Abstract

We propose a simple microresonator scheme for a Mach–Zehnder interferometer in which a microresonator is side coupled to one arm and a phase shifter is introduced into the other arm, to produce an asymmetric Fano-resonance line shape. In this system, a phase shifter is used to control the variation of the asymmetric line shape, with another reverse resonance next to a resonance minimum over a very narrow frequency range, which results from the interference between a direct channel and a high-Q resonance indirect channel. We also theoretically investigate the novel bistability characteristic based on these shapes.

© 2005 Optical Society of America

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  1. S. Arnold, C. T. Liu, W. B. Whitten, and J. M. Ramsey, Opt. Lett. 16, 420 (1991).
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    [CrossRef]
  5. S. Fan, Appl. Phys. Lett. 80, 908 (2002).
    [CrossRef]
  6. L. Maleki, A. B. Matsko, A. A. Savchenkov, and V. S. Ilchenko, Opt. Lett. 29, 626 (2004).
    [CrossRef] [PubMed]
  7. C. Y. Chao and L. J. Guo, Appl. Phys. Lett. 83, 1527 (2003).
    [CrossRef]
  8. P. Absil, J. Hryniewicz, B. Little, R. Wilson, L. Joneckis, and P. Ho, IEEE Photon. Technol. Lett. 12, 398 (2000).
    [CrossRef]
  9. L. F. Stokes, M. Chodorow, and H. J. Shaw, Opt. Lett. 7, 289 (1982).
  10. S. Pereira, P. Chak, J. Sipe, T. Tkeshlashvilli, and K. Busch, Photonics Nanostruct. Fundam. Appl. 2, 181 (2004).
    [CrossRef]
  11. A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Y. S. Kivshar, Phys. Rev. E 71, 036626 (2005).
    [CrossRef]
  12. A. R. Cowan and J. F. Young, Phys. Rev. E 68, 046606 (2003).
    [CrossRef]
  13. V. Lousse and J. P. Vigneron, Phys. Rev. B 69, 155106 (2004).
    [CrossRef]
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    [CrossRef]
  15. Y. Lu, J. Y. Wang, X. X. Xu, S. H. Pan, and C. Z. Zhang, Opt. Laser Technol. 32, 245 (2000).
    [CrossRef]

2005 (1)

A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Y. S. Kivshar, Phys. Rev. E 71, 036626 (2005).
[CrossRef]

2004 (3)

S. Pereira, P. Chak, J. Sipe, T. Tkeshlashvilli, and K. Busch, Photonics Nanostruct. Fundam. Appl. 2, 181 (2004).
[CrossRef]

V. Lousse and J. P. Vigneron, Phys. Rev. B 69, 155106 (2004).
[CrossRef]

L. Maleki, A. B. Matsko, A. A. Savchenkov, and V. S. Ilchenko, Opt. Lett. 29, 626 (2004).
[CrossRef] [PubMed]

2003 (2)

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

A. R. Cowan and J. F. Young, Phys. Rev. E 68, 046606 (2003).
[CrossRef]

2002 (1)

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

2000 (2)

Y. Lu, J. Y. Wang, X. X. Xu, S. H. Pan, and C. Z. Zhang, Opt. Laser Technol. 32, 245 (2000).
[CrossRef]

P. Absil, J. Hryniewicz, B. Little, R. Wilson, L. Joneckis, and P. Ho, IEEE Photon. Technol. Lett. 12, 398 (2000).
[CrossRef]

1997 (1)

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

1996 (1)

1994 (1)

C. J. Capamny, F. J. Fraile-Pelaez, and M. A. Muriel, IEEE J. Quantum Electron. 30, 2578 (1994).
[CrossRef]

1991 (2)

1982 (1)

L. F. Stokes, M. Chodorow, and H. J. Shaw, Opt. Lett. 7, 289 (1982).

Absil, P.

P. Absil, J. Hryniewicz, B. Little, R. Wilson, L. Joneckis, and P. Ho, IEEE Photon. Technol. Lett. 12, 398 (2000).
[CrossRef]

Arnold, S.

Busch, K.

S. Pereira, P. Chak, J. Sipe, T. Tkeshlashvilli, and K. Busch, Photonics Nanostruct. Fundam. Appl. 2, 181 (2004).
[CrossRef]

Capamny, C. J.

C. J. Capamny, F. J. Fraile-Pelaez, and M. A. Muriel, IEEE J. Quantum Electron. 30, 2578 (1994).
[CrossRef]

Chak, P.

