OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 59, Iss. 5 — May. 1, 1969
  • pp: 559–564

Boundary-Diffraction-Wave Theory of Cascaded-Apertures Diffraction

JOHN W. Y. LIT and RÉAL TREMBLAY  »View Author Affiliations


JOSA, Vol. 59, Issue 5, pp. 559-564 (1969)
http://dx.doi.org/10.1364/JOSA.59.000559


View Full Text Article

Acrobat PDF (960 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Systems of cascaded circular apertures may be built to focus electromagnetic waves if the difference (d) between the Fresnel numbers of any two apertures pertaining to two points (A and B) is an even number. With a point source at A, the spherical incident wave will be focused to B. In general, the irradiance at B (principal focus) is roughly proportional to (n±1)2 where n is the number of apertures; the plus sign is used when the Fresnel numbers are odd integers, and minus when even. A system of a few apertures with d = 0 can focus waves over a wide range of frequencies, though the actual irradiance at the principal focus is a function of frequency. A condition to maximize the irradiance at the principal focus has been found. Theoretically such systems have been analyzed by the boundary-diffraction-wave theory generalized by Miyamoto and Wolf. Analytical expressions for the diffraction wave amplitude have been obtained for axial and off-axial points, when the iteration method of Fox and Li is also applicable, the two theoretical results agree very well with each other. Experimental data obtained agree well with the theoretical results.

Citation
JOHN W. Y. LIT and RÉAL TREMBLAY, "Boundary-Diffraction-Wave Theory of Cascaded-Apertures Diffraction," J. Opt. Soc. Am. 59, 559-564 (1969)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-59-5-559


Sort:  Author  |  Journal  |  Reset

References

  1. M. De, J. W. Y. Lit, and R. Tremblay, Appl. Opt. 7, 483 (1968).
  2. R. Tremblay and M. De, Appl. Phys. Letters 9, 136 (1966).
  3. M. De, R. Tremblay and J. W. Y. Lit, J. Opt. Soc. Am. 54, 1437 (1966).
  4. T. Young, A Course of Lectures an Natural Philosophy and Mechanical Arts (London, 1807).
  5. A. Rubinowicz, Ann. Physik 4, 53, 257 (1917).
  6. K. Miyamoto and E. Wolf, J. Opt. Soc. Am. 52, 615 (1962).
  7. K. Miyamoto and E. Wolf, J. Opt. Soc. Am. 52, 626 (1962).
  8. The subscript n in Un(j) (Q) means the number of diffractions the wave has undergone, while the superscript (j) indicates the last aperture which diffracts the wave and from which the wave propagates to the point Q.
  9. Since the scalar wave theory is the basis of the calculations, the point Q must be far enough from the edge so that the theory is applicable. Also, Q must be off the axis by a distance great enough so that the contribution from the points with stationary phase represents reasonably well the boundary wave.
  10. E. T. Copson, Asymptotic Expansions (Cambridge University Press, Cambridge, 1965).
  11. E. W. Marchand and E. Wolf, J. Opt. Soc. Am. 58, 720 (1968).
  12. A. Boivin, Théorie et calcul des figures de diffraction de révolution (Les Presses de l’Université Laval, Québec, 1964).
  13. E. H. Linfoot and E. Wolf, Proc. Phys. Soc. (London) B66, 145 (1953).
  14. G. Toraldo di Francia, Atti. Fond. Giorgio Ronchi Contrib. Inst. Natl. Optica 6, 3 (1951).
  15. R. W. Wood, Phil. Mag. 45, 511 (1898).
  16. J. L. Soret, Arch. Sci. Phys. Nature 52, 320 (1875).
  17. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Natl. Bur. Stds., Washington, D. C., 1964; Dover Publications, Inc., New York, 1965), p. 361.
  18. G. N. Watson, Treatise on the Theory of Bessel Functions (Cambridge University Press, London, 1958).
  19. M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon Press, Inc., New York, 1964).
  20. A. G. Fox and T. Li, Bell System Tech. J. 40, 453 (1961).

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