OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 43, Iss. 11 — Apr. 10, 2004
  • pp: 2242–2250

Modeling Microlenses by Use of Vectorial Field Rays and Diffraction Integrals

Miguel A. Alvarez-Cabanillas, Fang Xu, and Yeshaiahu Fainman  »View Author Affiliations


Applied Optics, Vol. 43, Issue 11, pp. 2242-2250 (2004)
http://dx.doi.org/10.1364/AO.43.002242


View Full Text Article

Acrobat PDF (297 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A nonparaxial vector-field method is used to describe the behavior of low-<i>f</i>-number microlenses by use of ray propagation, Fresnel coefficients and the solution of Maxwell equations to determine the field propagating through the lens boundaries, followed by use of the Rayleigh-Sommerfeld method to find the diffracted field behind the lenses. This approach enables the phase, the amplitude, and the polarization of the diffracted fields to be determined. Numerical simulations for a convex-plano lens illustrate the effects of the radii of curvature, the lens apertures, the index of refraction, and the wavelength on the variations of the focal length, the focal plane field distribution, and the cross polarization of the field in the focal plane.

© 2004 Optical Society of America

OCIS Codes
(080.3630) Geometric optics : Lenses
(220.3630) Optical design and fabrication : Lenses
(260.1960) Physical optics : Diffraction theory

Citation
Miguel A. Alvarez-Cabanillas, Fang Xu, and Yeshaiahu Fainman, "Modeling Microlenses by Use of Vectorial Field Rays and Diffraction Integrals," Appl. Opt. 43, 2242-2250 (2004)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-43-11-2242


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. E. Park, M. Kim, and Y. Kwon, “Microlens for efficient coupling between LED and optical fiber,” IEEE Photon. Technol. Lett. 11, 439–441 (1999).
  2. S. Calixto and M. Ornelas-Rodriguez, “Mid-infrared microlenses fabricated by melting method,” IEEE Photon. Technol. Lett. 17, 1212–1214 (1999).
  3. A. Walther, The Ray and Wave Theory of Lenses (Cambridge University, Cambridge, England, 1995).
  4. Y. Li and E. Wolf, “Focal shift in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981).
  5. M. A. Alonso, A. A. Asatryan, and G. W. Forbes, “Beyond the Fresnel approximation for focused waves,” J. Opt. Soc. Am. A 16, 1958–1969 (1999).
  6. A. Wünsche, “Transition from the paraxial approximation to exact solution of the wave equation and application to Gaussian beams,” J. Opt. Soc. Am. A 9, 765–774 (1992).
  7. W. Hsu and R. Barakat, “Stratton-Chu vectorial diffraction of electromagnetic fields by apertures with application to small-Fresnel-number systems,” J. Opt. Soc. Am. A 11, 623–629 (1994).
  8. A. Wang and A. Prata, Jr., “Lenslet analysis by rigorous vector diffraction theory,” J. Opt. Soc. Am. A 12, 1161–1169 (1995).
  9. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A 253, 358–379 (1959).
  10. M. Gu, Advanced Optical Imaging Theory, Vol. 75 of Springer Series in Optical Sciences(Springer-Verlag, Berlin, 2000).
  11. J. W. M. Chon, X. Gan, and M. Gu, “Splitting of the focal spot of a high numerical-aperture objective in free space,” Appl. Phys. Lett. 81, 1576–1578 (2002).
  12. M. Lax, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
  13. Q. Cao and X. Deng, “Correction to the paraxial approximation of an arbitrary free-propagation beam,” J. Opt. Soc. Am. A 15, 1144–1148 (1998).
  14. Q. Cao, “Correction to the paraxial approximation solutions in transversely nonuniform refractive-index media,” J. Opt. Soc. Am. A 16, 2494–2499 (1999).
  15. A. I. Carswell, “Measurements of the longitudinal component of the electromagnetic field at the focus of a coherent beam,” Phys. Rev. Lett. 15, 647–649 (1965).
  16. M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, Cambridge, England, 1999).
  17. J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974–980 (1979).
  18. W. H. Southwell, “Validity of the Fresnel approximation in the near field,” J. Opt. Soc. Am. 71, 7–14 (1981).
  19. C. J. R. Sheppard and M. Hrynevych, “Diffraction by a circular aperture: a generalization of Fresnel diffraction theory,” J. Opt. Soc. Am. A 9, 274–281 (1992).
  20. Y. Fainman and J. Shamir, “Polarization of nonplanar wave fronts,” Appl. Opt. 23, 3188–3195 (1984).

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