Abstract

We discuss a self-imaging phenomenon in a multimode interference (MMI) coupler. From experiment, different self-images, which are undefined in MMI theory, are observed. These undefined self-images are named “extraneous self-images” (Ex̱SIs) for convenience. To estimate the applicability of the Ex̱SIs, the characteristics of both the single self-image (0dB self-image, 0dB SI), which is defined in MMI theory, and the Ex̱SI are compared and analyzed through simulation and experiment. The results show that the Ex̱SI has an imaging period that is the same as the 0dB SI and that the excess loss and the extinction ratio of the Ex̱SI improve more than that of the 0dB SI as the imaging period increases.

© 2007 Optical Society of America

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References

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  1. L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
    [CrossRef]
  2. E. C. M. Pennings, R. van Roijen, B. H. Verbeek, R. J. Deri, and L. B. Soldano, in Conference Proceedings, IEEE Lasers and Electro-Optics Society Annual Meeting (IEEE, 1993), p. 193.
  3. J. K. Hong, S. S. Lee, and D. W. Shin, J. Korean Phys. Soc. 45, 84 (2004).
  4. L. J. Harrison, T. J. Tayag, G. J. Simonis, M. Stead, G. W. Euliss, and R. P. Leavitt, IEEE Photon. Technol. Lett. 12, 657 (2000).
    [CrossRef]
  5. D. G. Rabus and M. Hamacher, IEEE Photon. Technol. Lett. 13, 812 (2001).
    [CrossRef]
  6. K. C. Lin and W. Y. Lee, Electron. Lett. 32, 1259 (1996).
    [CrossRef]
  7. B. Li, S. J. Chua, C. W. Leitz, and E. A. Fitzgerald, Opt. Eng. 41, 723 (2002).
    [CrossRef]
  8. A. Himeno, H. Terui, and M. Kobayashi, J. Lightwave Technol. 6, 41 (1988).
    [CrossRef]
  9. R. Ulrich and G. Ankele, Appl. Phys. Lett. 27, 337 (1975).
    [CrossRef]
  10. C. R. Pollock, Fundamentals of Optoelectronics (Richard D. Irwin, 1995), pp. 49-72, 555-557.

2004 (1)

J. K. Hong, S. S. Lee, and D. W. Shin, J. Korean Phys. Soc. 45, 84 (2004).

2002 (1)

B. Li, S. J. Chua, C. W. Leitz, and E. A. Fitzgerald, Opt. Eng. 41, 723 (2002).
[CrossRef]

2001 (1)

D. G. Rabus and M. Hamacher, IEEE Photon. Technol. Lett. 13, 812 (2001).
[CrossRef]

2000 (1)

L. J. Harrison, T. J. Tayag, G. J. Simonis, M. Stead, G. W. Euliss, and R. P. Leavitt, IEEE Photon. Technol. Lett. 12, 657 (2000).
[CrossRef]

1996 (1)

K. C. Lin and W. Y. Lee, Electron. Lett. 32, 1259 (1996).
[CrossRef]

1995 (1)

L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
[CrossRef]

1988 (1)

A. Himeno, H. Terui, and M. Kobayashi, J. Lightwave Technol. 6, 41 (1988).
[CrossRef]

1975 (1)

R. Ulrich and G. Ankele, Appl. Phys. Lett. 27, 337 (1975).
[CrossRef]

Ankele, G.

R. Ulrich and G. Ankele, Appl. Phys. Lett. 27, 337 (1975).
[CrossRef]

Chua, S. J.

B. Li, S. J. Chua, C. W. Leitz, and E. A. Fitzgerald, Opt. Eng. 41, 723 (2002).
[CrossRef]

Deri, R. J.

E. C. M. Pennings, R. van Roijen, B. H. Verbeek, R. J. Deri, and L. B. Soldano, in Conference Proceedings, IEEE Lasers and Electro-Optics Society Annual Meeting (IEEE, 1993), p. 193.

Euliss, G. W.

L. J. Harrison, T. J. Tayag, G. J. Simonis, M. Stead, G. W. Euliss, and R. P. Leavitt, IEEE Photon. Technol. Lett. 12, 657 (2000).
[CrossRef]

Fitzgerald, E. A.

B. Li, S. J. Chua, C. W. Leitz, and E. A. Fitzgerald, Opt. Eng. 41, 723 (2002).
[CrossRef]

Hamacher, M.

D. G. Rabus and M. Hamacher, IEEE Photon. Technol. Lett. 13, 812 (2001).
[CrossRef]

Harrison, L. J.

L. J. Harrison, T. J. Tayag, G. J. Simonis, M. Stead, G. W. Euliss, and R. P. Leavitt, IEEE Photon. Technol. Lett. 12, 657 (2000).
[CrossRef]

Himeno, A.

A. Himeno, H. Terui, and M. Kobayashi, J. Lightwave Technol. 6, 41 (1988).
[CrossRef]

Hong, J. K.

J. K. Hong, S. S. Lee, and D. W. Shin, J. Korean Phys. Soc. 45, 84 (2004).

Kobayashi, M.

A. Himeno, H. Terui, and M. Kobayashi, J. Lightwave Technol. 6, 41 (1988).
[CrossRef]

Leavitt, R. P.

L. J. Harrison, T. J. Tayag, G. J. Simonis, M. Stead, G. W. Euliss, and R. P. Leavitt, IEEE Photon. Technol. Lett. 12, 657 (2000).
[CrossRef]

Lee, S. S.

J. K. Hong, S. S. Lee, and D. W. Shin, J. Korean Phys. Soc. 45, 84 (2004).

Lee, W. Y.

K. C. Lin and W. Y. Lee, Electron. Lett. 32, 1259 (1996).
[CrossRef]

Leitz, C. W.

