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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. 17, Iss. 11 — Nov. 1, 2000
  • pp: 2081–2089

Focusing of electromagnetic waves by paraboloid mirrors. I. Theory

Peter Varga and Peter Török  »View Author Affiliations


JOSA A, Vol. 17, Issue 11, pp. 2081-2089 (2000)
http://dx.doi.org/10.1364/JOSAA.17.002081


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Abstract

We derive a solution to the problem of a plane electromagnetic wave focused by a parabolic mirror. The solution is obtained from the Stratton–Chu integral by solving a boundary-value problem. Our solution can be considered self-consistent. We also derive the far-field, i.e., Debye, approximation of our formulas. The solution shows that when the paraboloid is infinite, its focusing properties exhibit a dispersive behavior; that is, the structure of the field distribution in the vicinity of the focus strongly depends on the wavelength of the illumination. We show that for an infinite paraboloid the confinement of the focused energy worsens, with the energy distribution spreading in the focal plane.

© 2000 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

History
Original Manuscript: December 10, 1999
Revised Manuscript: April 27, 2000
Manuscript Accepted: April 27, 2000
Published: November 1, 2000

Citation
Peter Varga and Peter Török, "Focusing of electromagnetic waves by paraboloid mirrors. I. Theory," J. Opt. Soc. Am. A 17, 2081-2089 (2000)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-11-2081


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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). [CrossRef]
  2. B. Richards, 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). [CrossRef]
  3. A. Boivin, E. Wolf, “Electromagnetic field in the neighborhood of a focus of a coherent beam,” Phys. Rev. 138, B1561–B1565 (1965). [CrossRef]
  4. A. Boivin, J. Dow, E. Wolf, “Energy flow in the neighborhood of the focus of a coherent beam,” J. Opt. Soc. Am. 57, 1171–1175 (1967). [CrossRef]
  5. C. J. R. Sheppard, T. Wilson, “The image of a single point in microscopes of large numerical aperture,” Proc. R. Soc. London, Ser. A 379, 145–158 (1982). [CrossRef]
  6. P. Török, P. Varga, Z. Laczik, 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]
  7. J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986), Sec. 16.1.
  8. W. Wang, A. T. Friberg, E. Wolf, “Structure of focused fields in systems with large Fresnel numbers,” J. Opt. Soc. Am. A 12, 1947–1953 (1995). [CrossRef]
  9. P. Török, “Focusing of electromagnetic waves through a dielectric interface by lenses of finite Fresnel number,” J. Opt. Soc. Am. A 15, 3009–3015 (1998). [CrossRef]
  10. V. S. Ignatowsky, “The relationship between geometrical and wave optics and diffraction of homocentrical beams,” Trans. Opt. Inst. 1(3), 1–30 (1920).
  11. V. S. Ignatowsky, “Diffraction by a paraboloid mirror with arbitrary aperture,” Trans. Opt. Inst. 1(5), 1–30 (1920).
  12. V. Galindo-Israel, R. Mittra, “A new series representation for the radiation integral with application to reflector antennas,” IEEE Trans. Antennas Propag. AP-25, 631–641 (1985).
  13. H. Ling, S.-W. Lee, P. T. C. Lam, W. V. T. Rusch, “Focal shift in parabolic reflectors,” IEEE Trans. Antennas Propag. AP-33, 744–748 (1977).
  14. J. Stratton, L. Chu, “Diffraction theory of electromagnetic waves,” Phys. Rev. 56, 99–107 (1939). [CrossRef]
  15. F. Kottler, “Diffraction at a black screen, Part I,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1965), Vol. IV, Chap. VII, and F. Kottler, “Diffraction at a black screen, Part II,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1967), Vol. VI, Chap. I.
  16. P. Debye, “Das Verhalten von Lichtwellen in der Nähe eines Brennpunktes oder einer Brennlinie,” Ann. Phys. (Leipzig) 30, 755–776 (1909). [CrossRef]
  17. R. K. Luneburg, Mathematical Theory of Optics (University of California, Berkeley, Berkeley, Calif., 1964), Sec. 47.
  18. D. J. Innes, A. L. Bloom, “Design of optical systems for use with laser beams,” Spectra-Phys. Laser Tech. Bull. 5, 1–10 (1966).
  19. C. J. R. Sheppard, A. Choudhury, J. Gannaway, “Electromagnetic field near the focus of wide-angular lens and mirror systems,” Microwave Opt. Acoust. 1, 129–132 (1977). [CrossRef]
  20. J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986), Sec. 16.1.2.
  21. P. Varga, P. Török, “Focusing of electromagnetic waves by paraboloid mirrors. II. Numerical results,” J. Opt. Soc. Am. A 17, 2090–2095 (2000). [CrossRef]
  22. Y. Li, E. Wolf, “Three-dimensional intensity distribution near the focus in systems of different Fresnel numbers,” J. Opt. Soc. Am. A 1, 801–808 (1984). [CrossRef]

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