Abstract

We theoretically study a parallel configuration of two interacting whispering-gallery-mode optical resonators and show a narrowband modal structure as a basis for a widely tunable delay line. For the optimum coupling configuration the system can possess an unusually narrow spectral feature with a much narrower bandwidth than the loaded bandwidth of each individual resonator. The effect has a direct analogy with the phenomenon of electromagnetically induced transparency in quantum systems for which the interference of spontaneous emission results in ultranarrow resonances.

© 2004 Optical Society of America

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  1. S. E. Harris, Phys. Today 50(7), 36 (1997).
    [CrossRef]
  2. J. P. Marangos, J. Mod. Opt. 45, 471 (1998).
    [CrossRef]
  3. A. B. Matsko, O. Kocharovskaya, Y. Rostovtsev, G. R. Welch, A. S. Zibrov, and M. O. Scully, Adv. Atom. Mol. Opt. Phys. 46, 191 (2001).
    [CrossRef]
  4. R. W. Boyd and D. J. Gauthier, Prog. Opt. 43, 497 (2002).
    [CrossRef]
  5. J. E. Heebner, R. W. Boyd, and Q. Park, Phys. Rev. E 65, 036619 (2002).
    [CrossRef]
  6. A. Melloni, F. Morichetti, and M. Martinelli, Opt. Quantum Electron. 35, 365 (2003).
    [CrossRef]
  7. T. Opatrny and D. G. Welsch, Fortschr. Phys. 49, 1065 (2001).
    [CrossRef]
  8. S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kokubun, IEEE Photon. Technol. Lett. 11, 1426 (1999).
    [CrossRef]
  9. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, 1997).
    [CrossRef]
  10. A. Imamoglu, Phys. Rev. A 40, 2835 (1989).
    [CrossRef] [PubMed]
  11. S. Fan, Appl. Phys. Lett. 80, 908 (2002).
    [CrossRef]
  12. S. Fan, W. Suh, and J. D. Joannopoulos, J. Opt. Soc. Am. A 20, 569 (2003).
    [CrossRef]
  13. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
    [CrossRef]
  14. P. Urquhart, J. Opt. Soc. Am. A 5, 803 (1988).
    [CrossRef]
  15. K. Oda, N. Takato, and H. Toba, J. Lightwave Technol. 9, 728 (1991).
    [CrossRef]
  16. V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, J. Opt. Soc. Am. B 20, 333 (2003).
    [CrossRef]
  17. A. Melloni, Opt. Lett. 26, 917 (2001).
    [CrossRef]

2003 (3)

2002 (3)

S. Fan, Appl. Phys. Lett. 80, 908 (2002).
[CrossRef]

R. W. Boyd and D. J. Gauthier, Prog. Opt. 43, 497 (2002).
[CrossRef]

J. E. Heebner, R. W. Boyd, and Q. Park, Phys. Rev. E 65, 036619 (2002).
[CrossRef]

2001 (3)

T. Opatrny and D. G. Welsch, Fortschr. Phys. 49, 1065 (2001).
[CrossRef]

A. B. Matsko, O. Kocharovskaya, Y. Rostovtsev, G. R. Welch, A. S. Zibrov, and M. O. Scully, Adv. Atom. Mol. Opt. Phys. 46, 191 (2001).
[CrossRef]

A. Melloni, Opt. Lett. 26, 917 (2001).
[CrossRef]

1999 (1)

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kokubun, IEEE Photon. Technol. Lett. 11, 1426 (1999).
[CrossRef]

1998 (1)

J. P. Marangos, J. Mod. Opt. 45, 471 (1998).
[CrossRef]

1997 (2)

S. E. Harris, Phys. Today 50(7), 36 (1997).
[CrossRef]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

1991 (1)

K. Oda, N. Takato, and H. Toba, J. Lightwave Technol. 9, 728 (1991).
[CrossRef]

1989 (1)

A. Imamoglu, Phys. Rev. A 40, 2835 (1989).
[CrossRef] [PubMed]

1988 (1)

Boyd, R. W.

