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

E N Glytsis¹, M E Harrigan, K Hirayama

¹School of Electrical and Computer Engineering and Microelectronics Research Center, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.

|February 13, 2008

Summary

Rigorous electromagnetic analysis of diffractive cylindrical lenses shows wave-front quality below 0.05 wavelengths. Scalar approximations for lens performance are less accurate, especially at lower f-numbers.

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Area of Science:

Optics and Photonics
Electromagnetics
Computational Physics

Background:

Diffractive optical elements (DOEs) offer compact and lightweight alternatives to refractive lenses.
Accurate modeling of DOEs is crucial for predicting their performance, especially for cylindrical and multi-level designs.

Purpose of the Study:

To rigorously analyze the performance of multi-level diffractive cylindrical lenses using the boundary-element method (BEM).
To compare the rigorous BEM results with approximate scalar diffraction analyses.
To evaluate the impact of lens f-number on the validity of scalar approximations.

Main Methods:

Sequential application of the two-region formulation of the rigorous electromagnetic boundary-element method (BEM).
Simulation of Gaussian beams (TE/TM polarization) incident on finite-thickness diffractive cylindrical lenses.
Quantification of near-field wave-front quality and determination of far-field intensity patterns.

Main Results:

Near-field wave-front deviation was consistently below 0.05 free-space wavelengths for analyzed lenses.
Rigorous BEM yielded lower diffraction efficiencies compared to the approximate Fraunhofer scalar diffraction analysis.
The validity of scalar approximation significantly deteriorates as the lens f-number decreases.

Conclusions:

The BEM provides a more accurate assessment of diffractive cylindrical lens performance than scalar methods.
Multi-level diffractive lenses can achieve high wave-front quality, but their efficiency is best predicted by rigorous electromagnetic methods.
Designers must use rigorous methods for low f-number lenses to ensure accurate performance predictions.