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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 19, Iss. 8 — Aug. 1, 2002
  • pp: 1658–1667

Focusing of electromagnetic radiation by hyperboloidal and ellipsoidal lenses

Peter Varga  »View Author Affiliations


JOSA A, Vol. 19, Issue 8, pp. 1658-1667 (2002)
http://dx.doi.org/10.1364/JOSAA.19.001658


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Abstract

A solution to the problem of plane electromagnetic waves focused by an ellipsoidal or a hyperboloidal lens is derived from the Stratton–Chu integral by solving a boundary-value problem. The current method is more rigorous than those hitherto published in the literature. Results show that for linearly polarized incident illumination and in the vicinity of the focus, the distribution of the time-averaged electric energy density is almost fully transverse electric.

© 2002 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(260.0260) Physical optics : Physical optics
(260.2110) Physical optics : Electromagnetic optics
(260.5430) Physical optics : Polarization

Citation
Peter Varga, "Focusing of electromagnetic radiation by hyperboloidal and ellipsoidal lenses," J. Opt. Soc. Am. A 19, 1658-1667 (2002)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-8-1658


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References

  1. E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
  2. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
  3. J. A. Stratton and L. J. Chu, “Diffraction theory of electromagnetic waves,” Phys. Rev. 56, 99–107 (1939).
  4. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  5. P. Varga and P. Török, “Electromagnetic focusing by a paraboloid mirror. I. Theory,” J. Opt. Soc. Am. A 17, 2081–2089 (2000).
  6. P. Varga and P. Török, “Electromagnetic focusing by a paraboloid mirror. II. Numerical results,” J. Opt. Soc. Am. A 17, 2090–2095 (2000).
  7. A. Hardy and D. Treves, “Structure of the electromagnetic field near the focus of a stigmatic lens,” J. Opt. Soc. Am. 63, 85–90 (1973).
  8. P. Török, P. D. Higdon, and T. Wilson, “On the general properties of polarising conventional and confocal microscopes,” Opt. Commun. 148, 300–315 (1998).
  9. N. Sergienko, V. Dhayalan, and J. J. Stamnes, “Comparison of focusing properties of conventional and diffractive lenses,” Opt. Commun. 194, 225–234 (2001).
  10. A. Sommerfeld, Optics, Vol. IV in Lectures on Theoretical Physics (Academic, New York, 1954).

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