • |
  • Publication
  1. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
    [Crossref]
  2. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature. 397, 594–598 (1999).
    [Crossref]
  3. M. M. Kash, V.A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M.O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
    [Crossref]
  4. A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3, 706–714 (2009).
    [Crossref]
  5. H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
    [Crossref]
  6. H. N. Dai, H. Zhang, S.-J. Yang, T.-M. Zhao, J. Rui, Y.-J. Deng, L. Li, N.-L. Liu, S. Chen, X.-H. Bao, X.-M. Jin, B. Zhao, and J.-W. Pan, “Holographic storage of biphoton entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
    [Crossref] [PubMed]
  7. C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
    [Crossref] [PubMed]
  8. C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
    [Crossref]
  9. Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904 (2004).
    [Crossref] [PubMed]
  10. G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E. 72, 016617 (2005).
    [Crossref]
  11. S. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. Engeness, M. Soljacic, S. Jacobs, J. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–779 (2001).
    [Crossref] [PubMed]
  12. S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
    [Crossref] [PubMed]
  13. S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, and A. L. Gaeta, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
    [Crossref] [PubMed]
  14. P. S. Light, F. Benabid, F. Couny, M. Maric, and A. N. Luiten, “Electromagnetically induced transparency in Rb-filled coated hollow-core photonic crystal fiber,” Opt. Lett. 32, 1323–1325 (2007).
    [Crossref] [PubMed]
  15. F. Benabid, P. Light, F. Couny, and P. Russell, “Electromagnetically-induced transparency grid in acetylene-filled hollow-core PCF,” Opt. Express 13, 5694–5703 (2005).
    [Crossref] [PubMed]
  16. M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
    [Crossref] [PubMed]
  17. A. D. Slepkov, A. R. Bhagwat, V. Venkataraman, P. Londero, and A. L. Gaeta, “Spectroscopy of Rb atoms in hollow-core fibers,” Phys. Rev. A 81, 053825 (2010).
    [Crossref]
  18. F. L. Kien and K. Hakuta, “Slowing down of a guided light field along a nanofiber in a cold atomic gas,” Phys. Rev. A. 79, 013818 (2009).
    [Crossref]
  19. V. R. Almeida, Q. Xu, C. A. Barrios, R. R. Panepucci, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29, 1209–1211 (2004).
    [Crossref] [PubMed]
  20. Q. Xu, V. R. Almeida, R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29, 1626–1628 (2004).
    [Crossref] [PubMed]
  21. M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. L. Savio, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
    [Crossref]
  22. K. Foubert, L. Lalouat, B. Cluzel, E. Picard, D. Peyrade, F. de Fornel, and E. Hadji, “An air-slotted nanoresonator relying on coupled high Q small V Fabry-Perot nanocavities,” Appl. Phys. Lett. 94, 251111 (2009).
    [Crossref]
  23. T. Yamamoto, M. Notomi, H. Taniyama, E. Kuramochi, Y. Yoshikawa, Y. Torii, and T. Kuga, “Design of a high-Q air-slot cavity based on a width-modulated line-defect in a photonic crystal slab,” Opt. Express 16, 13809–13817 (2008).
    [Crossref] [PubMed]
  24. Y. Li, J. Zheng, J. Gao, J. Shu, M. S. Aras, and C. W. Wong, “Design of dispersive optomechanical coupling and cooling in ultrahigh-Q/V slot-type photonic crystal cavities,” Opt. Express 18, 23844–23856 (2010).
    [Crossref] [PubMed]
  25. M. P. Hiscocks, C. Su, B. C. Gibson, A. D. Greentree, L. C. L. Hollenberg, and F. Ladouceur, “Slot-waveguide cavities for optical quantum information applications,” Opt. Express 17, 7295–7303 (2009).
    [Crossref] [PubMed]
  26. H. Ryu, J. Kim, Y. M. Jhon, S. Lee, and N. Park, “Effect of index contrasts in the wide spectral-range control of slot waveguide dispersion,” Opt. Express 20, 13189–13194 (2012)
    [Crossref] [PubMed]
  27. C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express 15, 5976–5990 (2007).
    [Crossref] [PubMed]
  28. P. Muellner, M. Wellenzohn, and R. Hainberger, “Nonlinearity of optimized silicon photonic slot waveguides,” Opt. Express 17, 9282–9287 (2009).
    [Crossref] [PubMed]
  29. Q. Quan, I. Bulu, and M. Lončar, “Broadband waveguide QED system on a chip,” Phys. Rev. A. 80, 011810(R) (2009).
    [Crossref]
  30. L. Zhang, Y. Yue, Y. X. Li, J. Wang, R. G. Beausoleil, and A. E. Willner, “Flat and low dispersion in highly nonlinear slot waveguides,” Opt. Express 18, 13187–13193 (2010).
    [Crossref] [PubMed]
  31. Y. Yue, L. Zhang, J. Wang, R. G. Beausoleil, and A. E. Willner, “Highly efficient nonlinearity reduction in silicon-on-insulator waveguides using vertical slots,” Opt. Express 18, 22061–22066 (2010).
    [Crossref] [PubMed]
  32. R. Guo, B. Wang, X. Wang, L. Wang, L. Jiang, and Z. Zhou, “Optical amplification in Er/Yb silicate slot waveguide,” Opt. Lett. 37, 1427–1429 (2012).
    [Crossref] [PubMed]
  33. H. Lee, Y. Rostovtsev, C. J. Bednar, and A. Javan, “From laser-induced line narrowing to electromagnetically induced transparency: closed system analysis,” Appl. Phys. B 76, 33 (2003).
    [Crossref]
  34. L. Li and G. Huang, “Linear and nonlinear light propagations in a Doppler-broadened medium via electromagnetically induced transparency,” Phys. Rev. A 82, 023809 (2010).
    [Crossref]

2012 (3)

2011 (1)

H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
[Crossref]

