Abstract

Recently Qu and Agarwal [Phys. Rev. A 87, 031802 (2013)] found a three-pathway electromagnetically induced absorption (TEIA) phenomenon within a mechanically coupled two-cavity system, where there exist a sharp EIA dip in the broad electromagnetically induced transparency peak in the transmission spectrum. In this work, we study the response of a probe light in a pair of directly coupled microcavities with one mechanical mode. We find that in addition to the sharp TEIA dip within a broad EIT window as found by Qu and Agarwal, three-pathway electromagnetically induced transparency (TEIT) within the broad EIT window could also exist under certain conditions. We give explicit physical explanations and detailed calculations. Our results provide a method for controlling transition between TEIA and TEIT in coupled optomechanical systems, and reveal the multiple pathways interference is versatile for controlling light.

© 2015 Optical Society of America

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References

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    [Crossref]
  2. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997).
    [Crossref]
  3. S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
    [Crossref] [PubMed]
  4. K.-J. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
    [Crossref] [PubMed]
  5. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
    [Crossref]
  6. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
    [Crossref]
  7. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
    [Crossref]
  8. S. Fan, W. Suh, and J. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003).
    [Crossref]
  9. F. Lei, B. Peng, Ş. K. Özdemir, G. L. Long, and L. Yang, “Dynamic Fano-like resonances in erbium-doped whispering-gallery-mode microresonators,” Appl. Phys. Lett. 105, 101112 (2014).
    [Crossref]
  10. L. 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]
  11. C. Liu, Z. Dutton, C. H. Behroozi, and L. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
    [Crossref] [PubMed]
  12. M. D. Lukin, “Colloquium: Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. 75, 457–472 (2003).
    [Crossref]
  13. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
    [Crossref] [PubMed]
  14. N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial analog of electromagnetically induced transparency,” Phys. Rev. Lett. 101, 253903 (2008).
    [Crossref] [PubMed]
  15. P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102, 053901 (2009).
    [Crossref] [PubMed]
  16. S. E. Harris, “Electromagnetically induced transparency in an ideal plasma,” Phys. Rev. Lett. 77, 5357–5360 (1996).
    [Crossref] [PubMed]
  17. E. Kawamori, W.-J. Syugu, T.-Y. Hsieh, S.-X. Song, and C. Z. Cheng, “Experimental identification of electromagnetically induced transparency in magnetized plasma,” Phys. Rev. Lett. 108, 075003 (2012).
    [Crossref] [PubMed]
  18. G. Shvets and A. Pukhov, “Electromagnetically induced guiding of counterpropagating lasers in plasmas,” Phys. Rev. E 59, 1033–1037 (1999).
    [Crossref]
  19. T. Wang, Y. Zhang, Z. Hong, and Z. Han, “Analogue of electromagnetically induced transparency in integrated plasmonics with radiative and subradiant resonators,” Opt. Express 22, 21529–21534 (2014).
    [Crossref] [PubMed]
  20. D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
    [Crossref]
  21. A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, “Induced transparency and absorption in coupled whispering-gallery microresonators,” Phys. Rev. A 71, 043804 (2005).
    [Crossref]
  22. K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98, 213904 (2007).
    [Crossref] [PubMed]
  23. B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Comm. 5, 5082 (2014).
    [Crossref]
  24. A. Naweed, D. Goldberg, and V. M. Menon, “All-optical electromagnetically induced transparency using one-dimensional coupled microcavities,” Opt. Express 22, 18818–18823 (2014).
    [Crossref] [PubMed]
  25. G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A 81, 041803 (2010).
    [Crossref]
  26. S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
    [Crossref] [PubMed]
  27. J. D. Teufel, D. Li, M. Allman, K. Cicak, A. Sirois, J. Whittaker, and R. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature 471, 204–208 (2011).
    [Crossref] [PubMed]
  28. P.-C. Ma, J.-Q. Zhang, Y. Xiao, M. Feng, and Z.-M. Zhang, “Tunable double optomechanically induced transparency in an optomechanical system,” Phys. Rev. A 90, 043825 (2014).
    [Crossref]
  29. C. G. Alzar, M. Martinez, and P. Nussenzveig, “Classical analog of electromagnetically induced transparency,” Am. J. Phys. 70, 37–41 (2002).
    [Crossref]
  30. Y. He, “Optomechanically induced transparency associated with steady-state entanglement,” Phys. Rev. A 91, 013827 (2015).
    [Crossref]
  31. I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104, 083901 (2010).
    [Crossref] [PubMed]
  32. M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, “Optical modes in photonic molecules,” Phys. Rev. Lett. 81, 2582–2585 (1998).
    [Crossref]
  33. B. Peng, Ş. K. Özdemir, J. Zhu, and L. Yang, “Photonic molecules formed by coupled hybrid resonators,” Opt. Lett. 37, 3435–3437 (2012).
    [Crossref]
  34. B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Physics 10, 394–398 (2014).
    [Crossref]
  35. T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
    [Crossref] [PubMed]
  36. M. Gao, F.-C. Lei, C.-G. Du, and G.-L. Long, “Self-sustained oscillation and dynamical multistability of optomechanical systems in the extremely-large-amplitude regime,” Phys. Rev. A 91, 013833 (2015).
    [Crossref]
  37. L. Zhang and Z. Song, “Modification on static responses of a nano-oscillator by quadratic optomechanical couplings,” Sci China- Phys Mech Astron 57, 880–886 (2014).
    [Crossref]
  38. W. Nie, Y. Lan, Y. Li, and S. Zhu, “Generating large steady-state optomechanical entanglement by the action of casimir force,” Sci China- Phys Mech Astron 57, 2276–2284 (2014).
    [Crossref]
  39. H. Xiong, L.-G. Si, A.-S. Zheng, X. Yang, and Y. Wu, “Higher-order sidebands in optomechanically induced transparency,” Phys. Rev. A 86, 013815 (2012).
    [Crossref]
  40. M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
    [Crossref] [PubMed]
  41. P. Anisimov and O. Kocharovskaya, “Decaying-dressed-state analysis of a coherently driven three-level λ system,” J. Mod. Opt. 55, 3159–3171 (2008).
    [Crossref]
  42. J. M. Dobrindt, I. Wilson-Rae, and T. J. Kippenberg, “Parametric normal-mode splitting in cavity optomechanics,” Phys. Rev. Lett. 101, 263602 (2008).
    [Crossref] [PubMed]
  43. S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724–727 (2009).
    [Crossref] [PubMed]
  44. F. Lei, M. Gao, C. Du, S.-Y. Hou, X. Yang, and G. L. Long, “Engineering optomechanical normal modes for single-phonon transfer and entanglement preparation,” J. Opt. Soc. Am. B 32, 588–594 (2015).
    [Crossref]

