Abstract

A new beam-propagation scheme based on a finite-difference algorithm is proposed. The main property of this scheme is to avoid the boundary conditions altogether, by mapping the infinite space onto a finite-size domain. This mapping, together with a rescaling of the field, leads to a fast and easy-to-implement algorithm that can be used when boundary condition constraints are important.

© 1996 Optical Society of America

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References

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  1. M. D. Feit, J. A. Fleck, Appl. Opt. 17, 3990 (1978).
    [CrossRef] [PubMed]
  2. Y. Chung, N. Dagli, IEEE J. Quantum Electron. 26, 1335 (1990).
    [CrossRef]
  3. G. R. Hadley, Opt. Lett. 17, 1426 (1992).
    [CrossRef] [PubMed]
  4. G. R. Hadley, Opt. Lett. 16, 624 (1991).
    [CrossRef] [PubMed]
  5. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  6. F. Schmidt,J. Lightwave Technol. 11, 1425 (1993).
    [CrossRef]
  7. C. Vassallo, Electron. Lett. 31, 130 (1995).
    [CrossRef]
  8. D. Yevick, W. Bardyszewski, Opt. Lett. 17, 329 (1992).
    [CrossRef] [PubMed]

1995 (1)

C. Vassallo, Electron. Lett. 31, 130 (1995).
[CrossRef]

1993 (1)

F. Schmidt,J. Lightwave Technol. 11, 1425 (1993).
[CrossRef]

1992 (2)

1991 (1)

1990 (1)

Y. Chung, N. Dagli, IEEE J. Quantum Electron. 26, 1335 (1990).
[CrossRef]

1978 (1)

Bardyszewski, W.

Chung, Y.

Y. Chung, N. Dagli, IEEE J. Quantum Electron. 26, 1335 (1990).
[CrossRef]

Dagli, N.

Y. Chung, N. Dagli, IEEE J. Quantum Electron. 26, 1335 (1990).
[CrossRef]

Feit, M. D.

Fleck, J. A.

Hadley, G. R.

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Schmidt, F.

F. Schmidt,J. Lightwave Technol. 11, 1425 (1993).
[CrossRef]

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Vassallo, C.

C. Vassallo, Electron. Lett. 31, 130 (1995).
[CrossRef]

Yevick, D.

Appl. Opt. (1)

Electron. Lett. (1)

C. Vassallo, Electron. Lett. 31, 130 (1995).
[CrossRef]

IEEE J. Quantum Electron (1)

Y. Chung, N. Dagli, IEEE J. Quantum Electron. 26, 1335 (1990).
[CrossRef]

J. Lightwave Technol. (1)

F. Schmidt,J. Lightwave Technol. 11, 1425 (1993).
[CrossRef]

Opt. Lett. (3)

Other (1)

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

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Figures (1)

Fig. 1
Fig. 1

Comparison between the transparent boundary condition and the boundaryless alogorithms. (a) Field behavior as a function of propagation; power freely goes through the fictitious boundary. (b) Amount of power left in the simulation domain as a function of the propagation distance for the two beam-propagation methods discussed in the text (the two curves are virtually superimposed).

Equations (10)

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2 i k n ¯ ϕ ( x , z ) z = 2 ϕ ( x , z ) x 2 + k 2 [ n 2 ( x , z ) n ¯ 2 ] ϕ ( x , z ) ,
x = α ​  tan ( u )  ,
ϕ ( x , z ) = e ( x , z ) / cos ( u ) ,
2 i k n ¯ e ( u , z ) z = cos 4 ( u ) α 2 [ 2 e ( u , ​  z ) u 2 + e ( u , z ) ] + k 2 [ n 2 ( u , z ) n ¯ 2 ] e ( u , z ) .
z + | ϕ ( x , z ) | 2 d x = 0 ,
z π 2 π / 2 | e ( u , z ) | 2 / cos 4 ( u ) d u = 0 ,
a i ( n + 1 ) e i ( n + 1 ) + c i [ e i 1 ( n + 1 ) + e i + 1 ( n + 1 ) ] = b i ( n ) e i ( n ) c i [ e i 1 ( n + 1 ) + e i + 1 ( n + 1 ) ] ,
α i ( n + 1 ) = 4 i k n ¯ Δ u 2 Δ z cos 4 ( u i ) α 2 ( 2 Δ u 2 ) + k 2 Δ u 2 { [ n i ( n + 1 ) ] 2 n ¯ 2 } ,
b i ( n ) = 4 i k n ¯ Δ u 2 Δ z + cos 4 ( u i ) α 2 ( 2 Δ u 2 ) k 2 Δ u 2 { [ n i ( n ) ] 2 n ¯ 2 } ,
c i = cos 4 ( u i ) α 2 ,

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