2010 (5)

2009 (7)

M. P. Hiscocks, C. Su, B. C. Gibson, A. D. Greentree, L. C. L. Hollenberg, and F. Ladouceur, “Slot-waveguide cavities for optical quantum information applications,” Opt. Express 17, 7295–7303 (2009).
[Crossref] [PubMed]

K. Foubert, L. Lalouat, B. Cluzel, E. Picard, D. Peyrade, F. de Fornel, and E. Hadji, “An air-slotted nanoresonator relying on coupled high Q small V Fabry-Perot nanocavities,” Appl. Phys. Lett. 94, 251111 (2009).
[Crossref]

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

P. Muellner, M. Wellenzohn, and R. Hainberger, “Nonlinearity of optimized silicon photonic slot waveguides,” Opt. Express 17, 9282–9287 (2009).
[Crossref] [PubMed]

Q. Quan, I. Bulu, and M. Lončar, “Broadband waveguide QED system on a chip,” Phys. Rev. A. 80, 011810(R) (2009).
[Crossref]

F. L. Kien and K. Hakuta, “Slowing down of a guided light field along a nanofiber in a cold atomic gas,” Phys. Rev. A. 79, 013818 (2009).
[Crossref]

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3, 706–714 (2009).
[Crossref]

2008 (1)

2007 (2)

2006 (3)

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. L. Savio, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
[Crossref]

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, and A. L. Gaeta, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
[Crossref] [PubMed]

2005 (4)

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[Crossref] [PubMed]

G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E. 72, 016617 (2005).
[Crossref]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

F. Benabid, P. Light, F. Couny, and P. Russell, “Electromagnetically-induced transparency grid in acetylene-filled hollow-core PCF,” Opt. Express 13, 5694–5703 (2005).
[Crossref] [PubMed]

2004 (3)

2003 (2)

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[Crossref] [PubMed]

H. Lee, Y. Rostovtsev, C. J. Bednar, and A. Javan, “From laser-induced line narrowing to electromagnetically induced transparency: closed system analysis,” Appl. Phys. B 76, 33 (2003).
[Crossref]

2001 (1)

1999 (2)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature. 397, 594–598 (1999).
[Crossref]

M. M. Kash, V.A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M.O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

Almeida, V. R.

Andreani, L. C.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. L. Savio, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Aras, M. S.

Artoni, M.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[Crossref] [PubMed]

Bajcsy, M.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Balic, V.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Bao, X.-H.

H. N. Dai, H. Zhang, S.-J. Yang, T.-M. Zhao, J. Rui, Y.-J. Deng, L. Li, N.-L. Liu, S. Chen, X.-H. Bao, X.-M. Jin, B. Zhao, and J.-W. Pan, “Holographic storage of biphoton entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
[Crossref]

Barrios, C. A.

Beausoleil, R. G.

Bednar, C. J.

H. Lee, Y. Rostovtsev, C. J. Bednar, and A. Javan, “From laser-induced line narrowing to electromagnetically induced transparency: closed system analysis,” Appl. Phys. B 76, 33 (2003).
[Crossref]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature. 397, 594–598 (1999).
[Crossref]

Benabid, F.

Bhagwat, A. R.

A. D. Slepkov, A. R. Bhagwat, V. Venkataraman, P. Londero, and A. L. Gaeta, “Spectroscopy of Rb atoms in hollow-core fibers,” Phys. Rev. A 81, 053825 (2010).
[Crossref]

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, and A. L. Gaeta, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
[Crossref] [PubMed]

Bulu, I.

Q. Quan, I. Bulu, and M. Lončar, “Broadband waveguide QED system on a chip,” Phys. Rev. A. 80, 011810(R) (2009).
[Crossref]

Canino, A.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. L. Savio, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Cataliotti, F.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[Crossref] [PubMed]

Chen, S.

H. N. Dai, H. Zhang, S.-J. Yang, T.-M. Zhao, J. Rui, Y.-J. Deng, L. Li, N.-L. Liu, S. Chen, X.-H. Bao, X.-M. Jin, B. Zhao, and J.-W. Pan, “Holographic storage of biphoton entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
[Crossref]

Chen, Z.-B.

H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
[Crossref]

Cluzel, B.

K. Foubert, L. Lalouat, B. Cluzel, E. Picard, D. Peyrade, F. de Fornel, and E. Hadji, “An air-slotted nanoresonator relying on coupled high Q small V Fabry-Perot nanocavities,” Appl. Phys. Lett. 94, 251111 (2009).
[Crossref]

Couny, F.

Dai, H. N.

H. N. Dai, H. Zhang, S.-J. Yang, T.-M. Zhao, J. Rui, Y.-J. Deng, L. Li, N.-L. Liu, S. Chen, X.-H. Bao, X.-M. Jin, B. Zhao, and J.-W. Pan, “Holographic storage of biphoton entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

Dai, H.-N.

H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
[Crossref]

de Fornel, F.

K. Foubert, L. Lalouat, B. Cluzel, E. Picard, D. Peyrade, F. de Fornel, and E. Hadji, “An air-slotted nanoresonator relying on coupled high Q small V Fabry-Perot nanocavities,” Appl. Phys. Lett. 94, 251111 (2009).
[Crossref]

Deng, L.

G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E. 72, 016617 (2005).
[Crossref]

Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904 (2004).
[Crossref] [PubMed]

Deng, Y.

H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
[Crossref]

Deng, Y.-J.

H. N. Dai, H. Zhang, S.-J. Yang, T.-M. Zhao, J. Rui, Y.-J. Deng, L. Li, N.-L. Liu, S. Chen, X.-H. Bao, X.-M. Jin, B. Zhao, and J.-W. Pan, “Holographic storage of biphoton entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature. 397, 594–598 (1999).
[Crossref]

Engeness, T.

Fink, Y.

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

Foubert, K.

K. Foubert, L. Lalouat, B. Cluzel, E. Picard, D. Peyrade, F. de Fornel, and E. Hadji, “An air-slotted nanoresonator relying on coupled high Q small V Fabry-Perot nanocavities,” Appl. Phys. Lett. 94, 251111 (2009).
[Crossref]

Freude, W.

Fry, E. S.

M. M. Kash, V.A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M.O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

Gaeta, A. L.

A. D. Slepkov, A. R. Bhagwat, V. Venkataraman, P. Londero, and A. L. Gaeta, “Spectroscopy of Rb atoms in hollow-core fibers,” Phys. Rev. A 81, 053825 (2010).
[Crossref]

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, and A. L. Gaeta, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
[Crossref] [PubMed]

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[Crossref] [PubMed]

Galli, M.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. L. Savio, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Gao, J.

Gerace, D.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. L. Savio, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Ghosh, S.

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, and A. L. Gaeta, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
[Crossref] [PubMed]

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[Crossref] [PubMed]

Gibson, B. C.

Goh, S.

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, and A. L. Gaeta, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
[Crossref] [PubMed]

Greentree, A. D.

Guo, R.

Hadji, E.

K. Foubert, L. Lalouat, B. Cluzel, E. Picard, D. Peyrade, F. de Fornel, and E. Hadji, “An air-slotted nanoresonator relying on coupled high Q small V Fabry-Perot nanocavities,” Appl. Phys. Lett. 94, 251111 (2009).
[Crossref]

Hafezi, M.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Hainberger, R.

Hakuta, K.

F. L. Kien and K. Hakuta, “Slowing down of a guided light field along a nanofiber in a cold atomic gas,” Phys. Rev. A. 79, 013818 (2009).
[Crossref]

Hang, C.

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
[Crossref]

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature. 397, 594–598 (1999).
[Crossref]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature. 397, 594–598 (1999).
[Crossref]

He, Y.

H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
[Crossref]

Hiscocks, M. P.

Hofferberth, S.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Hollberg, L.

M. M. Kash, V.A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M.O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

Hollenberg, L. C. L.

Huang, G.

L. Li and G. Huang, “Linear and nonlinear light propagations in a Doppler-broadened medium via electromagnetically induced transparency,” Phys. Rev. A 82, 023809 (2010).
[Crossref]

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
[Crossref]

G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E. 72, 016617 (2005).
[Crossref]

Ibanescu, M.

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

Irrera, A.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. L. Savio, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Jacobs, S.

Jacome, L.

Javan, A.

H. Lee, Y. Rostovtsev, C. J. Bednar, and A. Javan, “From laser-induced line narrowing to electromagnetically induced transparency: closed system analysis,” Appl. Phys. B 76, 33 (2003).
[Crossref]

Jhon, Y. M.

Jiang, L.

Jiang, X.

H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
[Crossref]

Jin, X.-M.

H. N. Dai, H. Zhang, S.-J. Yang, T.-M. Zhao, J. Rui, Y.-J. Deng, L. Li, N.-L. Liu, S. Chen, X.-H. Bao, X.-M. Jin, B. Zhao, and J.-W. Pan, “Holographic storage of biphoton entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
[Crossref]

Joannopoulos, J.

Johnson, S.

Kash, M. M.

M. M. Kash, V.A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M.O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

Kien, F. L.

F. L. Kien and K. Hakuta, “Slowing down of a guided light field along a nanofiber in a cold atomic gas,” Phys. Rev. A. 79, 013818 (2009).
[Crossref]

Kim, J.

Koos, C.

Kuga, T.

Kuramochi, E.

Ladouceur, F.

Lalouat, L.

K. Foubert, L. Lalouat, B. Cluzel, E. Picard, D. Peyrade, F. de Fornel, and E. Hadji, “An air-slotted nanoresonator relying on coupled high Q small V Fabry-Perot nanocavities,” Appl. Phys. Lett. 94, 251111 (2009).
[Crossref]

Lee, H.

H. Lee, Y. Rostovtsev, C. J. Bednar, and A. Javan, “From laser-induced line narrowing to electromagnetically induced transparency: closed system analysis,” Appl. Phys. B 76, 33 (2003).
[Crossref]

Lee, S.

Leuthold, J.

Li, L.

H. N. Dai, H. Zhang, S.-J. Yang, T.-M. Zhao, J. Rui, Y.-J. Deng, L. Li, N.-L. Liu, S. Chen, X.-H. Bao, X.-M. Jin, B. Zhao, and J.-W. Pan, “Holographic storage of biphoton entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

L. Li and G. Huang, “Linear and nonlinear light propagations in a Doppler-broadened medium via electromagnetically induced transparency,” Phys. Rev. A 82, 023809 (2010).
[Crossref]

Li, Y.

Y. Li, J. Zheng, J. Gao, J. Shu, M. S. Aras, and C. W. Wong, “Design of dispersive optomechanical coupling and cooling in ultrahigh-Q/V slot-type photonic crystal cavities,” Opt. Express 18, 23844–23856 (2010).
[Crossref] [PubMed]

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
[Crossref]

Li, Y. X.

Light, P.

Light, P. S.

Lipson, M.

Liscidini, M.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. L. Savio, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Liu, N.-L.

H. N. Dai, H. Zhang, S.-J. Yang, T.-M. Zhao, J. Rui, Y.-J. Deng, L. Li, N.-L. Liu, S. Chen, X.-H. Bao, X.-M. Jin, B. Zhao, and J.-W. Pan, “Holographic storage of biphoton entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

Loncar, M.

Q. Quan, I. Bulu, and M. Lončar, “Broadband waveguide QED system on a chip,” Phys. Rev. A. 80, 011810(R) (2009).
[Crossref]

Londero, P.

A. D. Slepkov, A. R. Bhagwat, V. Venkataraman, P. Londero, and A. L. Gaeta, “Spectroscopy of Rb atoms in hollow-core fibers,” Phys. Rev. A 81, 053825 (2010).
[Crossref]

Luiten, A. N.

