Abstract

The design principle of a single-mode arrayed-waveguide grating multiplexer with flat spectral response is proposed on the basis of a discrete Fourier transform. By a beam propagation-method simulation, a flat spectral region (within 1-dB loss increase) is obtained over 57.2 GHz for 100-GHz channel spacing.

© 1995 Optical Society of America

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References

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  1. H. Takahashi, S. Suzuki, K. Kato, Electron. Lett. 26, 87 (1990).
    [CrossRef]
  2. K. Okamoto, H. Takahashi, in Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper MP2.
  3. Y. Inoue, Y. Ohmori, M. Kawachi, S. Ando, T. Sawada, H. Takahashi, IEEE Photon. Technol. Lett. 6, 626 (1994).
    [CrossRef]
  4. M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, A. Kuntze, Electron. Lett. 30, 300 (1994).
    [CrossRef]
  5. E. O. Bringham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J., 1974), Chap. 6, p. 110.
  6. M. Kawachi, Opt. Quantum Electron. 22, 391 (1990).
    [CrossRef]

1994 (2)

Y. Inoue, Y. Ohmori, M. Kawachi, S. Ando, T. Sawada, H. Takahashi, IEEE Photon. Technol. Lett. 6, 626 (1994).
[CrossRef]

M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, A. Kuntze, Electron. Lett. 30, 300 (1994).
[CrossRef]

1990 (2)

M. Kawachi, Opt. Quantum Electron. 22, 391 (1990).
[CrossRef]

H. Takahashi, S. Suzuki, K. Kato, Electron. Lett. 26, 87 (1990).
[CrossRef]

Amersfoort, M. R.

M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, A. Kuntze, Electron. Lett. 30, 300 (1994).
[CrossRef]

Ando, S.

Y. Inoue, Y. Ohmori, M. Kawachi, S. Ando, T. Sawada, H. Takahashi, IEEE Photon. Technol. Lett. 6, 626 (1994).
[CrossRef]

Bringham, E. O.

E. O. Bringham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J., 1974), Chap. 6, p. 110.

de Boer, C. R.

M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, A. Kuntze, Electron. Lett. 30, 300 (1994).
[CrossRef]

Demeester, P.

M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, A. Kuntze, Electron. Lett. 30, 300 (1994).
[CrossRef]

Inoue, Y.

Y. Inoue, Y. Ohmori, M. Kawachi, S. Ando, T. Sawada, H. Takahashi, IEEE Photon. Technol. Lett. 6, 626 (1994).
[CrossRef]

Kato, K.

H. Takahashi, S. Suzuki, K. Kato, Electron. Lett. 26, 87 (1990).
[CrossRef]

Kawachi, M.

Y. Inoue, Y. Ohmori, M. Kawachi, S. Ando, T. Sawada, H. Takahashi, IEEE Photon. Technol. Lett. 6, 626 (1994).
[CrossRef]

M. Kawachi, Opt. Quantum Electron. 22, 391 (1990).
[CrossRef]

Kuntze, A.

M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, A. Kuntze, Electron. Lett. 30, 300 (1994).
[CrossRef]

Ohmori, Y.

Y. Inoue, Y. Ohmori, M. Kawachi, S. Ando, T. Sawada, H. Takahashi, IEEE Photon. Technol. Lett. 6, 626 (1994).
[CrossRef]

Okamoto, K.

K. Okamoto, H. Takahashi, in Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper MP2.

Sawada, T.

Y. Inoue, Y. Ohmori, M. Kawachi, S. Ando, T. Sawada, H. Takahashi, IEEE Photon. Technol. Lett. 6, 626 (1994).
[CrossRef]

Smit, M. K.

M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, A. Kuntze, Electron. Lett. 30, 300 (1994).
[CrossRef]

Suzuki, S.

H. Takahashi, S. Suzuki, K. Kato, Electron. Lett. 26, 87 (1990).
[CrossRef]

Takahashi, H.

