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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 10 — May. 12, 2008
  • pp: 7203–7213

Vectorial beam shaping

Toufic G. Jabbour and Stephen M. Kuebler  »View Author Affiliations

Optics Express, Vol. 16, Issue 10, pp. 7203-7213 (2008)

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An algorithm is reported for the design of a phase-only diffractive optical element (DOE) that reshapes a beam focused using a high numerical aperture (NA) lens. The vector diffraction integrals are used to relate the field distributions in the DOE plane and focal plane. The integrals are evaluated using the chirp-z transform and computed iteratively within the Method of Generalized Projections (MGP) to identify a solution that simultaneously satisfies the beam shaping and DOE constraints. The algorithm is applied to design a DOE that transforms a circularly apodized flat-top beam of wavelength λ to a square irradiance pattern when focused using a 1.4-NA objective. A DOE profile is identified that generates a 50λ×50λ square irradiance pattern having 7% uniformity error and 74.5% diffraction efficiency (fraction of focused power). The diffraction efficiency and uniformity decrease as the size of the focused profile is reduced toward the diffraction limited spot size. These observations can be understood as a manifestation of the uncertainty principle.

© 2008 Optical Society of America

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(050.1940) Diffraction and gratings : Diffraction
(050.1960) Diffraction and gratings : Diffraction theory
(050.1970) Diffraction and gratings : Diffractive optics
(050.5080) Diffraction and gratings : Phase shift
(140.3300) Lasers and laser optics : Laser beam shaping

ToC Category:
Diffraction and Gratings

Original Manuscript: March 24, 2008
Revised Manuscript: April 28, 2008
Manuscript Accepted: April 29, 2008
Published: May 2, 2008

Toufic G. Jabbour and Stephen M. Kuebler, "Vectorial beam shaping," Opt. Express 16, 7203-7213 (2008)

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