Lukin, M. D.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

M. M. Kash, V.A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M.O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

Lvovsky, A. I.

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3, 706–714 (2009).
[Crossref]

Ma, L.

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
[Crossref]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

Maric, M.

Miritello, M.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. L. Savio, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Muellner, P.

Notomi, M.

Ottaviani, C.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[Crossref] [PubMed]

Ouzounov, D. G.

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[Crossref] [PubMed]

Pan, G.-S.

H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
[Crossref]

Pan, J.-W.

H. N. Dai, H. Zhang, S.-J. Yang, T.-M. Zhao, J. Rui, Y.-J. Deng, L. Li, N.-L. Liu, S. Chen, X.-H. Bao, X.-M. Jin, B. Zhao, and J.-W. Pan, “Holographic storage of biphoton entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
[Crossref]

Panepucci, R.

Panepucci, R. R.

Park, N.

Patrini, M.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. L. Savio, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Payne, M. G.

G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E. 72, 016617 (2005).
[Crossref]

Peyrade, D.

K. Foubert, L. Lalouat, B. Cluzel, E. Picard, D. Peyrade, F. de Fornel, and E. Hadji, “An air-slotted nanoresonator relying on coupled high Q small V Fabry-Perot nanocavities,” Appl. Phys. Lett. 94, 251111 (2009).
[Crossref]

Peyronel, T.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Picard, E.

K. Foubert, L. Lalouat, B. Cluzel, E. Picard, D. Peyrade, F. de Fornel, and E. Hadji, “An air-slotted nanoresonator relying on coupled high Q small V Fabry-Perot nanocavities,” Appl. Phys. Lett. 94, 251111 (2009).
[Crossref]

Politi, A.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. L. Savio, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Poulton, C.

Priolo, F.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. L. Savio, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Quan, Q.

Q. Quan, I. Bulu, and M. Lončar, “Broadband waveguide QED system on a chip,” Phys. Rev. A. 80, 011810(R) (2009).
[Crossref]

Renshaw, C. K.

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, and A. L. Gaeta, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
[Crossref] [PubMed]

Rostovtsev, Y.

H. Lee, Y. Rostovtsev, C. J. Bednar, and A. Javan, “From laser-induced line narrowing to electromagnetically induced transparency: closed system analysis,” Appl. Phys. B 76, 33 (2003).
[Crossref]

M. M. Kash, V.A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M.O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

Rui, J.

H. N. Dai, H. Zhang, S.-J. Yang, T.-M. Zhao, J. Rui, Y.-J. Deng, L. Li, N.-L. Liu, S. Chen, X.-H. Bao, X.-M. Jin, B. Zhao, and J.-W. Pan, “Holographic storage of biphoton entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
[Crossref]

Russell, P.

Ryu, H.

Sanders, B. C.

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3, 706–714 (2009).
[Crossref]

Sautenkov, V.A.

M. M. Kash, V.A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M.O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

Savio, R. L.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. L. Savio, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

Scully, M.O.

M. M. Kash, V.A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M.O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

Sharping, J. E.

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[Crossref] [PubMed]

Shu, J.

Skorobogatiy, M.

Slepkov, A. D.

A. D. Slepkov, A. R. Bhagwat, V. Venkataraman, P. Londero, and A. L. Gaeta, “Spectroscopy of Rb atoms in hollow-core fibers,” Phys. Rev. A 81, 053825 (2010).
[Crossref]

Soljacic, M.

Su, C.

Taniyama, H.

Tittel, W.

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3, 706–714 (2009).
[Crossref]

Tombesi, P.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[Crossref] [PubMed]

Torii, Y.

Venkataraman, V.

A. D. Slepkov, A. R. Bhagwat, V. Venkataraman, P. Londero, and A. L. Gaeta, “Spectroscopy of Rb atoms in hollow-core fibers,” Phys. Rev. A 81, 053825 (2010).
[Crossref]

Vitali, D.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[Crossref] [PubMed]

Vuletic, V.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Wang, B.

Wang, J.

Wang, L.

Wang, X.

Weisberg, O.

Welch, G. R.

M. M. Kash, V.A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M.O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

Wellenzohn, M.

Willner, A. E.

Wong, C. W.

Wu, Y.

Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904 (2004).
[Crossref] [PubMed]

Xu, Q.

Yamamoto, T.

Yang, F.

H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
[Crossref]

Yang, J.

H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
[Crossref]

Yang, S.-J.

H. N. Dai, H. Zhang, S.-J. Yang, T.-M. Zhao, J. Rui, Y.-J. Deng, L. Li, N.-L. Liu, S. Chen, X.-H. Bao, X.-M. Jin, B. Zhao, and J.-W. Pan, “Holographic storage of biphoton entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
[Crossref]

Yoshikawa, Y.

Yuan, Z.-S.

H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
[Crossref]

Yue, Y.

Zhang, H.

H. N. Dai, H. Zhang, S.-J. Yang, T.-M. Zhao, J. Rui, Y.-J. Deng, L. Li, N.-L. Liu, S. Chen, X.-H. Bao, X.-M. Jin, B. Zhao, and J.-W. Pan, “Holographic storage of biphoton entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
[Crossref]

Zhang, L.

Zhao, B.

H. N. Dai, H. Zhang, S.-J. Yang, T.-M. Zhao, J. Rui, Y.-J. Deng, L. Li, N.-L. Liu, S. Chen, X.-H. Bao, X.-M. Jin, B. Zhao, and J.-W. Pan, “Holographic storage of biphoton entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
[Crossref]

Zhao, T.-M.

H. N. Dai, H. Zhang, S.-J. Yang, T.-M. Zhao, J. Rui, Y.-J. Deng, L. Li, N.-L. Liu, S. Chen, X.-H. Bao, X.-M. Jin, B. Zhao, and J.-W. Pan, “Holographic storage of biphoton entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
[Crossref]

Zheng, J.

