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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 8, Iss. 5 — May. 1, 1991
  • pp: 724–731

Comparison of finite-difference and Fourier-transform solutions of the parabolic wave equation with emphasis on integrated-optics applications

R. Scarmozzino and R. M. Osgood, Jr.  »View Author Affiliations

JOSA A, Vol. 8, Issue 5, pp. 724-731 (1991)

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The solution of the scalar wave equation in the parabolic approximation is considered through the finite-difference and the Fourier-transform (i.e., beam propagation method) techniques. Examples are taken from the field of integrated optics and include propagation in straight, tapered, Y-branched, and coupled waveguides. A comparison of numerical results obtained by the two methods is presented, and a comparison with other analytical or numerical methods is also given. In the numerous cases studied it is shown that the finite-difference method yields a large, order-of-magnitude range improvement in accuracy or computational speed when compared with the Fourier-transform method.

© 1991 Optical Society of America

Original Manuscript: April 23, 1990
Manuscript Accepted: December 19, 1990
Published: May 1, 1991

R. Scarmozzino and R. M. Osgood, "Comparison of finite-difference and Fourier-transform solutions of the parabolic wave equation with emphasis on integrated-optics applications," J. Opt. Soc. Am. A 8, 724-731 (1991)

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  1. J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high-energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976). [CrossRef]
  2. M. D. Feit, J. A. Fleck, “Light propagation in graded-index optical fibers,” Appl. Opt. 17, 3990–3998 (1978). [CrossRef] [PubMed]
  3. C. Yeh, W. P. Brown, R. Szejn, “Multimode inhomogeneous fiber couplers,” Appl. Opt. 18, 489–495 (1979). [CrossRef] [PubMed]
  4. J. Van Roey, J. van der Donk, P. E. Lagasse, “Beam propagation method: analysis and assessment,”J. Opt. Soc. Am. 71, 803–810 (1981). [CrossRef]
  5. P. E. Lagasse, R. Baets, “The beam propagating method in integrated optics,” in Hybrid Formulation of Wave Propagation and Scattering, L. B. Felsen, ed. (Nijhoff, Dordrecht, The Netherlands, 1984), pp. 375–393. [CrossRef]
  6. J. F. Claerbout, Fundamentals of Geophysical Data Processing (McGraw-Hill, New York, 1976).
  7. R. Scarmozzino, D. V. Podlesnik, R. M. Osgood, “Losses of tapered dielectric slab waveguides with axial variations in index of refraction,” IEEE Trans. Microwave Theory Tech. 38, 141–147 (1990). [CrossRef]
  8. M. Kuznetsov, “Radiation loss in dielectric waveguide Y-branch structures,” IEEE J. Lightwave Technol. LT-3, 674–677 (1985). [CrossRef]
  9. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), p. 361.
  10. D. Yevick, B. Hermansson, “Split-step finite difference analysis of rib waveguides,” Electron. Lett. 25, 461–462 (1989). [CrossRef]
  11. D. Yevick, B. Hermansson, “Efficient beam propagation techniques,” IEEE J. Quantum Electron. 26, 109–112 (1990). [CrossRef]
  12. Y. Chung, N. Dagli, “Explicit finite difference beam propagation method: application to semiconductor rib waveguide Y-junction analysis,” Electron. Lett. 26, 711–713 (1990). [CrossRef]

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