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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 39, Iss. 34 — Dec. 1, 2000
  • pp: 6332–6340

Comparison of exact and asymptotic results for the focusing of electromagnetic waves through a plane interface

Velauthapillai Dhayalan and Jakob J. Stamnes  »View Author Affiliations


Applied Optics, Vol. 39, Issue 34, pp. 6332-6340 (2000)
http://dx.doi.org/10.1364/AO.39.006332


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Abstract

Recently, exact Kirchhoff solutions and the corresponding asymptotic solutions for the focusing of electromagnetic waves through a plane interface between two different dielectrics were reported. But the computation of exact results takes a long time because it requires the quadruple integration of a rapidly oscillating integrand. By using asymptotic techniques to perform two of the integrations, one can reduce the computing time dramatically. Therefore it is important to establish the accuracy and the range of validity of the asymptotic technique. To that end, we compare the exact and the asymptotic results for high-aperture, near-field focusing systems with a total distance from the aperture to the focal point of a few wavelengths and with a distance from the aperture to the interface as small as a fraction of a wavelength. The systems examined have f-numbers in the range from 0.6 to 0.9 and Fresnel numbers in the range from 0.4 to 3.5. Our results show that the accuracy of the asymptotic method increases with the aperture–interface distance when the aperture–focus distance is kept fixed and that it increases with the aperture–focus distance when the aperture–interface distance is kept fixed. To an accuracy of 7.8%, the asymptotic techniques are valid for aperture–interface distances as small as 0.5λ as long as the total distance from the aperture to the focal point exceeds 8λ. It is also shown that an accuracy of better than 1% can be obtained for the same aperture–interface distance of 0.5λ and for interface–observation-point distances as small as 0.1λ as long as the total distance from the aperture to the focal point exceeds 12λ. By use of the asymptotic technique the computing time is reduced by a factor of 103.

© 2000 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(080.2710) Geometric optics : Inhomogeneous optical media
(180.0180) Microscopy : Microscopy
(260.1960) Physical optics : Diffraction theory
(260.2110) Physical optics : Electromagnetic optics

History
Original Manuscript: April 26, 2000
Revised Manuscript: July 10, 2000
Published: December 1, 2000

Citation
Velauthapillai Dhayalan and Jakob J. Stamnes, "Comparison of exact and asymptotic results for the focusing of electromagnetic waves through a plane interface," Appl. Opt. 39, 6332-6340 (2000)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-34-6332

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