Abstract

A new beam-propagation method is presented whereby the Padé approximant wide-angle propagation operator is factored into a series of simpler Padé (1, 1) operators, thus leading naturally to a multistep method whose component steps are each solvable by using readily available paraxiallike solution techniques. The resulting method allows accurate approximations to true Helmholtz propagation while incurring only a modest numerical penalty. In addition, the tridiagonal form of the component steps allows the straightforward use of the previously reported transparent boundary condition.

© 1992 Optical Society of America

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References

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  1. D. Yevick, M. Glasner, Opt. Lett. 15, 174 (1990).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  5. B. Hermansson, D. Yevick, W. Bardyszewski, M. Glasner, IEEE J. Lightwave Technol. 10, 772 (1992).
    [Crossref]
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    [Crossref]
  7. D. Yevick, M. Glasner, B. Hermansson, Opt. Lett. 17, 725 (1992).
    [Crossref] [PubMed]
  8. G. R Hadley, IEEE J. Quantum Electron. 28, 363 (1992).
    [Crossref]
  9. W. P. Huang, C. L. Xu, S. K Chaudhuri, IEEE Photon. Technol. Lett. 4, 148 (1992).
    [Crossref]

1992 (5)

G. R Hadley, Opt. Lett. 17, 1426 (1992).
[Crossref] [PubMed]

B. Hermansson, D. Yevick, W. Bardyszewski, M. Glasner, IEEE J. Lightwave Technol. 10, 772 (1992).
[Crossref]

D. Yevick, M. Glasner, B. Hermansson, Opt. Lett. 17, 725 (1992).
[Crossref] [PubMed]

G. R Hadley, IEEE J. Quantum Electron. 28, 363 (1992).
[Crossref]

W. P. Huang, C. L. Xu, S. K Chaudhuri, IEEE Photon. Technol. Lett. 4, 148 (1992).
[Crossref]

1991 (2)

1990 (2)

M. D. Collins, J. Acoust. Soc. Am. 87, 1535 (1990).
[Crossref]

D. Yevick, M. Glasner, Opt. Lett. 15, 174 (1990).
[Crossref] [PubMed]

Bardyszewski, W.

B. Hermansson, D. Yevick, W. Bardyszewski, M. Glasner, IEEE J. Lightwave Technol. 10, 772 (1992).
[Crossref]

Chaudhuri, S. K

W. P. Huang, C. L. Xu, S. K Chaudhuri, IEEE Photon. Technol. Lett. 4, 148 (1992).
[Crossref]

Collins, M. D.

M. D. Collins, J. Acoust. Soc. Am. 87, 1535 (1990).
[Crossref]

Fleck, J. A

Gerdes, J.

Glasner, M.

Hadley, G. R

G. R Hadley, Opt. Lett. 17, 1426 (1992).
[Crossref] [PubMed]

G. R Hadley, IEEE J. Quantum Electron. 28, 363 (1992).
[Crossref]

Hermansson, B.

B. Hermansson, D. Yevick, W. Bardyszewski, M. Glasner, IEEE J. Lightwave Technol. 10, 772 (1992).
[Crossref]

D. Yevick, M. Glasner, B. Hermansson, Opt. Lett. 17, 725 (1992).
[Crossref] [PubMed]

Huang, W. P.

W. P. Huang, C. L. Xu, S. K Chaudhuri, IEEE Photon. Technol. Lett. 4, 148 (1992).
[Crossref]

Pregla, R.

Ratowsky, R. P.

Xu, C. L.

W. P. Huang, C. L. Xu, S. K Chaudhuri, IEEE Photon. Technol. Lett. 4, 148 (1992).
[Crossref]

Yevick, D.

IEEE J. Lightwave Technol. (1)

B. Hermansson, D. Yevick, W. Bardyszewski, M. Glasner, IEEE J. Lightwave Technol. 10, 772 (1992).
[Crossref]

IEEE J. Quantum Electron. (1)

G. R Hadley, IEEE J. Quantum Electron. 28, 363 (1992).
[Crossref]

IEEE Photon. Technol. Lett. (1)

W. P. Huang, C. L. Xu, S. K Chaudhuri, IEEE Photon. Technol. Lett. 4, 148 (1992).
[Crossref]

J. Acoust. Soc. Am. (1)

M. D. Collins, J. Acoust. Soc. Am. 87, 1535 (1990).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Lett. (4)

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Figures (3)

Fig. 1
Fig. 1

Intensity profiles resulting from the propagation of an initial Gaussian beam having a 45° phase tilt a distance of 10 μm through a uniform medium. Results for the two-step method are compared with the exact analytic results. Paraxial results are included for additional perspective.

Fig. 2
Fig. 2

Intensity profiles resulting from the propagation of an initial Gaussian beam having a 45° phase tilt a distance of 10 μm through a uniform medium. Results for the three-step method are compared with the exact analytic results. An increase in accuracy compared with the results shown in Fig. 1 is clearly indicated.

Fig. 3
Fig. 3

Error in the calculated mode index of a simple ridge waveguide is plotted versus the reference index error (reference index minus the correct mode index) for several propagation schemes. Parameters for the calculation are given in the text.

Equations (8)

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

H z = i N D H ,
P k 0 2 [ ( x ¯ ) 0 n ¯ 2 ] + 2 ,
D ( H m + 1 H m ) = i Δ z 2 N ( H m + H m + 1 ) ,
H m + 1 = i = 0 n ξ i P i i = 0 n ξ i * P i H m ,
H m + 1 = ( 1 + a 1 P ) ( 1 + a 2 P ) ( 1 + a n P ) ( 1 + a 1 * P ) ( 1 + a 2 * P ) ( 1 + a n * P ) H m .
a 1 + a 2 = ξ 1 , a 1 a 2 = ξ 2 ,
a 1 + a 2 + a 3 = ξ 1 , a 1 a 2 + a 2 a 3 + a 1 a 3 = ξ 2 , a 1 a 2 a 3 = ξ 3 .
H m + i n = 1 + a i P 1 + a i * P H m + i 1 n .

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