Abstract

We propose an optical circuit design method for coherent waves as a boundary value problem. The method produces a very compact circuit in which the refractive index pattern is automatically synthesized for given input and output fields with a numerical calculation. We employ the method to design a 1.31.55μm wavelength demultiplexer and also describe the features of a circuit generated by use of the method.

© 2005 Optical Society of America

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References

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  1. T. W. Mossberg, Opt. Lett. 26, 414 (2001).
    [CrossRef]
  2. G. Barbastathis and D. J. Brady, Proc. IEEE,  87, 2098 (1999).
    [CrossRef]
  3. H. Rao, M. J. Steel, R. Scarmozzino, and R. M. Osgood, J. Lightwave Technol. 18, 1155 (2000).
    [CrossRef]
  4. M. Kawachi, Opt. Quantum Electron. 22, 391 (1990).
    [CrossRef]
  5. Y. Hibino, T. Maruno, and K. Okamoto, NTT Rev. 13, 4 (2001).
  6. G. A. Tsihrintzis and A. J. Devaney, IEEE Trans. Inf. Theory 46, 1748 (2000).
    [CrossRef]
  7. T. Matsui, in Fluctuating Paths and Fields, W. Janke, A. Pelster, and M. Bachmann, eds. (World Scientific, 2001), and references therein.

2001

T. W. Mossberg, Opt. Lett. 26, 414 (2001).
[CrossRef]

Y. Hibino, T. Maruno, and K. Okamoto, NTT Rev. 13, 4 (2001).

2000

G. A. Tsihrintzis and A. J. Devaney, IEEE Trans. Inf. Theory 46, 1748 (2000).
[CrossRef]

H. Rao, M. J. Steel, R. Scarmozzino, and R. M. Osgood, J. Lightwave Technol. 18, 1155 (2000).
[CrossRef]

1999

G. Barbastathis and D. J. Brady, Proc. IEEE,  87, 2098 (1999).
[CrossRef]

1990

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

Barbastathis, G.

G. Barbastathis and D. J. Brady, Proc. IEEE,  87, 2098 (1999).
[CrossRef]

Brady, D. J.

G. Barbastathis and D. J. Brady, Proc. IEEE,  87, 2098 (1999).
[CrossRef]

Devaney, A. J.

G. A. Tsihrintzis and A. J. Devaney, IEEE Trans. Inf. Theory 46, 1748 (2000).
[CrossRef]

Hibino, Y.

Y. Hibino, T. Maruno, and K. Okamoto, NTT Rev. 13, 4 (2001).

Kawachi, M.

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

Maruno, T.

Y. Hibino, T. Maruno, and K. Okamoto, NTT Rev. 13, 4 (2001).

Matsui, T.

T. Matsui, in Fluctuating Paths and Fields, W. Janke, A. Pelster, and M. Bachmann, eds. (World Scientific, 2001), and references therein.

Mossberg, T. W.

Okamoto, K.

Y. Hibino, T. Maruno, and K. Okamoto, NTT Rev. 13, 4 (2001).

Osgood, R. M.

Rao, H.

Scarmozzino, R.

Steel, M. J.

Tsihrintzis, G. A.

G. A. Tsihrintzis and A. J. Devaney, IEEE Trans. Inf. Theory 46, 1748 (2000).
[CrossRef]

IEEE Trans. Inf. Theory

G. A. Tsihrintzis and A. J. Devaney, IEEE Trans. Inf. Theory 46, 1748 (2000).
[CrossRef]

J. Lightwave Technol.

NTT Rev.

Y. Hibino, T. Maruno, and K. Okamoto, NTT Rev. 13, 4 (2001).

Opt. Lett.

Opt. Quantum Electron.

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

Proc. IEEE

G. Barbastathis and D. J. Brady, Proc. IEEE,  87, 2098 (1999).
[CrossRef]

Other

T. Matsui, in Fluctuating Paths and Fields, W. Janke, A. Pelster, and M. Bachmann, eds. (World Scientific, 2001), and references therein.

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Figures (3)

Fig. 1
Fig. 1

Calculated result designed for a 1.31 1.55 μ m wavelength demultiplexer. (a) Refractive index distribution. White, n ref + s ; black, n ref s . (b) Light-wave field intensity, λ = 1310 nm . (c) Optical field intensity, λ = 1550 nm .

Fig. 2
Fig. 2

Output change along calculation reciprocation count.

Fig. 3
Fig. 3

Wavelength dependence of transmittance.

Equations (9)

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i z ψ ( x , z ) = L ( x , z ) ψ ( x , z )
1 2 β [ x 2 + β 2 k 0 2 n ( x , z ) 2 ] ψ ( x , z ) ,
E ( z ) = j φ j ( x , z ) ψ j ( x , z ) 2
δ E δ n ( p ) = j δ φ j φ j + 2 Re δ φ j ψ j + δ ψ j ψ j δ n ( p ) ,
q ( p ) 2 k 0 j Im φ j ( p ) * ψ j ( p ) ,
n ( p ) n ( p ) α q ( p )
i z φ j = L φ j ,
i z ψ j = ( L + δ L ) ψ j ,
z E ( z ) = 2 k 0 j δ Δ n Im φ * ψ d x 0 .

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