Zhou, Z.

Zibrov, A. S.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

M. M. Kash, V.A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M.O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

Appl. Phys. B (1)

H. Lee, Y. Rostovtsev, C. J. Bednar, and A. Javan, “From laser-induced line narrowing to electromagnetically induced transparency: closed system analysis,” Appl. Phys. B 76, 33 (2003).
[Crossref]

Appl. Phys. Lett. (2)

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. L. Savio, A. Irrera, and F. Priolo, “Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides,” Appl. Phys. Lett. 89, 241114 (2006).
[Crossref]

K. Foubert, L. Lalouat, B. Cluzel, E. Picard, D. Peyrade, F. de Fornel, and E. Hadji, “An air-slotted nanoresonator relying on coupled high Q small V Fabry-Perot nanocavities,” Appl. Phys. Lett. 94, 251111 (2009).
[Crossref]

Nat. Photon. (1)

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3, 706–714 (2009).
[Crossref]

Nat. Photonics (1)

H. Zhang, X.-M. Jin, J. Yang, H.-N. Dai, S.-J. Yang, T.-M. Zhao, J. Rui, Y. He, X. Jiang, F. Yang, G.-S. Pan, Z.-S. Yuan, Y. Deng, Z.-B. Chen, X.-H. Bao, S. Chen, B. Zhao, and J.-W. Pan, “Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion,” Nat. Photonics 5, 628–632 (2011).
[Crossref]

Nature. (1)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature. 397, 594–598 (1999).
[Crossref]

Opt. Express (10)

S. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. Engeness, M. Soljacic, S. Jacobs, J. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–779 (2001).
[Crossref] [PubMed]

F. Benabid, P. Light, F. Couny, and P. Russell, “Electromagnetically-induced transparency grid in acetylene-filled hollow-core PCF,” Opt. Express 13, 5694–5703 (2005).
[Crossref] [PubMed]

T. Yamamoto, M. Notomi, H. Taniyama, E. Kuramochi, Y. Yoshikawa, Y. Torii, and T. Kuga, “Design of a high-Q air-slot cavity based on a width-modulated line-defect in a photonic crystal slab,” Opt. Express 16, 13809–13817 (2008).
[Crossref] [PubMed]

Y. Li, J. Zheng, J. Gao, J. Shu, M. S. Aras, and C. W. Wong, “Design of dispersive optomechanical coupling and cooling in ultrahigh-Q/V slot-type photonic crystal cavities,” Opt. Express 18, 23844–23856 (2010).
[Crossref] [PubMed]

M. P. Hiscocks, C. Su, B. C. Gibson, A. D. Greentree, L. C. L. Hollenberg, and F. Ladouceur, “Slot-waveguide cavities for optical quantum information applications,” Opt. Express 17, 7295–7303 (2009).
[Crossref] [PubMed]

H. Ryu, J. Kim, Y. M. Jhon, S. Lee, and N. Park, “Effect of index contrasts in the wide spectral-range control of slot waveguide dispersion,” Opt. Express 20, 13189–13194 (2012)
[Crossref] [PubMed]

C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express 15, 5976–5990 (2007).
[Crossref] [PubMed]

P. Muellner, M. Wellenzohn, and R. Hainberger, “Nonlinearity of optimized silicon photonic slot waveguides,” Opt. Express 17, 9282–9287 (2009).
[Crossref] [PubMed]

L. Zhang, Y. Yue, Y. X. Li, J. Wang, R. G. Beausoleil, and A. E. Willner, “Flat and low dispersion in highly nonlinear slot waveguides,” Opt. Express 18, 13187–13193 (2010).
[Crossref] [PubMed]

Y. Yue, L. Zhang, J. Wang, R. G. Beausoleil, and A. E. Willner, “Highly efficient nonlinearity reduction in silicon-on-insulator waveguides using vertical slots,” Opt. Express 18, 22061–22066 (2010).
[Crossref] [PubMed]

Opt. Lett. (4)

Phys. Rev. A (3)

L. Li and G. Huang, “Linear and nonlinear light propagations in a Doppler-broadened medium via electromagnetically induced transparency,” Phys. Rev. A 82, 023809 (2010).
[Crossref]

A. D. Slepkov, A. R. Bhagwat, V. Venkataraman, P. Londero, and A. L. Gaeta, “Spectroscopy of Rb atoms in hollow-core fibers,” Phys. Rev. A 81, 053825 (2010).
[Crossref]

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
[Crossref]

Phys. Rev. A. (2)

F. L. Kien and K. Hakuta, “Slowing down of a guided light field along a nanofiber in a cold atomic gas,” Phys. Rev. A. 79, 013818 (2009).
[Crossref]

Q. Quan, I. Bulu, and M. Lončar, “Broadband waveguide QED system on a chip,” Phys. Rev. A. 80, 011810(R) (2009).
[Crossref]

Phys. Rev. E. (1)

G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E. 72, 016617 (2005).
[Crossref]

Phys. Rev. Lett. (7)

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[Crossref] [PubMed]

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, and A. L. Gaeta, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
[Crossref] [PubMed]

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904 (2004).
[Crossref] [PubMed]

M. M. Kash, V.A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M.O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

H. N. Dai, H. Zhang, S.-J. Yang, T.-M. Zhao, J. Rui, Y.-J. Deng, L. Li, N.-L. Liu, S. Chen, X.-H. Bao, X.-M. Jin, B. Zhao, and J.-W. Pan, “Holographic storage of biphoton entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1 Left: Schematic of slot waveguide structure. The slot width (index nS) is 2a, the width of the high-index silicon slabs (index nH) is 2b − 2a. The index of the cladding material is nC. Right: Level diagram of the three-level atomic system. Ground state |1〉 couples to the exited |2〉 and |3〉 with the control field Ωc and the probe field Ωp. Δ2 and Δ3 are the detunings of control and probe fields, respectively. Γ31 (Γ32) is the spontaneous emission decay rate from |3〉 to |1〉 (|2〉). Γ12 and Γ21 are incoherent population exchange rates. Below the level diagram is the coordinate system chosen for theoretical calculations. The slot region is |z| ≤ a, and the slabs are in the region a < |z| < b.