S. Pereira, P. Chak, J. Sipe, T. Tkeshlashvilli, and K. Busch, Photonics Nanostruct. Fundam. Appl. 2, 181 (2004).
[CrossRef]

Chao, C. Y.

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

Chodorow, M.

L. F. Stokes, M. Chodorow, and H. J. Shaw, Opt. Lett. 7, 289 (1982).

Chu, S. T.

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

Cowan, A. R.

A. R. Cowan and J. F. Young, Phys. Rev. E 68, 046606 (2003).
[CrossRef]

Fan, S.

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

Flach, S.

A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Y. S. Kivshar, Phys. Rev. E 71, 036626 (2005).
[CrossRef]

Foresi, J.

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

Fraile-Pelaez, F. J.

C. J. Capamny, F. J. Fraile-Pelaez, and M. A. Muriel, IEEE J. Quantum Electron. 30, 2578 (1994).
[CrossRef]

Gorodetsky, M. I.

Guo, L. J.

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

H. A. Haus and Y. Lai, J. Lightwave Technol. 9, 754 (1991).
[CrossRef]

Ho, P.

P. Absil, J. Hryniewicz, B. Little, R. Wilson, L. Joneckis, and P. Ho, IEEE Photon. Technol. Lett. 12, 398 (2000).
[CrossRef]

Hryniewicz, J.

P. Absil, J. Hryniewicz, B. Little, R. Wilson, L. Joneckis, and P. Ho, IEEE Photon. Technol. Lett. 12, 398 (2000).
[CrossRef]

Ilchenko, V. S.

Joneckis, L.

P. Absil, J. Hryniewicz, B. Little, R. Wilson, L. Joneckis, and P. Ho, IEEE Photon. Technol. Lett. 12, 398 (2000).
[CrossRef]

Kivshar, Y. S.

A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Y. S. Kivshar, Phys. Rev. E 71, 036626 (2005).
[CrossRef]

Lai, Y.

H. A. Haus and Y. Lai, J. Lightwave Technol. 9, 754 (1991).
[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.

P. Absil, J. Hryniewicz, B. Little, R. Wilson, L. Joneckis, and P. Ho, IEEE Photon. Technol. Lett. 12, 398 (2000).
[CrossRef]

Little, B. E.

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

Liu, C. T.

Lousse, V.

V. Lousse and J. P. Vigneron, Phys. Rev. B 69, 155106 (2004).
[CrossRef]

Lu, Y.

Y. Lu, J. Y. Wang, X. X. Xu, S. H. Pan, and C. Z. Zhang, Opt. Laser Technol. 32, 245 (2000).
[CrossRef]

Maleki, L.

Matsko, A. B.

Mingaleev, S. F.

A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Y. S. Kivshar, Phys. Rev. E 71, 036626 (2005).
[CrossRef]

Miroshnichenko, A. E.

A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Y. S. Kivshar, Phys. Rev. E 71, 036626 (2005).
[CrossRef]

Muriel, M. A.

C. J. Capamny, F. J. Fraile-Pelaez, and M. A. Muriel, IEEE J. Quantum Electron. 30, 2578 (1994).
[CrossRef]

Pan, S. H.

Y. Lu, J. Y. Wang, X. X. Xu, S. H. Pan, and C. Z. Zhang, Opt. Laser Technol. 32, 245 (2000).
[CrossRef]

Pereira, S.

S. Pereira, P. Chak, J. Sipe, T. Tkeshlashvilli, and K. Busch, Photonics Nanostruct. Fundam. Appl. 2, 181 (2004).
[CrossRef]

Ramsey, J. M.

Savchenkov, A. A.

Shaw, H. J.

L. F. Stokes, M. Chodorow, and H. J. Shaw, Opt. Lett. 7, 289 (1982).

Sipe, J.

S. Pereira, P. Chak, J. Sipe, T. Tkeshlashvilli, and K. Busch, Photonics Nanostruct. Fundam. Appl. 2, 181 (2004).
[CrossRef]

Stokes, L. F.

L. F. Stokes, M. Chodorow, and H. J. Shaw, Opt. Lett. 7, 289 (1982).

Tkeshlashvilli, T.

S. Pereira, P. Chak, J. Sipe, T. Tkeshlashvilli, and K. Busch, Photonics Nanostruct. Fundam. Appl. 2, 181 (2004).
[CrossRef]

Vigneron, J. P.

V. Lousse and J. P. Vigneron, Phys. Rev. B 69, 155106 (2004).
[CrossRef]

Wang, J. Y.

