Abstract

We solve the coupled-mode equations for linearly chirped codirectional mode couplers and use the results to develop design rules for broadband couplers. By comparing a chirped coupler with a uniform coupler having the same effective coupling length we find that high coupling efficiency can be obtained over a substantially wider bandwidth. We design a chirped device to have a 99% bandwidth of 47 nm at 1090 nm, which is 5.8 times larger than for the uniform coupler. Experimentally the bandwidth was improved by a factor of 5.4.

© 1996 Optical Society of America

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References

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1995

1994

C. D. Poole, H. M. Presby, J. P. Meester, Electron. Lett. 30, 1437 (1994).
[CrossRef]

1992

1988

H. E. Engan, J. N. Blake, B. Y. Kim, H. J. Shaw, J. Lightwave Technol. 6, 428 (1988).
[CrossRef]

1986

1975

1971

R. H. Tancrell, M. G. Holland, Proc. IEEE 59, 393 (1971).
[CrossRef]

Albert, J.

Bilodeau, F.

Blake, J. N.

H. E. Engan, J. N. Blake, B. Y. Kim, H. J. Shaw, J. Lightwave Technol. 6, 428 (1988).
[CrossRef]

J. N. Blake, B. Y. Kim, H. J. Shaw, Opt. Lett. 11, 177 (1986).
[CrossRef] [PubMed]

Engan, H. E.

D. Östling, H. E. Engan, Opt. Lett. 20, 1247 (1995).
[CrossRef] [PubMed]

H. E. Engan, J. N. Blake, B. Y. Kim, H. J. Shaw, J. Lightwave Technol. 6, 428 (1988).
[CrossRef]

Hill, K. O.

Holland, M. G.

R. H. Tancrell, M. G. Holland, Proc. IEEE 59, 393 (1971).
[CrossRef]

Johnson, D. C.

Kim, B. Y.

H. E. Engan, J. N. Blake, B. Y. Kim, H. J. Shaw, J. Lightwave Technol. 6, 428 (1988).
[CrossRef]

J. N. Blake, B. Y. Kim, H. J. Shaw, Opt. Lett. 11, 177 (1986).
[CrossRef] [PubMed]

Malo, B.

Matsuhara, M.

McCormick, A. R.

Meester, J. P.

C. D. Poole, H. M. Presby, J. P. Meester, Electron. Lett. 30, 1437 (1994).
[CrossRef]

Nelson, K. T.

Östling, D.

Poole, C. D.

Presby, H. M.

C. D. Poole, H. M. Presby, J. P. Meester, Electron. Lett. 30, 1437 (1994).
[CrossRef]

Shaw, H. J.

H. E. Engan, J. N. Blake, B. Y. Kim, H. J. Shaw, J. Lightwave Technol. 6, 428 (1988).
[CrossRef]

J. N. Blake, B. Y. Kim, H. J. Shaw, Opt. Lett. 11, 177 (1986).
[CrossRef] [PubMed]

Tancrell, R. H.

R. H. Tancrell, M. G. Holland, Proc. IEEE 59, 393 (1971).
[CrossRef]

Thériault, S.

Watanabe, A.

Wiesenfeld, J. M.

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 186.

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 186.

Electron. Lett.

C. D. Poole, H. M. Presby, J. P. Meester, Electron. Lett. 30, 1437 (1994).
[CrossRef]

J. Lightwave Technol.

H. E. Engan, J. N. Blake, B. Y. Kim, H. J. Shaw, J. Lightwave Technol. 6, 428 (1988).
[CrossRef]

J. Opt. Soc. Am.

Opt. Lett.

Proc. IEEE

R. H. Tancrell, M. G. Holland, Proc. IEEE 59, 393 (1971).
[CrossRef]

Other

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 186.

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Figures (4)

Fig. 1
Fig. 1

Schematic of a modal notch filter.

Fig. 2
Fig. 2

Normalized contour plots of the coupling efficiency as a function of the normalized mismatch Δβn0(λ) and the normalized device length zn for different amounts of chirp α. The contour levels represent coupling efficiencies of 90% (−10 dB), 99% (−20 dB), and 99.9% (−30 dB). The solid line in each plot represents wave-number matching, i.e., Δβ(λ, z) = 0.

Fig. 3
Fig. 3

Bandwidth and device length versus chirp α. The solid curve (left-hand scale) represents the improvement in the 99% coupling bandwidth compared with a uniform coupler of length L = Lc, whereas the dashed curve (right-hand scale) represents the corresponding normalized device length L/Lc.

Fig. 4
Fig. 4

(a) Experimental and (b) calculated transmission characteristics of a notch filter with a uniform coupler (α = 0, dashed curves) and a chirped coupler (α = 4, solid curves).

Tables (1)

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Table 1 Design Parameters for a Chirped and a Uniform Coupler

Equations (4)

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d a 01 d z = i κ a 11 exp [ i 0 z Δ β ( λ , x ) d x ] , d a 11 d z = i κ a 01 exp [ i 0 z Δ β ( λ , x ) d x ] .
Δ λ 99 % = 0 . 100 L c L B ( λ 0 ) 2 ( L B λ ) 1 .
Δ β n ( λ , z ) = 2 π L c ( 1 L B ( λ ) 1 Λ 0 + α 2 π z L c 2 ) = Δ β n 0 ( λ ) + α z n .
1 Λ 0 = 1 L B ( λ 0 ) + α L 4 π L c 2 .

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