Download Full Size | PPT Slide | PDF

Fig. 2
Fig. 2 (a): Im(K) as a function of frequency ω for different slot width 2a. The red solid, black dashed, and blue dashed-dotted lines are for the slot width 2a = 50, 30 and 10 nm, respectively. (b): Im(K0) as a function of |Ωc| for different slot width 2a. The red solid, black dashed, and blue dashed-dotted lines are for the slot width 2a = 50, 30, 10 nm, respectively.

Download Full Size | PPT Slide | PDF

Fig. 3
Fig. 3 (a): Im(K) as a function of ω. (b): Im(K0) as a function of |Ωc| with Γ21 = 0 (red solid line), Γ21 = 0.5Γ12 (black dashed line) and Γ21 = Γ12 (blue dashed-dotted line), respectively.

Download Full Size | PPT Slide | PDF

Fig. 4
Fig. 4 Third-order susceptibility Re ( χ p p ( 3 ) ) as a function of detunning Δ3 for different slot width 2a. The red solid, black dashed and blue dashed-dotted lines are for 2a = 50,25 and 5 nm, respectively.

Download Full Size | PPT Slide | PDF

Fig. 5
Fig. 5 (a) The three-dimensional plot of the wave shape |Ωp/U0|2 as a function of z/LD and t/τ0. The solution is numerically obtained from Eq. (14) with full complex coefficients taken into account. The values of parameters are given in the text. (b): The interaction between two identical bright solitons.

Download Full Size | PPT Slide | PDF

Equations (50)

