## Abstract

Infrared multilayer diffractive optical elements (MLDOEs) usually own microstructure heights of a few hundred micrometers. The design and fabrication of those elements are more difficult than MLDOEs working in the visible waveband, especially for MLDOEs with high numerical aperture and finite feature sizes. Based on scalar diffraction theory and manufacturing errors, the effective area method for improving diffraction efficiency of infrared MLDOEs is developed. Closed-form analytical relations among diffraction efficiency, microstructure heights, microstructure periods, and incident angles are derived and verified in the infrared waveband. Then, optimized microstructure heights of infrared MLDOEs with different microstructure zone widths in the infrared wavelengths 3–5 μm and 8–12 μm at normal incidence can be obtained. The results indicate that the microstructure heights of infrared MLDOEs determined by the method have higher diffraction efficiency than former design methods. The method is verified by the rigorous electromagnetic method. Finally, the influence of incident angles on infrared MLDOEs is investigated. Our results show that the suggested microstructure parameters of MLDOEs both produce higher diffraction efficiencies than that of structure designed by scalar diffraction theory and may lead to more efficient hybrid diffractive–diffractive optical systems based on MLDOEs.

© 2019 Optical Society of America

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