2015 (3)

Y. He, “Optomechanically induced transparency associated with steady-state entanglement,” Phys. Rev. A 91, 013827 (2015).
[Crossref]

M. Gao, F.-C. Lei, C.-G. Du, and G.-L. Long, “Self-sustained oscillation and dynamical multistability of optomechanical systems in the extremely-large-amplitude regime,” Phys. Rev. A 91, 013833 (2015).
[Crossref]

F. Lei, M. Gao, C. Du, S.-Y. Hou, X. Yang, and G. L. Long, “Engineering optomechanical normal modes for single-phonon transfer and entanglement preparation,” J. Opt. Soc. Am. B 32, 588–594 (2015).
[Crossref]

2014 (8)

L. Zhang and Z. Song, “Modification on static responses of a nano-oscillator by quadratic optomechanical couplings,” Sci China- Phys Mech Astron 57, 880–886 (2014).
[Crossref]

W. Nie, Y. Lan, Y. Li, and S. Zhu, “Generating large steady-state optomechanical entanglement by the action of casimir force,” Sci China- Phys Mech Astron 57, 2276–2284 (2014).
[Crossref]

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Physics 10, 394–398 (2014).
[Crossref]

P.-C. Ma, J.-Q. Zhang, Y. Xiao, M. Feng, and Z.-M. Zhang, “Tunable double optomechanically induced transparency in an optomechanical system,” Phys. Rev. A 90, 043825 (2014).
[Crossref]

T. Wang, Y. Zhang, Z. Hong, and Z. Han, “Analogue of electromagnetically induced transparency in integrated plasmonics with radiative and subradiant resonators,” Opt. Express 22, 21529–21534 (2014).
[Crossref] [PubMed]

B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Comm. 5, 5082 (2014).
[Crossref]

A. Naweed, D. Goldberg, and V. M. Menon, “All-optical electromagnetically induced transparency using one-dimensional coupled microcavities,” Opt. Express 22, 18818–18823 (2014).
[Crossref] [PubMed]

F. Lei, B. Peng, Ş. K. Özdemir, G. L. Long, and L. Yang, “Dynamic Fano-like resonances in erbium-doped whispering-gallery-mode microresonators,” Appl. Phys. Lett. 105, 101112 (2014).
[Crossref]

2013 (1)

K. Qu and G. S. Agarwal, “Phonon-mediated electromagnetically induced absorption in hybrid opto-electromechanical systems,” Phys. Rev. A 87, 031802 (2013).
[Crossref]

2012 (3)

E. Kawamori, W.-J. Syugu, T.-Y. Hsieh, S.-X. Song, and C. Z. Cheng, “Experimental identification of electromagnetically induced transparency in magnetized plasma,” Phys. Rev. Lett. 108, 075003 (2012).
[Crossref] [PubMed]