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

E TM ( r , t ) = ∑ k h ¯ ω 1 ( k ) 2 ε 0 V 1 u 1 , k ( z ) a 1 ( k ) e i [ k y − ω 1 ( k ) t ] + c . c . ,
u 1 , k ( z ) = c 2 N 1 ω 1 ( k ) n 2 ( z ) [ k H 1 , k ( z ) e z + i d H 1 , k ( z ) d z e y ] .
E TM ( r , t ) = ∑ l = p , c ℰ 1 ( W 1 V 1 ) 1 2 u 1 , l ( z ) exp { i [ k ( ω l ) y − ω l t ] } + c . c ..
ℋ ^ = − h ¯ ∑ j 3 Δ j | j 〉 〈 j | − h ¯ [ ζ p * ( z ) Ω p * | 1 〉 〈 3 | + ζ c * ( z ) Ω c * | 2 〉 〈 3 | + h . c . ] ,
i ∂ ∂ t σ 11 + i Γ 21 σ 11 − i Γ 12 σ 22 − i Γ 13 σ 33 + ζ p * ( z ) Ω p * σ 31 − ζ p ( z ) Ω p σ 31 * = 0 ,
i ∂ ∂ t σ 22 − i Γ 21 σ 11 + i Γ 12 σ 22 − i Γ 23 σ 33 + ζ c * ( z ) Ω c * σ 32 − ζ c ( z ) Ω c σ 32 * = 0 ,
i ∂ ∂ t σ 33 + i ( Γ 13 + Γ 23 ) σ 33 − ζ p * ( z ) Ω p * σ 31 + ζ p ( z ) Ω p σ 31 * − ζ c * ( z ) Ω c * σ 32 + ζ c ( z ) Ω c σ 32 * = 0 ,
( i ∂ ∂ t + d 21 ) σ 21 − ζ p ( z ) Ω p σ 32 * + ζ c * ( z ) Ω c * σ 31 = 0 ,
( i ∂ ∂ t + d 31 ) σ 31 − ζ p ( z ) Ω p ( σ 33 − σ 11 ) + ζ c ( z ) Ω c σ 21 = 0 ,
( i ∂ ∂ t + d 32 ) σ 32 − ζ c ( z ) Ω c ( σ 33 − σ 22 ) + ζ p ( z ) Ω p σ 21 * = 0 ,
P = 𝒩 a ∫ − ∞ ∞ d v f ( v ) [ p 13 σ 31 e i ( k p y − ω p t ) + p 23 σ 32 e i ( k c y − ω c t ) + c . c . ] ,
i ( ∂ ∂ y + 1 c 〈 n 2 ( z ) 〉 n eff ∂ ∂ t ) Ω p + c 2 ω p n eff ∂ 2 Ω p ∂ x 2 + κ 13 ∫ − ∞ ∞ d v f 〈 v 〉 〈 σ 31 ( v , z ) 〉 = 0 ,
σ 11 ( 0 ) = Γ 12 ( Γ 13 + Γ 23 ) X 1 + ( Γ 12 + Γ 13 ) | ζ ( z ) Ω c | 2 X 2 ,
σ 22 ( 0 ) = Γ 21 ( Γ 13 + Γ 23 ) X 1 + Γ 21 | ζ ( z ) Ω c | 2 X 2 ,
σ 33 ( 0 ) = Γ 21 | ζ ( z ) Ω c | 2 X 2 ,
σ 32 ( 0 ) = − ζ ( z ) Ω c d 32 Γ 21 ( Γ 13 + Γ 23 ) X 1 X 2 ,
K ( ω ) = 1 ∫ − ∞ ∞ d z | ζ ( z ) | 2 ∫ − ∞ ∞ d z | ζ ( z ) | 2 { ω c n 2 ( z ) n eff + κ 13 ∫ − ∞ ∞ d v f ( v ) ζ ( z ) Ω c σ 32 * ( 0 ) + ( ω + d 21 ) ( 2 σ 11 ( 0 ) + σ 22 ( 0 ) − 1 ) | ζ ( z ) Ω c | 2 − ( ω + d 21 ) ( ω + d 31 ) } .
K ( ω ) = ∫ − ∞ ∞ d z | ζ ( z ) | 2 ( ω c n 2 ( z ) n eff + 𝒦 1 ( z ) + 𝒦 2 ( z ) ) / ∫ − ∞ ∞ d z | ζ ( z ) | 2 ,
𝒦 1 ( z ) = π κ 13 { | ζ ( z ) Ω c | 2 Γ 21 Γ 3 ( − i Δ ω D − i γ 32 ) + ( ω + i γ 21 ) [ Γ 12 Γ 3 ( − Δ ω D 2 + γ 32 2 ) + 2 γ 32 ( Γ 12 − Γ 21 + Γ 13 ) | ζ ( z ) Ω c | 2 ] } / { ( − Δ ω D 2 + η 2 ) ( Γ 12 + Γ 21 ) Γ 3 [ | ζ ( z ) Ω c | 2 − ( ω + i γ 21 ) ( ω + i Δ ω D + i γ 31 ) ] } ,
𝒦 2 ( z ) = π κ 13 Δ ω D { | ζ ( z ) Ω c | 2 Γ 21 Γ 3 ( − i η − i γ 32 ) + ( ω + i γ 21 ) [ Γ 12 Γ 3 ( − η 2 + γ 32 2 ) + 2 γ 32 ( Γ 12 − Γ 21 + Γ 13 ) | ζ ( z ) Ω c | 2 ] } / { η ( Δ ω D 2 − η 2 ) ( Γ 12 + Γ 21 ) Γ 3 [ | ζ ( z ) Ω c | 2 − ( ω + i γ 21 ) ( ω + i η + i γ 31 ) ] } .
Im ( K 0 ) = 1 ∫ − ∞ ∞ d z | ζ ( z ) | 2 ∫ − ∞ ∞ d z | ζ ( z ) | 2 ∫ − ∞ ∞ d v f ( v ) κ 13 γ 21 | ζ ( z ) Ω c | 2 + γ 21 γ 31 × ( 1 − Γ 21 Γ 3 X 1 + 3 Γ 21 | ζ ( z ) Ω c | 2 ( Γ 21 + Γ 12 ) Γ 3 X 1 + ( 2 Γ 21 + Γ 12 + Γ 13 ) | ζ ( z ) Ω c | 2 ) .
χ p = ∫ − ∞ ∞ d v f ( v ) 𝒩 a | p 13 | 2 ε 0 h ¯ 〈 σ 31 ( v , z ) 〉 Ω p ≈ χ p ( 1 ) + χ p p ( 3 ) | ℰ p | 2 ,
χ p ( 1 ) = 𝒩 a | p 13 | 2 ε 0 h ¯ ∫ − ∞ ∞ d z | ζ ( z ) | 2 ∫ − ∞ ∞ d v f ( v ) × d 21 d 32 * ( σ 33 ( 0 ) − σ 11 ( 0 ) ) − | ζ ( z ) Ω c | 2 ( σ 33 ( 0 ) − σ 22 ( 0 ) ) d 32 * ( d 21 d 31 − | ζ ( z ) Ω c | 2 ) / ∫ − ∞ ∞ d z | ζ ( z ) | 2 ,
χ p p ( 3 ) = 𝒩 a | p 13 | 4 ε 0 h ¯ 3 1 ∫ − ∞ ∞ d z | ζ ( z ) | 2 ∫ − ∞ ∞ d z | ζ ( z ) | 2 ∫ − ∞ ∞ d v f ( v ) × | ζ ( z ) | 2 [ i d 32 ζ ( z ) Ω c Z 1 Z 4 − ( 2 d 21 | d 32 | 2 − d 32 | ζ ( z ) Ω c | 2 ) Z 2 − ( d 21 | d 32 | 2 − 2 d 32 | ζ ( z ) Ω c | 2 ) Z 3 ] / [ i Z 1 | d 32 | 2 ( | ζ ( z ) Ω c | 2 − d 21 d 31 ) ] ,
Ω p ( 1 ) = Fe i θ ,
