Abstract

The transmission spectra of a Fabry–Perot etalon coupled to a microtoroid resonator are studied theoretically and experimentally. The resonance line shapes depend strongly on the resonance wavelength detuning and coupling strength between the two resonators. A wide variety of line shapes, ranging from a single to triple peaks, symmetric to asymmetric Fano-like peaks, and notches were predicted and observed experimentally. The capability to modify the spectral line shapes by tuning the coupling between or losses of two resonators may find applications in optical filtering, switching, sensing, and dispersion engineering.

© 2006 Optical Society of America

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References

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  1. K. J. Vahala, Nature 424, 849 (2003).
    [CrossRef]
  2. A. Yariv, IEEE Photon. Technol. Lett. 14, 483 (2002).
    [CrossRef]
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    [CrossRef]
  4. S. Fan, Appl. Phys. Lett. 80, 908 (2002).
    [CrossRef]
  5. C. Y Chao and L. J. Guo, Appl. Phys. Lett. 83, 1527 (2003).
    [CrossRef]
  6. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
    [CrossRef] [PubMed]
  7. Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
    [CrossRef]
  8. A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, 1997).
  9. A. Yariv, Electron. Lett. 36, 321 (2000).
    [CrossRef]
  10. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
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    [CrossRef]
  12. M. L. Gorodetsky and I. S. Grudinin, J. Opt. Soc. Am. B 21, 697 (2004).
    [CrossRef]

2004 (1)

2003 (3)

C. Y Chao and L. J. Guo, Appl. Phys. Lett. 83, 1527 (2003).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

K. J. Vahala, Nature 424, 849 (2003).
[CrossRef]

2002 (3)

A. Yariv, IEEE Photon. Technol. Lett. 14, 483 (2002).
[CrossRef]

E. Krioukov, D. J. W. Klunder, A. Driessen, J. Greve, and C. Otto, Opt. Lett. 27, 512 (2002).
[CrossRef]

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

2000 (2)

A. Yariv, Electron. Lett. 36, 321 (2000).
[CrossRef]

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[CrossRef]

1997 (1)

A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, 1997).

1984 (1)

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

1961 (1)

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

Chao, C. Y

C. Y Chao and L. J. Guo, Appl. Phys. Lett. 83, 1527 (2003).
[CrossRef]

Driessen, A.

Fan, S.

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

Fano, U.

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

Gorodetsky, M. L.

Greve, J.

Grudinin, I. S.

Guo, L. J.

C. Y Chao and L. J. Guo, Appl. Phys. Lett. 83, 1527 (2003).
[CrossRef]

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

Kippenberg, T. J.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

Klunder, D. J.

Krioukov, E.

Lee, R. K.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[CrossRef]

Li, Y.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[CrossRef]

Otto, C.

Spillane, S. M.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

Vahala, K. J.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

K. J. Vahala, Nature 424, 849 (2003).
[CrossRef]

Xu, Y.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[CrossRef]

Yariv, A.

A. Yariv, IEEE Photon. Technol. Lett. 14, 483 (2002).
[CrossRef]

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[CrossRef]

A. Yariv, Electron. Lett. 36, 321 (2000).
[CrossRef]

A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, 1997).

Appl. Phys. Lett. (2)

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

C. Y Chao and L. J. Guo, Appl. Phys. Lett. 83, 1527 (2003).
[CrossRef]

Electron. Lett. (1)

A. Yariv, Electron. Lett. 36, 321 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. Yariv, IEEE Photon. Technol. Lett. 14, 483 (2002).
[CrossRef]

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

Nature (2)

K. J. Vahala, Nature 424, 849 (2003).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. (1)

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

Phys. Rev. E (1)

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[CrossRef]

Other (2)

A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, 1997).

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

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Figures (3)

Fig. 1
Fig. 1

(Color online) Schematic of a FP etalon coupled to a microtoroid resonator.

Fig. 2
Fig. 2

(Color online) Calculated transmission spectra of a single FP resonator, a single microtoroid resonator, and the coupled-resonator system. Some key parameters that we use in the calculations are α = 0.9998 and κ = 0.0063 ,  0.02,  0.0632,  0.0999,  0.0126,  0.0283, 0.0447,  0.0774, respectively in (a), (b), (c), (d), (e), (f), (g), (h). Δ n = 0.8 × 10 4 in (a)–(c) and (e)–(g); and Δ n = 1.3 × 10 4 in (d) and (h).

Fig. 3
Fig. 3

(Color online) Measurements and theoretical fits of the transmission spectra of the microtoroid–FP coupled-resonator system. Asterisk curves and dashed–dotted curves represent the measured and fitting data, respectively. Fitting parameters α and κ are also given in (a)–(d).

Equations (6)

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( a out b out ) = M ( a in b in ) ,
M FBG = [ cosh ( s L FBG ) i δ s sinh ( s L FBG ) i ζ s sinh ( s L FBG ) i ζ s sinh ( s L FBG ) cosh ( s L FBG ) + i δ s sinh ( s L FBG ) ] ,
M L = [ exp ( i β L ) 0 0 exp ( i β L ) ] ,
M WGM = [ t R 0 0 1 t R ] , t R = 1 κ 2 exp ( i β 2 π R ) α exp ( i β 2 π R ) 1 κ 2 α .
b in a in = M ( 2 , 1 ) M ( 2 , 2 ) ,
a out a in = [ M ( 1 , 1 ) M ( 2 , 2 ) M ( 1 , 2 ) M ( 2 , 1 ) ] M ( 2 , 2 ) .

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