H. Xiong, L.-G. Si, A.-S. Zheng, X. Yang, and Y. Wu, “Higher-order sidebands in optomechanically induced transparency,” Phys. Rev. A 86, 013815 (2012).
[Crossref]

B. Peng, Ş. K. Özdemir, J. Zhu, and L. Yang, “Photonic molecules formed by coupled hybrid resonators,” Opt. Lett. 37, 3435–3437 (2012).
[Crossref]

2011 (1)

J. D. Teufel, D. Li, M. Allman, K. Cicak, A. Sirois, J. Whittaker, and R. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature 471, 204–208 (2011).
[Crossref] [PubMed]

2010 (4)

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104, 083901 (2010).
[Crossref] [PubMed]

G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A 81, 041803 (2010).
[Crossref]

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref] [PubMed]

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

2009 (2)

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102, 053901 (2009).
[Crossref] [PubMed]

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724–727 (2009).
[Crossref] [PubMed]

2008 (4)

P. Anisimov and O. Kocharovskaya, “Decaying-dressed-state analysis of a coherently driven three-level λ system,” J. Mod. Opt. 55, 3159–3171 (2008).
[Crossref]

J. M. Dobrindt, I. Wilson-Rae, and T. J. Kippenberg, “Parametric normal-mode splitting in cavity optomechanics,” Phys. Rev. Lett. 101, 263602 (2008).
[Crossref] [PubMed]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial analog of electromagnetically induced transparency,” Phys. Rev. Lett. 101, 253903 (2008).
[Crossref] [PubMed]

2007 (1)

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

2005 (3)

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
[Crossref] [PubMed]

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, “Induced transparency and absorption in coupled whispering-gallery microresonators,” Phys. Rev. A 71, 043804 (2005).
[Crossref]

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

2004 (1)

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

2003 (2)

M. D. Lukin, “Colloquium: Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. 75, 457–472 (2003).
[Crossref]

S. Fan, W. Suh, and J. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003).
[Crossref]

2002 (1)

C. G. Alzar, M. Martinez, and P. Nussenzveig, “Classical analog of electromagnetically induced transparency,” Am. J. Phys. 70, 37–41 (2002).
[Crossref]

2001 (1)

C. Liu, Z. Dutton, C. H. Behroozi, and L. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[Crossref] [PubMed]

2000 (1)

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[Crossref] [PubMed]

1999 (2)

G. Shvets and A. Pukhov, “Electromagnetically induced guiding of counterpropagating lasers in plasmas,” Phys. Rev. E 59, 1033–1037 (1999).
[Crossref]

L. 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]

1998 (1)

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, “Optical modes in photonic molecules,” Phys. Rev. Lett. 81, 2582–2585 (1998).
[Crossref]

1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997).
[Crossref]

1996 (1)

S. E. Harris, “Electromagnetically induced transparency in an ideal plasma,” Phys. Rev. Lett. 77, 5357–5360 (1996).
[Crossref] [PubMed]

1991 (1)

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

1990 (1)

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[Crossref] [PubMed]

1961 (1)

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

Agarwal, G. S.

K. Qu and G. S. Agarwal, “Phonon-mediated electromagnetically induced absorption in hybrid opto-electromechanical systems,” Phys. Rev. A 87, 031802 (2013).
[Crossref]

G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A 81, 041803 (2010).
[Crossref]

Allman, M.

J. D. Teufel, D. Li, M. Allman, K. Cicak, A. Sirois, J. Whittaker, and R. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature 471, 204–208 (2011).
[Crossref] [PubMed]

Alzar, C. G.

C. G. Alzar, M. Martinez, and P. Nussenzveig, “Classical analog of electromagnetically induced transparency,” Am. J. Phys. 70, 37–41 (2002).
[Crossref]

Anisimov, P.

P. Anisimov and O. Kocharovskaya, “Decaying-dressed-state analysis of a coherently driven three-level λ system,” J. Mod. Opt. 55, 3159–3171 (2008).
[Crossref]

Arcizet, O.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref] [PubMed]

Aspelmeyer, M.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724–727 (2009).
[Crossref] [PubMed]

Bayer, M.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, “Optical modes in photonic molecules,” Phys. Rev. Lett. 81, 2582–2585 (1998).
[Crossref]

Behroozi, C. H.

C. Liu, Z. Dutton, C. H. Behroozi, and L. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[Crossref] [PubMed]

L. 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]

Bender, C. M.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Physics 10, 394–398 (2014).
[Crossref]

Boller, K.-J.

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

Boyd, R. W.

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

Cai, M.

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[Crossref] [PubMed]

Carmon, T.