B. Li, S. J. Chua, C. W. Leitz, and E. A. Fitzgerald, Opt. Eng. 41, 723 (2002).
[CrossRef]

Li, B.

B. Li, S. J. Chua, C. W. Leitz, and E. A. Fitzgerald, Opt. Eng. 41, 723 (2002).
[CrossRef]

Lin, K. C.

K. C. Lin and W. Y. Lee, Electron. Lett. 32, 1259 (1996).
[CrossRef]

Pennings, E. C. M.

L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
[CrossRef]

E. C. M. Pennings, R. van Roijen, B. H. Verbeek, R. J. Deri, and L. B. Soldano, in Conference Proceedings, IEEE Lasers and Electro-Optics Society Annual Meeting (IEEE, 1993), p. 193.

Pollock, C. R.

C. R. Pollock, Fundamentals of Optoelectronics (Richard D. Irwin, 1995), pp. 49-72, 555-557.

Rabus, D. G.

D. G. Rabus and M. Hamacher, IEEE Photon. Technol. Lett. 13, 812 (2001).
[CrossRef]

Shin, D. W.

J. K. Hong, S. S. Lee, and D. W. Shin, J. Korean Phys. Soc. 45, 84 (2004).

Simonis, G. J.

L. J. Harrison, T. J. Tayag, G. J. Simonis, M. Stead, G. W. Euliss, and R. P. Leavitt, IEEE Photon. Technol. Lett. 12, 657 (2000).
[CrossRef]

Soldano, L. B.

L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
[CrossRef]

E. C. M. Pennings, R. van Roijen, B. H. Verbeek, R. J. Deri, and L. B. Soldano, in Conference Proceedings, IEEE Lasers and Electro-Optics Society Annual Meeting (IEEE, 1993), p. 193.

Stead, M.

L. J. Harrison, T. J. Tayag, G. J. Simonis, M. Stead, G. W. Euliss, and R. P. Leavitt, IEEE Photon. Technol. Lett. 12, 657 (2000).
[CrossRef]

Tayag, T. J.

L. J. Harrison, T. J. Tayag, G. J. Simonis, M. Stead, G. W. Euliss, and R. P. Leavitt, IEEE Photon. Technol. Lett. 12, 657 (2000).
[CrossRef]

Terui, H.

A. Himeno, H. Terui, and M. Kobayashi, J. Lightwave Technol. 6, 41 (1988).
[CrossRef]

Ulrich, R.

R. Ulrich and G. Ankele, Appl. Phys. Lett. 27, 337 (1975).
[CrossRef]

van Roijen, R.

E. C. M. Pennings, R. van Roijen, B. H. Verbeek, R. J. Deri, and L. B. Soldano, in Conference Proceedings, IEEE Lasers and Electro-Optics Society Annual Meeting (IEEE, 1993), p. 193.

Verbeek, B. H.

E. C. M. Pennings, R. van Roijen, B. H. Verbeek, R. J. Deri, and L. B. Soldano, in Conference Proceedings, IEEE Lasers and Electro-Optics Society Annual Meeting (IEEE, 1993), p. 193.

Appl. Phys. Lett. (1)

R. Ulrich and G. Ankele, Appl. Phys. Lett. 27, 337 (1975).
[CrossRef]

Electron. Lett. (1)

K. C. Lin and W. Y. Lee, Electron. Lett. 32, 1259 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

L. J. Harrison, T. J. Tayag, G. J. Simonis, M. Stead, G. W. Euliss, and R. P. Leavitt, IEEE Photon. Technol. Lett. 12, 657 (2000).
[CrossRef]

D. G. Rabus and M. Hamacher, IEEE Photon. Technol. Lett. 13, 812 (2001).
[CrossRef]

J. Korean Phys. Soc. (1)

J. K. Hong, S. S. Lee, and D. W. Shin, J. Korean Phys. Soc. 45, 84 (2004).

J. Lightwave Technol. (2)

A. Himeno, H. Terui, and M. Kobayashi, J. Lightwave Technol. 6, 41 (1988).
[CrossRef]

L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
[CrossRef]

Opt. Eng. (1)

B. Li, S. J. Chua, C. W. Leitz, and E. A. Fitzgerald, Opt. Eng. 41, 723 (2002).
[CrossRef]

Other (2)

E. C. M. Pennings, R. van Roijen, B. H. Verbeek, R. J. Deri, and L. B. Soldano, in Conference Proceedings, IEEE Lasers and Electro-Optics Society Annual Meeting (IEEE, 1993), p. 193.

C. R. Pollock, Fundamentals of Optoelectronics (Richard D. Irwin, 1995), pp. 49-72, 555-557.

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Figures (4)

Fig. 1
Fig. 1

Schematic configuration of the MMI coupler with a lateral index profile of the multimode waveguide.

Fig. 2
Fig. 2

Simulation results of the MMI coupler: the beam propagation profile and the coupling efficiency to both the input–output waveguides along the propagation direction ( z = 0 10 mm ) .

Fig. 3
Fig. 3

Experimental results for the output intensities of the MMI couplers. The multimode waveguides’ lengths are 1600 9220 μ m .

Fig. 4
Fig. 4

Variation of the extinction ratios for both the 0 dB SI and the Ex̱SI.

Tables (1)

Tables Icon

Table 1 Characteristics of the 0 db SI and the Ex̱SI from Experimental Results

Equations (2)

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Ψ ( y , L MMI ) = ν = 0 m 1 c ν ψ ν ( y ) exp [ j ( β 0 β ν ) L MMI ] .
c bar , cross ( L MMI ) = Ψ ( y , L MMI ) ψ bar , cross ( y ) d y ψ bar , cross 2 ( y ) d y .

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