R. W. Boyd and D. J. Gauthier, Prog. Opt. 43, 497 (2002).
[CrossRef]

J. E. Heebner, R. W. Boyd, and Q. Park, Phys. Rev. E 65, 036619 (2002).
[CrossRef]

Chu, S. T.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kokubun, IEEE Photon. Technol. Lett. 11, 1426 (1999).
[CrossRef]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Fan, S.

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Gauthier, D. J.

R. W. Boyd and D. J. Gauthier, Prog. Opt. 43, 497 (2002).
[CrossRef]

Harris, S. E.

S. E. Harris, Phys. Today 50(7), 36 (1997).
[CrossRef]

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Heebner, J. E.

J. E. Heebner, R. W. Boyd, and Q. Park, Phys. Rev. E 65, 036619 (2002).
[CrossRef]

Ilchenko, V. S.

Imamoglu, A.

A. Imamoglu, Phys. Rev. A 40, 2835 (1989).
[CrossRef] [PubMed]

Joannopoulos, J. D.

Kaneko, T.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kokubun, IEEE Photon. Technol. Lett. 11, 1426 (1999).
[CrossRef]

Kocharovskaya, O.

A. B. Matsko, O. Kocharovskaya, Y. Rostovtsev, G. R. Welch, A. S. Zibrov, and M. O. Scully, Adv. Atom. Mol. Opt. Phys. 46, 191 (2001).
[CrossRef]

Kokubun, Y.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kokubun, IEEE Photon. Technol. Lett. 11, 1426 (1999).
[CrossRef]

Laine, J. P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Little, B. E.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kokubun, IEEE Photon. Technol. Lett. 11, 1426 (1999).
[CrossRef]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Maleki, L.

Marangos, J. P.

J. P. Marangos, J. Mod. Opt. 45, 471 (1998).
[CrossRef]

Martinelli, M.

A. Melloni, F. Morichetti, and M. Martinelli, Opt. Quantum Electron. 35, 365 (2003).
[CrossRef]

Matsko, A. B.

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, J. Opt. Soc. Am. B 20, 333 (2003).
[CrossRef]

A. B. Matsko, O. Kocharovskaya, Y. Rostovtsev, G. R. Welch, A. S. Zibrov, and M. O. Scully, Adv. Atom. Mol. Opt. Phys. 46, 191 (2001).
[CrossRef]

Melloni, A.

A. Melloni, F. Morichetti, and M. Martinelli, Opt. Quantum Electron. 35, 365 (2003).
[CrossRef]

A. Melloni, Opt. Lett. 26, 917 (2001).
[CrossRef]

Morichetti, F.

A. Melloni, F. Morichetti, and M. Martinelli, Opt. Quantum Electron. 35, 365 (2003).
[CrossRef]

Oda, K.

K. Oda, N. Takato, and H. Toba, J. Lightwave Technol. 9, 728 (1991).
[CrossRef]

Opatrny, T.

T. Opatrny and D. G. Welsch, Fortschr. Phys. 49, 1065 (2001).
[CrossRef]

Pan, W.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kokubun, IEEE Photon. Technol. Lett. 11, 1426 (1999).
[CrossRef]

Park, Q.

J. E. Heebner, R. W. Boyd, and Q. Park, Phys. Rev. E 65, 036619 (2002).
[CrossRef]

Rostovtsev, Y.

A. B. Matsko, O. Kocharovskaya, Y. Rostovtsev, G. R. Welch, A. S. Zibrov, and M. O. Scully, Adv. Atom. Mol. Opt. Phys. 46, 191 (2001).
[CrossRef]

Savchenkov, A. A.

Scully, M. O.

A. B. Matsko, O. Kocharovskaya, Y. Rostovtsev, G. R. Welch, A. S. Zibrov, and M. O. Scully, Adv. Atom. Mol. Opt. Phys. 46, 191 (2001).
[CrossRef]

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, 1997).
[CrossRef]

Suh, W.

Takato, N.

K. Oda, N. Takato, and H. Toba, J. Lightwave Technol. 9, 728 (1991).
[CrossRef]

Toba, H.

