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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 30, Iss. 2 — Feb. 1, 2013
  • pp: 259–263

Adaptive boundaryless finite-difference method

Dorilian Lopez-Mago and Julio C. Gutiérrez-Vega  »View Author Affiliations


JOSA A, Vol. 30, Issue 2, pp. 259-263 (2013)
http://dx.doi.org/10.1364/JOSAA.30.000259


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Abstract

The boundaryless beam propagation method uses a mapping function to transform the infinite real space into a finite-size computational domain [Opt. Lett. 21, 4 (1996)]. This leads to a bounded field that avoids the artificial reflections produced by the computational window. However, the method suffers from frequency aliasing problems, limiting the physical region to be sampled. We propose an adaptive boundaryless method that concentrates the higher density of sampling points in the region of interest. The method is implemented in Cartesian and cylindrical coordinate systems. It keeps the same advantages of the original method but increases accuracy and is not affected by frequency aliasing.

© 2013 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(080.1510) Geometric optics : Propagation methods
(350.5500) Other areas of optics : Propagation
(070.7345) Fourier optics and signal processing : Wave propagation

History
Original Manuscript: November 20, 2012
Revised Manuscript: January 11, 2013
Manuscript Accepted: January 14, 2013
Published: January 31, 2013

Citation
Dorilian Lopez-Mago and Julio C. Gutiérrez-Vega, "Adaptive boundaryless finite-difference method," J. Opt. Soc. Am. A 30, 259-263 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-2-259


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References

  1. C. Vassallo and F. Collino, “Highly efficient absorbing boundary conditions for the beam propagation method,” J. Lightwave Technol. 14, 1570–1577 (1996). [CrossRef]
  2. G. R. Hadley, “Transparent boundary condition for beam propagation,” Opt. Lett. 16, 624–626 (1991). [CrossRef]
  3. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]
  4. F. Ladouceur, “Boundaryless beam propagation,” Opt. Lett. 21, 4–5 (1996). [CrossRef]
  5. J. Shibayama, K. Matsubara, M. Sekiguchi, J. Yamauchi, and H. Nakano, “Efficient nonuniform schemes for paraxial and wide-angle finite-difference beam propagation methods,” J. Lightwave Technol. 17, 677–683 (1999). [CrossRef]
  6. M. Guizar-Sicairos and J. C. Gutiérrez-Vega, “Boundaryless finite-difference method for three-dimensional beam propagation,” J. Opt. Soc. Am. A 23, 866–871 (2006). [CrossRef]
  7. J. P. Hugonin, P. Lalanne, I. del Villar, and I. R. Matias, “Fourier modal methods for modeling optical dielectric waveguides,” Opt. Quantum Electron. 37, 107–119 (2005). [CrossRef]
  8. G. C. des Francs, J. P. Hugonin, and J. Čtyroký, “Mode solvers for very thin long-range plasmonic waveguides,” Opt. Quantum Electron. 42, 557–570 (2011). [CrossRef]
  9. C. Pozrikidis, Numerical Computation in Science and Engineering (Oxford, 1998).
  10. A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2005).
  11. J. C. Gutiérrez-Vega and M. A. Bandres, “Helmholtz–Gauss waves,” J. Opt. Soc. Am. A 22, 289–298 (2005). [CrossRef]
  12. G. R. Hadley, “Wide-angle beam propagation using Padé approximant operators,” Opt. Lett. 17, 1426–1428 (1992). [CrossRef]
  13. I. Ilić, R. Scarmozzino, and R. M. Osgood, “Investigation of the Padé approximant-based wide-angle beam propagation method for accurate modeling of waveguiding circuits,” J. Lightwave Technol. 14, 2813–2822 (1996). [CrossRef]
  14. A. Sharma and A. Agrawal, “A new finite-difference-based method for wide-angle beam propagation,” IEEE Photon. Technol. Lett. 18, 944–946 (2006). [CrossRef]

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