Abstract

A new boundary condition algorithm is presented that passes outgoing radiation freely with a minimum reflection coefficient (typically 10−5) while inhibiting the flux of incoming radiation. In contrast to the commonly used absorber method, this algorithm contains no adjustable parameters and is thus problem independent. It adapts naturally to a standard Crank–Nicholson difference scheme and is shown to be accurate and robust for both two-and three-dimensional problems.

© 1991 Optical Society of America

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References

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  1. A. Neyer, W. Mevenkamp, L. Thylen, B. Lagerstrom, IEEE J. Lightwave Technol. LT-3, 635 (1985).
    [Crossref]
  2. P. Kaczmarski, P. E. Lagasse, Electron. Lett. 24, 675 (1988).
    [Crossref]
  3. J. Saijonmaa, D. Yevick, J. Opt. Soc. Am. 73, 1785 (1983).
    [Crossref]
  4. D. Yevick, B. Hermansson, IEEE J. Quantum Electron. 25, 221 (1989).
    [Crossref]
  5. R. Pregla, J. Gerdes, in Digest of Meeting on Integrated Photonics Research (Optical Society of America, Washington, D.C., 1990), paper MG3.
  6. D. Yevick, B. Hermansson, IEEE J. Quantum Electron. 26, 109 (1990).
    [Crossref]

1990 (1)

D. Yevick, B. Hermansson, IEEE J. Quantum Electron. 26, 109 (1990).
[Crossref]

1989 (1)

D. Yevick, B. Hermansson, IEEE J. Quantum Electron. 25, 221 (1989).
[Crossref]

1988 (1)

P. Kaczmarski, P. E. Lagasse, Electron. Lett. 24, 675 (1988).
[Crossref]

1985 (1)

A. Neyer, W. Mevenkamp, L. Thylen, B. Lagerstrom, IEEE J. Lightwave Technol. LT-3, 635 (1985).
[Crossref]

1983 (1)

Gerdes, J.

R. Pregla, J. Gerdes, in Digest of Meeting on Integrated Photonics Research (Optical Society of America, Washington, D.C., 1990), paper MG3.

Hermansson, B.

D. Yevick, B. Hermansson, IEEE J. Quantum Electron. 26, 109 (1990).
[Crossref]

D. Yevick, B. Hermansson, IEEE J. Quantum Electron. 25, 221 (1989).
[Crossref]

Kaczmarski, P.

P. Kaczmarski, P. E. Lagasse, Electron. Lett. 24, 675 (1988).
[Crossref]

Lagasse, P. E.

P. Kaczmarski, P. E. Lagasse, Electron. Lett. 24, 675 (1988).
[Crossref]

Lagerstrom, B.

A. Neyer, W. Mevenkamp, L. Thylen, B. Lagerstrom, IEEE J. Lightwave Technol. LT-3, 635 (1985).
[Crossref]

Mevenkamp, W.

A. Neyer, W. Mevenkamp, L. Thylen, B. Lagerstrom, IEEE J. Lightwave Technol. LT-3, 635 (1985).
[Crossref]

Neyer, A.

A. Neyer, W. Mevenkamp, L. Thylen, B. Lagerstrom, IEEE J. Lightwave Technol. LT-3, 635 (1985).
[Crossref]

Pregla, R.

R. Pregla, J. Gerdes, in Digest of Meeting on Integrated Photonics Research (Optical Society of America, Washington, D.C., 1990), paper MG3.

Saijonmaa, J.

Thylen, L.

A. Neyer, W. Mevenkamp, L. Thylen, B. Lagerstrom, IEEE J. Lightwave Technol. LT-3, 635 (1985).
[Crossref]

Yevick, D.

D. Yevick, B. Hermansson, IEEE J. Quantum Electron. 26, 109 (1990).
[Crossref]

D. Yevick, B. Hermansson, IEEE J. Quantum Electron. 25, 221 (1989).
[Crossref]

J. Saijonmaa, D. Yevick, J. Opt. Soc. Am. 73, 1785 (1983).
[Crossref]

Electron. Lett. (1)

P. Kaczmarski, P. E. Lagasse, Electron. Lett. 24, 675 (1988).
[Crossref]

IEEE J. Lightwave Technol. (1)

A. Neyer, W. Mevenkamp, L. Thylen, B. Lagerstrom, IEEE J. Lightwave Technol. LT-3, 635 (1985).
[Crossref]

IEEE J. Quantum Electron. (2)

D. Yevick, B. Hermansson, IEEE J. Quantum Electron. 26, 109 (1990).
[Crossref]

D. Yevick, B. Hermansson, IEEE J. Quantum Electron. 25, 221 (1989).
[Crossref]

J. Opt. Soc. Am. (1)

Other (1)

R. Pregla, J. Gerdes, in Digest of Meeting on Integrated Photonics Research (Optical Society of America, Washington, D.C., 1990), paper MG3.

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Figures (4)

Fig. 1
Fig. 1

Propagation of two Gaussian pulses through the transparent boundary at different angles. Shown are snapshots of the pulses at 30-μm intervals.

Fig. 2
Fig. 2

Fraction of initial power remaining after the beam traverses a smooth two-dimensional Y junction (wavelength 1.55 μm) and the radiative loss of all but the single bound mode. The curves are for the TBC method (solid curve) and the more conventional artificial absorber method (dashed curve) using 145 absorption zones.

Fig. 3
Fig. 3

Cross-section schematic of the rib waveguide used to construct the three-dimensional Y junction for the third test. Only half of the device was zoned, with symmetry boundary conditions employed at the left boundary.

Fig. 4
Fig. 4

Fraction of initial power remaining in a three-dimensional Y junction (wavelength 1.55 μm) versus propagation distance. The absorber method results seem to approach the TBC results as the absorption region thickness is increased. The absorption profile used was that given in Ref. 4.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

E z = i 2 k 2 E x 2 ,
z a b E 2 d x = i 2 k ( E * E x - E E * x ) | a b - F b + F a ,
F b = R ( k x ) E ( b ) 2 k .
E M n E M - 1 n = E M - 1 n E M - 2 n = exp ( i k x Δ x ) .
E M n + 1 = E M - 1 n + 1 exp ( i k x Δ x ) .

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