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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 37, Iss. 1 — Jan. 1, 1998
  • pp: 9–21

Improved beam propagation method equations

Enrico Nichelatti and Giulio Pozzi  »View Author Affiliations


Applied Optics, Vol. 37, Issue 1, pp. 9-21 (1998)
http://dx.doi.org/10.1364/AO.37.000009


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Abstract

Improved beam propagation method (BPM) equations are derived for the general case of arbitrary refractive-index spatial distributions. It is shown that in the paraxial approximation the discrete equations admit an analytical solution for the propagation of a paraxial spherical wave, which converges to the analytical solution of the paraxial Helmholtz equation. The generalized Kirchhoff–Fresnel diffraction integral between the object and the image planes can be derived, with its coefficients expressed in terms of the standard ABCD matrix. This result allows the substitution, in the case of an unaberrated system, of the many numerical steps with a single analytical step. We compared the predictions of the standard and improved BPM equations by considering the cases of a Maxwell fish-eye and of a Luneburg lens.

© 1998 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(350.5500) Other areas of optics : Propagation

History
Original Manuscript: March 28, 1997
Revised Manuscript: July 28, 1997
Published: January 1, 1998

Citation
Enrico Nichelatti and Giulio Pozzi, "Improved beam propagation method equations," Appl. Opt. 37, 9-21 (1998)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-1-9


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