Abstract

We propose a transparent boundary for the finite-element beam-propagation method to analyze the beam propagation in a finite computational window. In this method, a transparent boundary condition is derived by assuming a beam to be a plane wave in the vicinity of a virtual boundary, which eliminates undesirable reflections from a virtual boundary.

© 1993 Optical Society of America

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References

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  1. G. Mur, IEEE Trans. Electromagn. Compat. EMC-23, 377 (1981).
    [CrossRef]
  2. A. Bayliss, M. Gunzburger, E. Turkel, SIAM J. Appl. Math. 42, 430 (1982).
    [CrossRef]
  3. G. R. Hadley, Opt. Lett. 16, 624 (1991).
    [CrossRef] [PubMed]
  4. M. Matsuhara, Trans. Inst. Electr. Inf. Commun. Eng. J72-C-I, 473 (1989) [Electron. Commun. Jpn. Pt. II 73, 41 (1990)].

1991 (1)

1989 (1)

M. Matsuhara, Trans. Inst. Electr. Inf. Commun. Eng. J72-C-I, 473 (1989) [Electron. Commun. Jpn. Pt. II 73, 41 (1990)].

1982 (1)

A. Bayliss, M. Gunzburger, E. Turkel, SIAM J. Appl. Math. 42, 430 (1982).
[CrossRef]

1981 (1)

G. Mur, IEEE Trans. Electromagn. Compat. EMC-23, 377 (1981).
[CrossRef]

Bayliss, A.

A. Bayliss, M. Gunzburger, E. Turkel, SIAM J. Appl. Math. 42, 430 (1982).
[CrossRef]

Gunzburger, M.

A. Bayliss, M. Gunzburger, E. Turkel, SIAM J. Appl. Math. 42, 430 (1982).
[CrossRef]

Hadley, G. R.

Matsuhara, M.

M. Matsuhara, Trans. Inst. Electr. Inf. Commun. Eng. J72-C-I, 473 (1989) [Electron. Commun. Jpn. Pt. II 73, 41 (1990)].

Mur, G.

G. Mur, IEEE Trans. Electromagn. Compat. EMC-23, 377 (1981).
[CrossRef]

Turkel, E.

A. Bayliss, M. Gunzburger, E. Turkel, SIAM J. Appl. Math. 42, 430 (1982).
[CrossRef]

IEEE Trans. Electromagn. Compat. (1)

G. Mur, IEEE Trans. Electromagn. Compat. EMC-23, 377 (1981).
[CrossRef]

Opt. Lett. (1)

SIAM J. Appl. Math. (1)

A. Bayliss, M. Gunzburger, E. Turkel, SIAM J. Appl. Math. 42, 430 (1982).
[CrossRef]

Trans. Inst. Electr. Inf. Commun. Eng. (1)

M. Matsuhara, Trans. Inst. Electr. Inf. Commun. Eng. J72-C-I, 473 (1989) [Electron. Commun. Jpn. Pt. II 73, 41 (1990)].

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Figures (1)

Fig. 1
Fig. 1

Gaussian beam propagation in free space at an angle of 45° to the virtual boundary. The boundary conditions are (a) the Neumann condition and (b) the transparent condition.

Equations (8)

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- j 2 k 0 n 0 ϕ z + 2 ϕ x 2 + k 0 2 [ n 2 ( x , z ) - n 0 2 ] ϕ = 0 ,
( ϕ x + α ϕ ) x 0 = 0 ,
[ - j 2 k 0 n 0 ϕ z u n + k 0 2 ( n 2 - n 0 2 ) ϕ u n - ϕ x d u n d x ] d x - ( α ϕ u n ) x 0 = 0 ,
[ A ] d d z { F ( z ) } + [ B ( z ) ] { F ( z ) } = 0 ,
a m n = - j 2 k 0 n 0 u m u n d x , b m n ( z ) = [ k 0 2 ( n 2 - n 0 2 ) u m u n - d u m d x d u n d x ] d x - ( α u m u n ) x 0 ,
ϕ ( x , z ) = a exp ( - α x - β z ) .
ϕ ( x 0 , z 0 - Δ z ) = f N = a exp [ - α x 0 - β ( z 0 - Δ z ) ] , ϕ ( x 0 - Δ x , z 0 - Δ z ) = f N - 1 = a exp [ - α ( x 0 - Δ x ) - β ( z 0 - Δ z ) ] .
α = - 1 Δ x log ( f N f N - 1 ) .

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