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
[Crossref] [PubMed]

Chang, H.

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

Chen, W.

B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Comm. 5, 5082 (2014).
[Crossref]

Cheng, C. Z.

E. Kawamori, W.-J. Syugu, T.-Y. Hsieh, S.-X. Song, and C. Z. Cheng, “Experimental identification of electromagnetically induced transparency in magnetized plasma,” Phys. Rev. Lett. 108, 075003 (2012).
[Crossref] [PubMed]

Cicak, K.

J. D. Teufel, D. Li, M. Allman, K. Cicak, A. Sirois, J. Whittaker, and R. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature 471, 204–208 (2011).
[Crossref] [PubMed]

Deléglise, S.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref] [PubMed]

Dobrindt, J. M.

J. M. Dobrindt, I. Wilson-Rae, and T. J. Kippenberg, “Parametric normal-mode splitting in cavity optomechanics,” Phys. Rev. Lett. 101, 263602 (2008).
[Crossref] [PubMed]

Dremin, A. A.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, “Optical modes in photonic molecules,” Phys. Rev. Lett. 81, 2582–2585 (1998).
[Crossref]

Du, C.

Du, C.-G.

M. Gao, F.-C. Lei, C.-G. Du, and G.-L. Long, “Self-sustained oscillation and dynamical multistability of optomechanical systems in the extremely-large-amplitude regime,” Phys. Rev. A 91, 013833 (2015).
[Crossref]

Dutton, Z.

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[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 The schematic of the considered system. Two WGM microcavities (a and c) are directly coupled by evanescent field. Cavity c contains a mechanical mode with frequency ωm. A fiber taper waveguide is side-coupled to cavity c for light input and output. Two laser fields with frequencies ωL and ωp are input to drive and probe the system, respectively.
Fig. 2
Fig. 2 Illustration of the three-pathway interference (a) in the real pathway picture and (b) in the decaying-normal-mode picture.
Fig. 3
Fig. 3 The real parts of (a) the response function (x) and (b) its three normal modes compenents. Here λ = 0.1ωm, β = 0.2ωm3, κc = ωm, γm = 10−3ωm, κa = 5γm, corresponding to the black point in area T of Fig. 5. It shows that the optomechanical interaction produces a more sharp TEIT peak within the CRIT window.
Fig. 4
Fig. 4 Same as in Fig. 3, expect for λ = 0.2ωm, β = 0.3ωm3, which corresponds to the black point in area A of Fig. 5. It shows that the optomechanical interaction produces a more sharp TEIA dip within the CRIT window.
Fig. 5
Fig. 5 The phase diagram of TEIT and TEIA. Line a denotes the stability, b denotes the boundary between TEIT and TEIA, and c denotes the boundary of normal-mode splitting. Parameters in the area A encircled by line a, b, and c can lead TEIA, while in the area T encircled by coordinate axis and line a, b, c can lead to TEIT. The other parameters are the same as Fig. 3.

Equations (9)

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

H = H 0 + H c + H I + H d , H 0 = ω c c c + ω a a a + p 2 2 m + 1 2 m ω m 2 q 2 , H c = λ ( a c c a ) , H I = g c c q , H d = i ε L ( c e i ω L t c e i ω L t ) + i ε p ( c e i ω p t c e i ω p t ) ,
d q d t = p m , d p d t = m ω m 2 q g c c γ m p , d c d t = [ κ c + i ( ω c ω L + g q ) ] c + ε L i λ a + ε p e i δ t , d a d t = [ κ a + i ( ω a ω L ) ] a i λ c ,
d X d t = D X + ζ
D = ( 0 1 m 0 0 0 0 m ω m 2 γ m g c 0 * 0 g c 0 0 i g c 0 0 ( κ c + i Δ c ) i λ 0 0 0 0 i λ ( κ a + i Δ a ) 0 0 i g c 0 * 0 0 0 ( κ c i Δ c ) i λ 0 0 0 0 i λ ( κ a i Δ a ) ) ,
δ c = c + e i δ t + c e i δ t , δ a = a + e i δ t + a e i δ t , δ q = q + e i δ t + q e i δ t .
R ( δ ) = 2 κ c X ( δ ) Λ ( δ ) + i β Λ ( δ ) Λ * ( δ ) X ( δ ) i β ( Λ ( δ ) Λ * ( δ ) ) 1 ,
R ˜ ( x ) = κ c ( κ c i x ) + λ 2 κ a i x + β / 2 ω m κ m i x 1 ,
1 κ c + λ 2 κ a + β / 2 ω m κ m > 1 κ c + λ 2 κ a .
R ˜ ( x ) = A 1 x i κ 1 + A 2 x i κ 2 + A 3 x i κ 3 1

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