Abstract

We report dispersion resulting from phase and amplitude errors in arrayed-waveguide grating (AWG) multiplexers–demultiplexers. We measure the phase- and amplitude-error distributions of two different types of AWG and discuss their effects on the dispersion. The results show that the origin of the dispersion in the AWG is the low-order Fourier components of the symmetric phase and the antisymmetric amplitude errors. We also discuss the dependence of the dispersion on the passband shape in the presence of the same fabrication errors.

© 2000 Optical Society of America

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References

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  1. H. Takahashi, S. Suzuki, and I. Nishi, in Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper PD-1-1.
  2. H. Takahashi, K. Oda, and H. Toba, J. Lightwave Technol. 14, 1097 (1996).
    [CrossRef]
  3. C. Casper, H.-M. Foisel, C. von Helmolt, B. Strebel, and Y. Sugaya, Electron. Lett. 33, 1624 (1997).
    [CrossRef]
  4. G. Lenz, B. J. Eggleton, C. K. Madsen, C. R. Giles, and G. Nykolak, IEEE Photon. Technol. Lett. 10, 567 (1998).
    [CrossRef]
  5. K. Takada, Y. Inoue, H. Yamada, and M. Horiguchi, Electron. Lett. 30, 1671 (1994).
    [CrossRef]
  6. H. Yamada, K. Takada, and K. Okamoto, in Proceedings of the 1998 IEICE General Conference (Institute of Electronics, Information and Communication Engineers, Tokyo, 1998), paper C3-111 (in Japanese).
  7. K. Okamoto, tutorial presented at the 24th European Conference on Optical Communication, Madrid, Spain, September 21, 1998.

1998

G. Lenz, B. J. Eggleton, C. K. Madsen, C. R. Giles, and G. Nykolak, IEEE Photon. Technol. Lett. 10, 567 (1998).
[CrossRef]

1997

C. Casper, H.-M. Foisel, C. von Helmolt, B. Strebel, and Y. Sugaya, Electron. Lett. 33, 1624 (1997).
[CrossRef]

1996

H. Takahashi, K. Oda, and H. Toba, J. Lightwave Technol. 14, 1097 (1996).
[CrossRef]

1994

K. Takada, Y. Inoue, H. Yamada, and M. Horiguchi, Electron. Lett. 30, 1671 (1994).
[CrossRef]

Casper, C.

C. Casper, H.-M. Foisel, C. von Helmolt, B. Strebel, and Y. Sugaya, Electron. Lett. 33, 1624 (1997).
[CrossRef]

Eggleton, B. J.

G. Lenz, B. J. Eggleton, C. K. Madsen, C. R. Giles, and G. Nykolak, IEEE Photon. Technol. Lett. 10, 567 (1998).
[CrossRef]

Foisel, H.-M.

C. Casper, H.-M. Foisel, C. von Helmolt, B. Strebel, and Y. Sugaya, Electron. Lett. 33, 1624 (1997).
[CrossRef]

Giles, C. R.

G. Lenz, B. J. Eggleton, C. K. Madsen, C. R. Giles, and G. Nykolak, IEEE Photon. Technol. Lett. 10, 567 (1998).
[CrossRef]

Horiguchi, M.

K. Takada, Y. Inoue, H. Yamada, and M. Horiguchi, Electron. Lett. 30, 1671 (1994).
[CrossRef]

Inoue, Y.

K. Takada, Y. Inoue, H. Yamada, and M. Horiguchi, Electron. Lett. 30, 1671 (1994).
[CrossRef]

Lenz, G.

G. Lenz, B. J. Eggleton, C. K. Madsen, C. R. Giles, and G. Nykolak, IEEE Photon. Technol. Lett. 10, 567 (1998).
[CrossRef]

Madsen, C. K.

G. Lenz, B. J. Eggleton, C. K. Madsen, C. R. Giles, and G. Nykolak, IEEE Photon. Technol. Lett. 10, 567 (1998).
[CrossRef]

Nishi, I.

H. Takahashi, S. Suzuki, and I. Nishi, in Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper PD-1-1.

Nykolak, G.

G. Lenz, B. J. Eggleton, C. K. Madsen, C. R. Giles, and G. Nykolak, IEEE Photon. Technol. Lett. 10, 567 (1998).
[CrossRef]

Oda, K.

H. Takahashi, K. Oda, and H. Toba, J. Lightwave Technol. 14, 1097 (1996).
[CrossRef]

Okamoto, K.

H. Yamada, K. Takada, and K. Okamoto, in Proceedings of the 1998 IEICE General Conference (Institute of Electronics, Information and Communication Engineers, Tokyo, 1998), paper C3-111 (in Japanese).

K. Okamoto, tutorial presented at the 24th European Conference on Optical Communication, Madrid, Spain, September 21, 1998.