σ 31 ( 1 ) = ( ω + d 21 ) ( 2 σ 11 ( 0 ) + σ 22 ( 0 ) − 1 ) + ζ ( z ) Ω c σ 32 * ( 0 ) | ζ 2 ( z ) Ω c | 2 − ( ω + d 21 ) ( ω + d 31 ) ζ ( z ) Fe i θ ,
σ 21 ( 1 ) = − ( ω + d 31 ) σ 32 * ( 0 ) + ζ c * ( z ) Ω c * ( 2 σ 11 ( 0 ) + σ 22 ( 0 ) − 1 ) | ζ 2 ( z ) Ω c | 2 − ( ω + d 21 ) ( ω + d 31 ) ζ ( z ) Fe i θ ,
i ∂ F ∂ y 2 + c 2 ω p n eff ∂ 2 F ∂ x 1 2 − K 2 2 ∂ 2 F ∂ t 1 2 − W | F | 2 Fe − 2 α ¯ y 2 = 0 ,
W = − κ 13 ∫ − ∞ ∞ d z | ζ ( z ) | 4 ∫ − ∞ ∞ d v f ( v ) ζ ( z ) Ω c a 32 * ( 2 ) + ( ω + d 21 ) ( 2 a 11 ( 2 ) + a 22 ( 2 ) ) | ζ 2 ( z ) Ω c | 2 − ( ω + d 21 ) ( ω + d 31 ) / ∫ − ∞ ∞ d z | ζ ( z ) | 2 ,
i ( ∂ ∂ y + α ) U + c 2 ω p n eff ∂ 2 U ∂ x 2 − K 2 2 ∂ 2 U ∂ τ 2 − W | U | 2 U = 0 ,
i ∂ u ∂ s + ∂ 2 u ∂ σ 2 + 2 u | u | 2 = i d 0 u + d 1 ∂ 2 u ∂ ξ 2 ,
u = 2 β sech [ 2 β ( σ − σ 0 + 4 δ s ) ] exp [ − 2 i δ σ − 4 i ( δ 2 − β 2 ) s − i ϕ 0 ] ,
Ω p = 1 τ 0 K ˜ 2 W ˜ sech [ 1 τ 0 ( t − y v ˜ g ) ] exp [ i K ˜ 0 y + i y 2 L D ] ,
H m , k | | TM ( r , t ) = ( k ^ | | × e z ) H m , k | | ( z ) e i ( k | | ⋅ r − ω m t ) + c . c . ,
E m , k | | TM ( r , t ) = i ω m ( k | | ) ε 0 ε ( z ) [ − i k | | H m , k | | ( z ) e z + d H m , k | | ( z ) d z k ^ | | ] e i ( k | | ⋅ r − ω m t ) + c . c . ,
d 2 d z 2 H m , k | | ( z ) + [ ( ω c ) 2 n 2 ( z ) − k | | 2 ] H m , k | | ( z ) = 0 ,
H m , k | | TM ( z ) = { cosh ( γ S m z ) , | z | < a C m cos [ κ H m ( | z | − a ) ] + D m sin [ κ H m ( | z | − a ) ] , a < | z | < b E m exp [ − γ S m ( | z | − b ) ] , | z | > b
tan [ κ H m ( b − a ) − arctan ( γ S m n H 2 κ H m n S 2 ) ] = γ S n n H 2 κ H m n S 2 tanh ( γ S m a ) .
E TM ( r , t ) = ∑ k x , k y ∑ m = 1 ∞ h ¯ ω m 2 ε 0 V m u m , k | | ( z ) a ^ m ( k ) e i ( k | | ⋅ r − ω m t ) + h . c . ,
H TM ( r , t ) = ∑ k x , k y ∑ m = 1 ∞ h ¯ ω m 2 ε 0 V m ( k ^ | | × e z ) ε 0 c N m H m , k | | ( z ) a ^ m ( k ) e i ( k | | ⋅ r − ω m t ) + h . c . ,
V m = S { 1 2 γ S m [ sinh ( 2 γ S m a ) + 2 E m 2 ] + a 2 + ( C m 2 + D m 2 ) ( b − a ) + 1 2 κ H m ( C m 2 − D m 2 ) sin [ 2 κ H m ( b − a ) ] } / N m ,
N m = ω m 2 / ( c P ) 2 ,
H m , k | | TM ( z ) = { sin ϕ m exp ( z + b 2 b ψ m cos ϕ m ) , z < − b cos ( ψ m z b sin ϕ m ) , − b < z < b sin ϕ m exp ( b − z 2 b ψ m cos ϕ m ) , z > b
E TM ( r , t ) = ∑ k x , k y ∑ m = 1 ∞ h ¯ ω m 2 ε 0 W m u m , k | | ( z ) a ^ n ( k ) e i ( k | | ⋅ r − ω m t ) + h . c . ,
H TM ( r , t ) = ∑ k x , k y ∑ m = 1 ∞ h ¯ ω m 2 ε 0 W m ( k ^ | | × e z ) ε 0 c M m H m , k | | ( z ) a ^ m ( k ) e i ( k | | ⋅ r − ω m t ) + h . c . ,
W m = S { b [ 2 sin 2 ϕ m + ψ m cos ϕ m ] / ( ψ m cos ϕ m ) + b sin ( 2 ψ m sin ϕ m ) / ( 2 ψ m sin ϕ m ) } / M m ,
M m = ω m 2 / ( c G ) 2 ,
a 11 ( 2 ) = − i { [ i ( Γ 12 + Γ 23 ) − 2 | ζ 2 ( z ) Ω c | 2 ( 1 d 32 − 1 d 32 * ) ] ⋅ [ ( ω + d 21 * ) ( 2 σ 11 ( 0 ) + σ 22 ( 0 ) − 1 ) + ζ * ( z ) Ω c * σ 32 ( 0 ) | ζ 2 ( z ) Ω c | 2 − ( ω + d 21 * ) ( ω + d 31 * ) − c . c . ] + i ( Γ 12 − Γ 13 ) [ − ζ * ( z ) Ω c * d 32 ( ω + d 31 * ) σ 32 ( 0 ) + ζ ( z ) Ω c ( 2 σ 11 ( 0 ) + σ 22 ( 0 ) − 1 ) | ζ 2 ( z ) Ω c | 2 − ( ω + d 21 * ) ( ω + d 31 * ) + c . c . ] } / [ i ( Γ 12 + Γ 21 ) ( Γ 13 + Γ 23 ) − ( 2 Γ 21 + Γ 12 + Γ 13 ) | ζ 2 ( z ) Ω c | 2 ( 1 d 32 − 1 d 32 * ) ] ,
a 22 ( 2 ) = i Γ 12 − Γ 13 [ ( ω + d 21 * ) ( 2 σ 11 ( 0 ) + σ 22 ( 0 ) − 1 ) + ζ * ( z ) Ω c * σ 32 ( 0 ) | ζ 2 ( z ) Ω c | 2 − ( ω + d 21 * ) ( ω + d 31 * ) − c . c . − i ( Γ 21 + Γ 13 ) a 11 ( 2 ) ] ,
a 32 ( 2 ) = 1 d 32 [ ( ω + d 31 * ) σ 32 ( 0 ) + ζ ( z ) Ω c ( 2 σ 11 ( 0 ) + σ 22 ( 0 ) − 1 ) | ζ 2 ( z ) Ω c | 2 − ( ω + d 21 * ) ( ω + d 31 * ) − ζ ( z ) Ω c ( a 11 ( 2 ) + 2 a 22 ( 2 ) ) ] .

Metrics