Y. Lu, J. Y. Wang, X. X. Xu, S. H. Pan, and C. Z. Zhang, Opt. Laser Technol. 32, 245 (2000).
[CrossRef]

Whitten, W. B.

Wilson, R.

P. Absil, J. Hryniewicz, B. Little, R. Wilson, L. Joneckis, and P. Ho, IEEE Photon. Technol. Lett. 12, 398 (2000).
[CrossRef]

Xu, X. X.

Y. Lu, J. Y. Wang, X. X. Xu, S. H. Pan, and C. Z. Zhang, Opt. Laser Technol. 32, 245 (2000).
[CrossRef]

Young, J. F.

A. R. Cowan and J. F. Young, Phys. Rev. E 68, 046606 (2003).
[CrossRef]

Zhang, C. Z.

Y. Lu, J. Y. Wang, X. X. Xu, S. H. Pan, and C. Z. Zhang, Opt. Laser Technol. 32, 245 (2000).
[CrossRef]

Appl. Phys. Lett. (2)

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

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

IEEE J. Quantum Electron. (1)

C. J. Capamny, F. J. Fraile-Pelaez, and M. A. Muriel, IEEE J. Quantum Electron. 30, 2578 (1994).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

P. Absil, J. Hryniewicz, B. Little, R. Wilson, L. Joneckis, and P. Ho, IEEE Photon. Technol. Lett. 12, 398 (2000).
[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]

H. A. Haus and Y. Lai, J. Lightwave Technol. 9, 754 (1991).
[CrossRef]

Opt. Laser Technol. (1)

Y. Lu, J. Y. Wang, X. X. Xu, S. H. Pan, and C. Z. Zhang, Opt. Laser Technol. 32, 245 (2000).
[CrossRef]

Opt. Lett. (4)

Photonics Nanostruct. Fundam. Appl. (1)

S. Pereira, P. Chak, J. Sipe, T. Tkeshlashvilli, and K. Busch, Photonics Nanostruct. Fundam. Appl. 2, 181 (2004).
[CrossRef]

Phys. Rev. B (1)

V. Lousse and J. P. Vigneron, Phys. Rev. B 69, 155106 (2004).
[CrossRef]

Phys. Rev. E (2)

A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Y. S. Kivshar, Phys. Rev. E 71, 036626 (2005).
[CrossRef]

A. R. Cowan and J. F. Young, Phys. Rev. E 68, 046606 (2003).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of a microcavity-resonator-coupled Mach–Zehnder interferometer; a microcavity resonator is side coupled to one arm, and a phase shifter is introduced into the other arm.

Fig. 2
Fig. 2

Transmission spectra through the optical system shown in Fig. 1, with microcavity radius a = 100 μ m , refractive index contrast n = 1.44 , t = 0.1 , α = 10 7 μ m 1 for phase shifts (a) Φ s = 0 , (b) Φ s = 0.5 π , (c) Φ s = π , (d) Φ s = 1.5 π , (e) Φ s = 0.5 π (curve 1), 0.25 π (curve 2), 0 (curve 3), 1.5 π (curve 4).

Fig. 3
Fig. 3

Input–output intensity characteristics of the optical system with a = 50 μ m , n = 1.44 , t = 0.1 , α = 1 × 10 5 μ m 1 , R = 3.13 × 10 9 : (a) Φ s = 1.7 π , δ = 0.017 ; (b) Φ s = 1.3 π , δ = 0.017 ; (c) Φ s = 1.3 π , δ = 0.069 ; (d) Φ s = 1.1 π , δ = 0.069 .

Equations (8)

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E 3 = 1 t 2 E 1 + i t E 2 ,
E 4 = i t E 1 + 1 t 2 E 2 ,
E 2 = exp ( α L 2 ) exp ( i ϕ ) E 4 ,
E 3 E 1 = E 3 E 1 exp ( i Φ r ) ,
E 3 E 1 2 = [ 1 t 2 exp ( α L 2 ) ] 2 + 4 1 t 2 exp ( α L 2 ) sin 2 ( ϕ 2 ) [ 1 1 t 2 exp ( α L 2 ) ] 2 + 4 1 t 2 exp ( α L 2 ) sin 2 ( ϕ 2 ) ,
Φ r = arg [ 1 t 2 exp ( i ϕ α L 2 ) 1 1 t 2 exp ( i ϕ α L 2 ) ] .
E out E in 2 = 1 4 [ 1 + 2 E 3 E 1 cos ( Φ r Φ s ) + E 3 E 1 2 ] .
ϕ = β L + R α 1 e α L 1 e α L ( E 3 2 E 1 2 ) ,

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