## Finite-substrate-thickness cylindrical diffractive lenses: exact and approximate boundary-element methods

JOSA A, Vol. 16, Issue 6, pp. 1294-1302 (1999)

http://dx.doi.org/10.1364/JOSAA.16.001294

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### Abstract

A novel approach based on the boundary-element method (BEM) with exact and approximate Green’s functions is presented for the analysis of the performance of finite-substrate-thickness cylindrical diffractive lenses. This approach can be applied to the analysis of lenses with thicknesses of thousands of wavelengths for both TE and TM polarization. Multiple interference resonance effects between the upper and the lower boundaries of the lens are included. Also, for the cases when multiple interference resonance effects can be neglected, another approach based on the BEM with a modified approximate Green’s function is developed. It is shown that the latter approach corresponds to the cascaded application of the BEM as previously published [Appl. Opt. 37, 34, 6591 (1998)]. To illustrate the advantages of the approaches presented, a cylindrical diffractive lens with a substrate thickness of 2 mm is analyzed. It is not possible to analyze this large-substrate-thickness lens with the previously published cascaded application of the BEM.

© 1999 Optical Society of America

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(050.1970) Diffraction and gratings : Diffractive optics

**History**

Original Manuscript: October 8, 1998

Revised Manuscript: January 19, 1999

Manuscript Accepted: January 22, 1999

Published: June 1, 1999

**Citation**

Koichi Hirayama, Ken Igarashi, Yoshio Hayashi, Elias N. Glytsis, and Thomas K. Gaylord, "Finite-substrate-thickness cylindrical diffractive lenses: exact and approximate boundary-element methods," J. Opt. Soc. Am. A **16**, 1294-1302 (1999)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-6-1294

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