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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 13 — Jul. 1, 2013
  • pp: 15815–15825

Higher-order wide-angle split-step spectral method for non-paraxial beam propagation

Brett H. Hokr, C. D. Clark, III, Rachel E. Grotheer, and Robert J. Thomas  »View Author Affiliations


Optics Express, Vol. 21, Issue 13, pp. 15815-15825 (2013)
http://dx.doi.org/10.1364/OE.21.015815


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Abstract

We develop a higher-order method for non-paraxial beam propagation based on the wide-angle split-step spectral (WASSS) method previously reported [Clark and Thomas, Opt. Quantum. Electron., 41, 849 (2010)]. The higher-order WASSS (HOWASSS) method approximates the Helmholtz equation by keeping terms up to third-order in the propagation step size, in the Magnus expansion. A symmetric exponential operator splitting technique is used to simplify the resulting exponential operators. The HOWASSS method is applied to the problem of waveguide propagation, where an analytical solution is known, to demonstrate the performance and accuracy of the method. The performance enhancement gained by implementing the HOWASSS method on a graphics processing unit (GPU) is demonstrated. When highly accurate results are required the HOWASSS method is shown to be substantially faster than the WASSS method.

© 2013 OSA

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(080.1510) Geometric optics : Propagation methods
(350.5500) Other areas of optics : Propagation
(080.1753) Geometric optics : Computation methods

ToC Category:
Physical Optics

History
Original Manuscript: March 25, 2013
Revised Manuscript: May 24, 2013
Manuscript Accepted: June 14, 2013
Published: June 25, 2013

Citation
Brett H. Hokr, C. D. Clark, Rachel E. Grotheer, and Robert J. Thomas, "Higher-order wide-angle split-step spectral method for non-paraxial beam propagation," Opt. Express 21, 15815-15825 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-13-15815


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References

  1. G. R. Hadley, “Multistep method for wide-angle beam propagation,” Opt. Lett.17, 1743–1745 (1992). [CrossRef] [PubMed]
  2. K. Q. Le, R. Godoy-Rubio, P. Bienstman, and G. R. Hadley, “The complex Jacobi iterative method for three-dimensional wide-angle beam propagation,” Opt. Express16, 17021–17030 (2008). [CrossRef] [PubMed]
  3. Y. Y. Lu and P. L. Ho, “Beam propagation method using a [(p−1)/p] Padé approximant of the propagator,” Opt. Lett.27, 683–685 (2002). [CrossRef]
  4. A. Sharma and A. Agrawal, “New method for nonparaxial beam propagation,” J. Opt. Soc. Am. B21, 1082–1087 (2004). [CrossRef]
  5. A. Sharma and A. Agrawal, “Non-paraxial split-step finite-difference method for beam propagation,” Opt. Quantum. Electron.38, 19–34 (2006). [CrossRef]
  6. C. D. Clark and R. Thomas, “Wide-angle split-step spectral method for 2D or 3D beam propagation,” Opt. Quantum. Electron.41, 849–857 (2010). [CrossRef]
  7. M. Guizar-Sicairos and J. C. Gutiérrez-Vega, “Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields,” J. Opt. Soc. Am. A21, 53–58 (2004). [CrossRef]
  8. W. Magnus, “On the exponential solution of differential equations for a linear operator,” Comm. Pure Appl. Math.7, 649–673 (1954). [CrossRef]
  9. M. Bauer, R. Chetrite, K. Ebrahimi-Fard, and F. Patras, “Time-ordering and a generalized Magnus expansion,” Lett. Math. Phys.103, 331–350 (2012). [CrossRef]
  10. M. J. Adams, An Introduction to Optical Waveguides (Wiley, 1981).

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