OSA's Digital Library

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


View Full Text Article

Enhanced HTML    Acrobat PDF (155 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. H. Ling, S. W. Lee, “Focusing of electromagnetic waves through a dielectric interface,” J. Opt. Soc. Am. A 1, 965–973 (1984). [CrossRef]
  2. J. J. Stamnes, Waves in Focal Regions (Adam Hilger, Boston, 1986).
  3. T. D. Visser, S. H. Wiersma, “Defocusing of a converging electromagnetic wave by a plane dielectric interface,” J. Opt. Soc. Am. A 13, 320–325 (1996). [CrossRef]
  4. P. Török, P. Varga, Z. Laczic, G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation,” J. Opt. Soc. Am. A 12, 325–332 (1995). [CrossRef]
  5. P. Török, P. Varga, G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: structure of the electromagnetic field. I,” J. Opt. Soc. Am. A 12, 2136–2144 (1995). [CrossRef]
  6. P. Török, P. Varga, G. Nemeth, “Analytical solution of the diffraction integrals and interpretation of wave-front distortion when light is focused through a planar interface between materials of mismatched refractive indices,” J. Opt. Soc. Am. A 12, 2660–2671 (1995). [CrossRef]
  7. B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959). [CrossRef]
  8. D. G. Flagello, T. Milster, A. E. Rosenbluth, “Theory of high-NA imaging in homogeneous thin films,” J. Opt. Soc. Am. A 13, 53–64 (1996). [CrossRef]
  9. J. H. Erkkila, M. E. Rogers, “Diffracted fields in the focal volume of a converging wave,” J. Opt. Soc. Am. 71, 904–905 (1981). [CrossRef]
  10. J. J. Stamnes, B. Spjelkavik, “Focusing at small angular apertures in the Debye and Kirchoff approximations,” Opt. Commun. 40, 81–85 (1981). [CrossRef]
  11. E. Wolf, Y. Li, “Conditions for the validity of the Debye integral representation of focused fields,” Opt. Commun. 39, 205–210 (1981). [CrossRef]
  12. Y. Li, “Encircled energy for systems of different Fresnel numbers,” Optik (Stuttgart) 64, 207–218 (1983).
  13. Y. Li, H. Platzer, “An experimental investigation of diffraction patterns in low-Fresnel-number focusing systems,” Opt. Acta 30, 1621–1643 (1983). [CrossRef]
  14. Y. Li, “Dependence of the focal shift on Fresnel number and f-number,” J. Opt. Soc. Am. 72, 770–774 (1982). [CrossRef]
  15. V. Dhayalan, J. J. Stamnes, “Focusing of electric-dipole waves in the Debye and Kirchoff approximations,” Pure Appl. Opt. 6, 347–372 (1997). [CrossRef]
  16. C. A. Taylor, B. J. Thompson, “Attempt to investigate experimentally the intensity distribution near the focus in the error-free diffraction patterns of circular and annular apertures,” J. Opt. Soc. Am. 48, 844–850 (1958). [CrossRef]
  17. G. W. Farnell, “Measured phase distribution in the image space of a microwave lens,” Can. J. Phys. 36, 935–943 (1958). [CrossRef]
  18. S. H. Wiersma, P. Török, T. D. Visser, P. Varga, “Comparison of different theories for focusing through a plane interface,” J. Opt. Soc. Am. A 14, 1482–1490 (1997). [CrossRef]
  19. D. Jiang, J. J. Stamnes, “Theoretical and experimental results for two-dimensional electromagnetic waves focused through an interface,” Pure Appl. Opt. 7, 627–641 (1998). [CrossRef]
  20. J. J. Stamnes, D. Jiang, “Focusing of two-dimensional electromagnetic waves through a plane interface,” Pure Appl. Opt. 7, 603–625 (1998). [CrossRef]
  21. J. J. Stamnes, H. A. Eide, “Exact and approximate solutions for focusing of two-dimensional waves. I. Theory,” J. Opt. Soc. Am. A 15, 1285–1291 (1998). [CrossRef]
  22. H. A. Eide, J. J. Stamnes, “Exact and approximate solutions for focusing of two-dimensional waves. II. Numerical comparisons between exact, Debye, and Kirchoff theories,” J. Opt. Soc. Am. A 15, 1308–1319 (1998). [CrossRef]
  23. H. A. Eide, J. J. Stamnes, “Exact and approximate solutions for focusing of two-dimensional waves. III. Numerical comparisons between exact and Rayleigh–Sommerfeld theories,” J. Opt. Soc. Am. A 15, 1292–1307 (1998). [CrossRef]
  24. V. Dhayalan, J. J. Stamnes, “Focusing of electromagnetic waves into a dielectric slab. I. Exact and asymptotic results,” Pure Appl. Opt. 7, 33–52 (1998). [CrossRef]
  25. J. J. Stamnes, B. Spjelkavik, H. M. Pedersen, “Evaluation of diffraction integrals using local phase and amplitude approximations,” Opt. Acta 30, 207–222 (1983). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited