Abstract

An extended split-step time-domain model for composite coupling structures is reported. Time-dependent coupled-wave equations are solved by splitting of the operators for phase accumulation, forward directional coupling, and reverse Bragg reflection. Through an analysis of an add–drop filter based on a grating-written directional-coupler structure, the proposed modeling method is shown to be an order of magnitude more efficient than the previous methods.

© 2000 Optical Society of America

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References

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  1. L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, New York, 1995).
  2. B. S. Kim and Y. Chung, Electron. Lett. 35, 84 (1999).
    [CrossRef]
  3. S. S. Orlov, A. Yariv, and S. V. Essen, Opt. Lett. 22, 688 (1997).
    [CrossRef] [PubMed]
  4. B. S. Kim, Y. Chung, and S. H. Kim, in Digest of Conference on Lasers and Electro-Optics/Pacific Rim ’99 (Optical Society of America, Washington, D.C., 1999), pp. 1147–1148.
  5. L. M. Zhang and J. E. Carroll, IEEE J. Quantum Electron. 30, 2573 (1994).
    [CrossRef]

1999

B. S. Kim and Y. Chung, Electron. Lett. 35, 84 (1999).
[CrossRef]

1997

1994

L. M. Zhang and J. E. Carroll, IEEE J. Quantum Electron. 30, 2573 (1994).
[CrossRef]

Carroll, J. E.

L. M. Zhang and J. E. Carroll, IEEE J. Quantum Electron. 30, 2573 (1994).
[CrossRef]

Chung, Y.

B. S. Kim and Y. Chung, Electron. Lett. 35, 84 (1999).
[CrossRef]

B. S. Kim, Y. Chung, and S. H. Kim, in Digest of Conference on Lasers and Electro-Optics/Pacific Rim ’99 (Optical Society of America, Washington, D.C., 1999), pp. 1147–1148.

Coldren, L. A.

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, New York, 1995).

Corzine, S. W.

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, New York, 1995).

Essen, S. V.

Kim, B. S.

B. S. Kim and Y. Chung, Electron. Lett. 35, 84 (1999).
[CrossRef]

B. S. Kim, Y. Chung, and S. H. Kim, in Digest of Conference on Lasers and Electro-Optics/Pacific Rim ’99 (Optical Society of America, Washington, D.C., 1999), pp. 1147–1148.

Kim, S. H.

B. S. Kim, Y. Chung, and S. H. Kim, in Digest of Conference on Lasers and Electro-Optics/Pacific Rim ’99 (Optical Society of America, Washington, D.C., 1999), pp. 1147–1148.

Orlov, S. S.

Yariv, A.

Zhang, L. M.

L. M. Zhang and J. E. Carroll, IEEE J. Quantum Electron. 30, 2573 (1994).
[CrossRef]

Electron. Lett.

B. S. Kim and Y. Chung, Electron. Lett. 35, 84 (1999).
[CrossRef]

IEEE J. Quantum Electron.

L. M. Zhang and J. E. Carroll, IEEE J. Quantum Electron. 30, 2573 (1994).
[CrossRef]

Opt. Lett.

Other

B. S. Kim, Y. Chung, and S. H. Kim, in Digest of Conference on Lasers and Electro-Optics/Pacific Rim ’99 (Optical Society of America, Washington, D.C., 1999), pp. 1147–1148.

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, New York, 1995).

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Figures (5)

Fig. 1
Fig. 1

Refractive-index distribution of general optical waveguide devices composed of gratings and a directional coupler. The coupling results from the corrugations, whose magnitudes are, respectively, Δnac,1 and Δnac,2, and the directional coupler consists of two waveguides whose refractive-index difference is Δndc,1-Δndc,2. n0 is a refractive index in the clad region, and Λ1,2 are grating pitches of two waveguides.

Fig. 2
Fig. 2

Schematic view of a semiconductor add–drop filter.

Fig. 3
Fig. 3

Comparison of the drop and return properties of the analytic approach3 and the proposed method when the semiconductor add–drop filter operates a drop function. (a) Drop output, (b) return loss, (c) drop phase, (d) return phase. Dotted curves with squares, analytic approach3; solid curves, proposed method.

Fig. 4
Fig. 4

Time response of the add–drop filter, which is designed to drop the 1550-nm wavelength. (a) Total input power at input port 1. (b) Solid curve, output power at drop port 3; dashed curve, input power at the 1550-nm wavelength.

Fig. 5
Fig. 5

Comparison of the forward finite-difference method and the proposed method. Filled circles, forward finite-difference method5; filled triangles, proposed method.

Equations (10)

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Ez,t=ϕ1x,yF1z,texp-iβ0z+ϕ2x,yF2z,texp-iβ0z+ϕ1x,yR1z,texpiβ0z+ϕ2x,yR2z,texpiβ0zexpiω0t,
1cgF1t+F1z=g1-iδ1F1+iκ11R1-iκ21F2,
1cgF2t+F2z=g2-iδ2F2+iκ22R2-iκ12F1,
1cgR1t-R1z=g1-iδ1R1+iκ11*F1-iκ21R2,
1cgR2t-R2z=g2-iδ2R2+iκ22*F2-iκ12R1,
zX1,2z,t=±g1,2-iδ1,2-1cgtX1,2z,t,
F1,2z+Δz,t=expg1,2-iδ1,2ΔzF1,2z,t-Δt,
R1,2z,t=expg1,2-iδ1,2Δz×R1,2z+Δz,t-Δt,
Xz,t-Δt=exp-/tΔtXz,t
F1z+Δz,tF2z+Δz,t=cosγΔz-i sinγΔz-i sinγΔzcosγΔz×F1z,tF2z,t,

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