Strebel, B.

C. Casper, H.-M. Foisel, C. von Helmolt, B. Strebel, and Y. Sugaya, Electron. Lett. 33, 1624 (1997).
[CrossRef]

Sugaya, Y.

C. Casper, H.-M. Foisel, C. von Helmolt, B. Strebel, and Y. Sugaya, Electron. Lett. 33, 1624 (1997).
[CrossRef]

Suzuki, S.

H. Takahashi, S. Suzuki, and I. Nishi, in Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper PD-1-1.

Takada, K.

K. Takada, Y. Inoue, H. Yamada, and M. Horiguchi, Electron. Lett. 30, 1671 (1994).
[CrossRef]

H. Yamada, K. Takada, and K. Okamoto, in Proceedings of the 1998 IEICE General Conference (Institute of Electronics, Information and Communication Engineers, Tokyo, 1998), paper C3-111 (in Japanese).

Takahashi, H.

H. Takahashi, K. Oda, and H. Toba, J. Lightwave Technol. 14, 1097 (1996).
[CrossRef]

H. Takahashi, S. Suzuki, and I. Nishi, in Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper PD-1-1.

Toba, H.

H. Takahashi, K. Oda, and H. Toba, J. Lightwave Technol. 14, 1097 (1996).
[CrossRef]

von Helmolt, C.

C. Casper, H.-M. Foisel, C. von Helmolt, B. Strebel, and Y. Sugaya, Electron. Lett. 33, 1624 (1997).
[CrossRef]

Yamada, H.

K. Takada, Y. Inoue, H. Yamada, and M. Horiguchi, Electron. Lett. 30, 1671 (1994).
[CrossRef]

H. Yamada, K. Takada, and K. Okamoto, in Proceedings of the 1998 IEICE General Conference (Institute of Electronics, Information and Communication Engineers, Tokyo, 1998), paper C3-111 (in Japanese).

Electron. Lett.

C. Casper, H.-M. Foisel, C. von Helmolt, B. Strebel, and Y. Sugaya, Electron. Lett. 33, 1624 (1997).
[CrossRef]

K. Takada, Y. Inoue, H. Yamada, and M. Horiguchi, Electron. Lett. 30, 1671 (1994).
[CrossRef]

IEEE Photon. Technol. Lett.

G. Lenz, B. J. Eggleton, C. K. Madsen, C. R. Giles, and G. Nykolak, IEEE Photon. Technol. Lett. 10, 567 (1998).
[CrossRef]

J. Lightwave Technol.

H. Takahashi, K. Oda, and H. Toba, J. Lightwave Technol. 14, 1097 (1996).
[CrossRef]

Other

H. Takahashi, S. Suzuki, and I. Nishi, in Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper PD-1-1.

H. Yamada, K. Takada, and K. Okamoto, in Proceedings of the 1998 IEICE General Conference (Institute of Electronics, Information and Communication Engineers, Tokyo, 1998), paper C3-111 (in Japanese).

K. Okamoto, tutorial presented at the 24th European Conference on Optical Communication, Madrid, Spain, September 21, 1998.

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Figures (4)

Fig. 1
Fig. 1

Phase and amplitude distributions of (a) the PF-AWG and (b) the G-AWG.

Fig. 2
Fig. 2

Fourier coefficients frs and hra of (a) the PF-AWG and (b) the G-AWG.

Fig. 3
Fig. 3

Dispersion and transmittance of (a) the PF-AWG and (b) the G-AWG. The solid curves show the dispersion without error reduction. The dashed curves show the dispersion after error reduction of frsr4 for the PF-AWG and of hrar4 for the G-AWG.

Fig. 4
Fig. 4

(a) Group delay and (b) dispersion of the PF-AWG and the G-AWG in the presence of the same fabrication errors.

Equations (7)

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Hσ=p=0M-1ap1+ηpexp-jϕpexp-j2πnc×p-M-1/2ΔLσexp-j2πncLσ=Tσexp-j2πncLσ,
Iσ=TσT*σ, Ψσ=arctanyσ/T0σ+xσ, τσ=1/2πcdΨσ/dσ, Dσ=-σ2/2πcd2 Ψσ/dσ2,
dΨ/dσ=T0y-T0y/I+xy-xy/I,
ϕp=r=1m2frscos2πp-M-1/2r/M+r=1m2frasin2πp-M-1/2r/M,
ηp=r=1m2hrscos2πp-M-1/2r/M+r=1m2hrasin2πp-M-1/2r/M,
Tσ=T0σ+hrs-fraT0σ-r/MΔσ+hrs+fraT0σ+r/MΔσ-jfrs+hraT0σ-r/MΔσ-jfrs-hraT0σ+r/MΔσ,
yσy-σ,   frs0,hra=0, yσ-y-σ,   frs=0,hra0,

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