We present a vector-based plane-wave spectrum (VPWS) method for efficient propagation of cylindrical electromagnetic fields. In comparison with electromagnetic propagation integrals, the VPWS method significantly reduces time of propagation. Numerical results that illustrate the utility of this method are presented.

© 1999 Optical Society of America

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  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 3, pp. 55–58.
  2. D. W. Prather, S. Shi, and J. S. Bergey, Opt. Lett. 24, 273 (1999).
  3. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  4. D. W. Prather and S. Shi, J. Opt. Soc. Am. A 16, 1131 (1999).
  5. J. N. Mait, D. W. Prather, and M. S. Mirotznik, Opt. Lett. 23, 1343 (1998).

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J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 3, pp. 55–58.

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Figures (2)

Fig. 1
Fig. 1

Geometry for an eight-level lens with a diameter of 36.66 µm and a focal length of 40 µm.

Fig. 2
Fig. 2

Overlay of line-scan plots of the electric-field amplitude for the VPWS and the EM-propagation methods in the focal plane of the eight-level lens: (a) ϕ=0°, (b) ϕ=90°.

Equations (21)

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Sk,α,0=002πEρ,ϕ,0×expjkρ cosα-ϕρdρdϕ.
Skk,α,0=m=0jm+1π cos mα0Eρmρ,0×Jm+1kρ-Jm-1kρ+Eϕmρ,0×Jm+1kρ+Jm-1kρρdρ
=m=0cos mαSkmk,0,
Sαk,α,0=m=0jm+1π sin mα0Eρρ,0×Jm+1kρ+Jm-1kρ+Eϕmρ,0×Jm+1kρ-Jm-1kρρdρ
=m=0sin mαSαmk,0,
Szk,α,0=m=0jm2π cos mα0Ezmρ,0×Jmkρρdρ=m=0cos mαSzmk,0,
Eρ,ϕ,z0=002πSk,α,z0×exp-jkρ cosα-ϕkdkdα.
Eρρ,ϕ,z0=m=0cos mϕjm+14π0Skmk,z0×Jm+1kρ-Jm-1kρ+Sαmk,z0×Jm+1kρ+Jm-1kρkdk
=m=0cos mϕEρmρ,z0,
Eϕρ,ϕ,z0=m=0sin mϕjm+14π0Skmk,z0×Jm+1kρ+Jm-1kρ+Sαmk,z0×Jm+1kρ-Jm-1kρkdk
=m=0sin mϕEϕmρ,z0,
Ezρ,ϕ,z0=m=0-jm2πcos mϕ0Szmk,z0×Jmkρkdk=m=0cos mϕEzmρ,z0.
Eρ,ϕ,z0=m=0ρˆEρmρ,z0cos mϕ+ϕˆEϕmρ,z0×sin mϕ+zˆEzmρ,z0×cos mϕ,