Abstract

A simple theoretical model of a Mach–Zehnder interferometer (MZI) consisting of two coupled-resonator optical waveguides with different lengths is proposed and experimentally demonstrated at microwave frequencies. Good agreement between theoretical and experimental results is observed. MZIs in planar photonic crystals may become key building blocks in the development of microscale optical integrated devices such as filters, demultiplexers, switches, and modulators.

© 2003 Optical Society of America

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References

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    [CrossRef] [PubMed]
  2. S. John, Phys. Rev. Lett. 58, 2486 (1987).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999).
    [CrossRef]
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    [CrossRef]
  7. S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001), http://www.opticsexpress.org .
    [CrossRef] [PubMed]

2001 (2)

1999 (1)

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

1987 (2)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Fan, S.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Joannopoulos, J. D.

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001), http://www.opticsexpress.org .
[CrossRef] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

John, S.

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Johnson, S. G.

Koshiba, M.

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Lee, R. K.

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Ramaswami, R.

R. Ramaswami and K. N. Sivajaran, Optical Networks: A Practical Perspective (Academic, San Diego, Calif., 1998).

Scherer, A.

Sivajaran, K. N.

R. Ramaswami and K. N. Sivajaran, Optical Networks: A Practical Perspective (Academic, San Diego, Calif., 1998).

Villeneuve, P. R.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Xu, Y.

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Yariv, A.

J. Lightwave Technol. (1)

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (3)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Other (1)

R. Ramaswami and K. N. Sivajaran, Optical Networks: A Practical Perspective (Academic, San Diego, Calif., 1998).

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of a 2×2 Mach–Zehnder interferometer. (b) Schematic of a Mach–Zehnder interferometer employing PhC couplers and CROWs.

Fig. 2
Fig. 2

Theoretical CROW-based MZI transmission responses for (a) ΔN=2, (b) ΔN=4. (c) ΔN=8, and (d) ΔN=16 resulting from the theoretical model. Dashed and solid curves, output ports 1 and 2, respectively.

Fig. 3
Fig. 3

Experimental transmission response of the alumina PhC in the ΓK direction: bulk crystal (dashed curve) and 10-cavities-long CROW (solid curve).

Fig. 4
Fig. 4

Experimental transmission response of the CROW-based MZI (solid curves) and one of two CROWs that compose the MZI (dashed curve) for (a) ΔN=2 and (b) ΔN=4. The theoretical frequencies of the transmission notches are shown as vertical dotted lines. Inset, detailed view of the spectral region about the notch for ΔN=2: experimental response (solid curve) and theoretical model of the MZI added to a single CROW response (dashed curve).

Equations (3)

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T11f=sin2βΔL/2T21f=cos2βΔL/2,
βf=1d arccosf-f01-Δα/2κf0,
T11f=sin2ΔN2 arccosf-f0κf0,T21f=cos2ΔN2 arccosf-f0κf0.

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