## Collimating cylindrical diffractive lenses: rigorous electromagnetic analysis and scalar approximation

Applied Optics, Vol. 37, Issue 1, pp. 34-43 (1998)

http://dx.doi.org/10.1364/AO.37.000034

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### Abstract

Practical collimating diffractive cylindrical lenses of 2, 4, 8,
and 16 discrete levels are analyzed with a sequential application of
the two-region formulation of the rigorous electromagnetic
boundary-element method (BEM). A Gaussian beam of TE or TM
polarization is incident upon the finite-thickness
lens. *F*/4, *F*/2, and *F*/1.4 lenses are
analyzed and near-field electric-field patterns are presented. The
near-field wave-front quality is quantified by its mean-square
deviation from a planar wave front. This deviation is found to be
less than 0.05 free-space wavelengths. The far-field intensity
patterns are determined and compared with the ones predicted by the
approximate Fraunhofer scalar diffraction analysis. The diffraction
efficiencies determined with the rigorous BEM are found to be generally
lower than those obtained with the scalar approximation. For
comparison, the performance characteristics of the corresponding
continuous Fresnel (continuous profile within a zone but
discontinuous at zone boundaries) and continuous refractive lenses
are determined by the use of both the BEM and the scalar
approximation. The diffraction efficiency of the continuous Fresnel
lens is found to be similar to that of the 16-level diffractive lens
but less than that of the continuous refractive lens. It is shown
that the validity of the scalar approximation deteriorates as the lens
*f*-number decreases.

© 1998 Optical Society of America

**OCIS Codes**

(050.1970) Diffraction and gratings : Diffractive optics

(220.3630) Optical design and fabrication : Lenses

**History**

Original Manuscript: April 11, 1997

Revised Manuscript: July 8, 1997

Published: January 1, 1998

**Citation**

Elias N. Glytsis, Michael E. Harrigan, Koichi Hirayama, and Thomas K. Gaylord, "Collimating cylindrical diffractive lenses: rigorous electromagnetic analysis and scalar approximation," Appl. Opt. **37**, 34-43 (1998)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-1-34

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