Y. Inoue, Y. Ohmori, M. Kawachi, S. Ando, T. Sawada, H. Takahashi, IEEE Photon. Technol. Lett. 6, 626 (1994).
[CrossRef]

H. Takahashi, S. Suzuki, K. Kato, Electron. Lett. 26, 87 (1990).
[CrossRef]

K. Okamoto, H. Takahashi, in Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper MP2.

van der Tol, J. J. G. M.

M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, A. Kuntze, Electron. Lett. 30, 300 (1994).
[CrossRef]

van Ham, F. P. G. M.

M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, A. Kuntze, Electron. Lett. 30, 300 (1994).
[CrossRef]

Electron. Lett. (2)

H. Takahashi, S. Suzuki, K. Kato, Electron. Lett. 26, 87 (1990).
[CrossRef]

M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, A. Kuntze, Electron. Lett. 30, 300 (1994).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Y. Inoue, Y. Ohmori, M. Kawachi, S. Ando, T. Sawada, H. Takahashi, IEEE Photon. Technol. Lett. 6, 626 (1994).
[CrossRef]

Opt. Quantum Electron. (1)

M. Kawachi, Opt. Quantum Electron. 22, 391 (1990).
[CrossRef]

Other (2)

E. O. Bringham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J., 1974), Chap. 6, p. 110.

K. Okamoto, H. Takahashi, in Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper MP2.

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Figures (4)

Fig. 1
Fig. 1

Schematic configuration of an arrayed-waveguide grating multiplexer.

Fig. 2
Fig. 2

Loss spectra of a conventional 32-channel 100-GHz-spaced arrayed-waveguide multiplexer.

Fig. 3
Fig. 3

(a) Electric field distribution E(i) in the ith waveguide. (b) Normalized excess path-length difference Q(i)/λg (λg = λ0/nc ) in the ith waveguide.

Fig. 4
Fig. 4

Calculated spectral response of the eight-channel 100-GHz-spaced arrayed-waveguide multiplexer. WG, waveguide.

Equations (15)

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ϕ i = β c [ L c + ( i - 1 ) Δ L ] ,
m = n c Δ L / λ 0 = n c Δ L f 0 / c ,
d x d λ = f s m n s d ,
G ( f ) = i = 1 N E ( i ) exp ( - j ϕ i ) ,
ϕ i = β c [ L c + ( i - 1 ) Δ L + Q ( i ) ] .
f f l = f 0 + l ( W / N )             ( l = - N / 2 ~ N / 2 - 1 ) ,
W = f 0 / m .
β c ( l ) Δ L = 2 π ( m + l / N ) .
ϕ i ( l ) = β c ( l ) L c + ( i - 1 ) 2 π ( m + l / N ) + β c ( l ) Q ( i ) .
G ( f l ) G ( l Δ f ) = exp [ - j β c ( l ) L c ] i = 1 N E ( i ) × exp [ - j 2 π ( i - 1 ) l N - j β c ( l ) Q ( i ) ] ,
G ( l Δ f ) = exp [ - j β c ( l ) L c ] n = 0 N - 1 E ( n + 1 ) × exp [ - j 2 π l n N - j β c ( 0 ) Q ( n + 1 ) ] ,
g ( n ) = E ( n + 1 ) exp [ - j β c ( 0 ) Q ( n + 1 ) ] ,
G ( l Δ f ) exp [ j β c ( l ) L c ] = n = 0 N = 1 g ( n ) exp ( - j 2 π l n N ) .
g ( n ) = 1 N l = - N / 2 N / 2 - 1 { G ( l Δ f ) exp [ j β c ( l ) L c ] } exp ( j 2 π l n N ) .
G ( l Δ f ) { 1 l = - 6 ~ 6 0 l = - N / 2 ~ - 7 ,             7 ~ N / 2 - 1 .

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