K. Oda, N. Takato, and H. Toba, J. Lightwave Technol. 9, 728 (1991).
[CrossRef]

Urquhart, P.

Welch, G. R.

A. B. Matsko, O. Kocharovskaya, Y. Rostovtsev, G. R. Welch, A. S. Zibrov, and M. O. Scully, Adv. Atom. Mol. Opt. Phys. 46, 191 (2001).
[CrossRef]

Welsch, D. G.

T. Opatrny and D. G. Welsch, Fortschr. Phys. 49, 1065 (2001).
[CrossRef]

Zibrov, A. S.

A. B. Matsko, O. Kocharovskaya, Y. Rostovtsev, G. R. Welch, A. S. Zibrov, and M. O. Scully, Adv. Atom. Mol. Opt. Phys. 46, 191 (2001).
[CrossRef]

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, 1997).
[CrossRef]

Adv. Atom. Mol. Opt. Phys. (1)

A. B. Matsko, O. Kocharovskaya, Y. Rostovtsev, G. R. Welch, A. S. Zibrov, and M. O. Scully, Adv. Atom. Mol. Opt. Phys. 46, 191 (2001).
[CrossRef]

Appl. Phys. Lett. (1)

S. Fan, Appl. Phys. Lett. 80, 908 (2002).
[CrossRef]

Fortschr. Phys. (1)

T. Opatrny and D. G. Welsch, Fortschr. Phys. 49, 1065 (2001).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kokubun, IEEE Photon. Technol. Lett. 11, 1426 (1999).
[CrossRef]

J. Lightwave Technol. (2)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

K. Oda, N. Takato, and H. Toba, J. Lightwave Technol. 9, 728 (1991).
[CrossRef]

J. Mod. Opt. (1)

J. P. Marangos, J. Mod. Opt. 45, 471 (1998).
[CrossRef]

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

J. Opt. Soc. Am. B (1)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

A. Melloni, F. Morichetti, and M. Martinelli, Opt. Quantum Electron. 35, 365 (2003).
[CrossRef]

Phys. Rev. A (1)

A. Imamoglu, Phys. Rev. A 40, 2835 (1989).
[CrossRef] [PubMed]

Phys. Rev. E (1)

J. E. Heebner, R. W. Boyd, and Q. Park, Phys. Rev. E 65, 036619 (2002).
[CrossRef]

Phys. Today (1)

S. E. Harris, Phys. Today 50(7), 36 (1997).
[CrossRef]

Prog. Opt. (1)

R. W. Boyd and D. J. Gauthier, Prog. Opt. 43, 497 (2002).
[CrossRef]

Other (1)

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, 1997).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Configurations of two WGM resonators and their ring-cavity equivalent schemes: (a) resonators coupled in parallel, (b) mixed series–parallel WGM resonator coupling, (c) WGM cavity interacting with a waveguide with partial reflectors.

Fig. 2
Fig. 2

Power transmission coefficient for two cavities coupled as shown in Fig. 1(c). Solid curve, γ/2γc=5×10-4 and ω1-ω2/2γc=0.1; dashed curve, γ/2γc=5×10-4 and ω1-ω2/2γc=0.5. Frequency ω0 corresponds to central frequency ω1+ω2/2.

Fig. 3
Fig. 3

Power transmission and reflection coefficients for two identical cavities with frequency ω0 coupled as shown in Fig. 1(b). Coupling between the cavities as well as between the cavities and the waveguides is taken to be equal and is characterized by coefficient γc. Absorption is neglected. TL, Lorentzian transmission profile. T1, T2, transmission and R1, R2 reflection in the two-cavity system.

Equations (6)

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

TP=γ+iω-ω1γ+iω-ω22γc+γ+iω-ω12γc+γ+iω-ω2-4expiψγc2,
TPmin2γ2/4γc2,
TPmax2ω1-ω2416γγc+ω1-ω222,
Γ16γγc+ω1-ω22216γcω1-ω22.
Tw=1-r2TL expiψr/21-TL2r2 expiψr,
TL=γc-γ-iω-ω0γc+γ+iω-ω0.

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