锥形入射下炽热光栅的拓扑优化

Simon Ans, Frédéric Zamkotsian, Guillaume Demésy
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摘要

本文提出了一种拓扑优化方法,并将其应用于锥形入射下反射的炽热衍射光栅。这种光栅的目的是将入射光分散到一个特定的衍射阶上,这一特性在光谱学中至关重要。传统上,炽热金属光栅是由锯齿形轮廓制成的,设计用于±1阶衍射反射。在本文中,我们对这种直观的三角形图案提出质疑,并根据麦克斯韦方程的有限元建模,利用拓扑优化技术寻找最佳光几何特性。在实际应用中,光栅的几何形状是单周期的,但它受到三维平面波的启发,其波矢量在不变平面之外。因此,本研究采用有限元法解决介于二维和三维之间的直接和反向问题:即所谓的锥形入射。为了获得宽带炽热效果,使用了多波长目标。最后,详细介绍了几个数值实验。我们的数值结果表明,如果在单一波长上进行优化,1阶衍射效率可以达到 98%;如果使用多波长优化准则,[400,1500] nm 波长范围内的反射积分绝对值可以比锯齿形炽热光栅高出 29%,相对值高出 56%(从 52% 到 81%)。
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Topology optimization of blazed gratings under conical incidence
A topology optimization method is presented and applied to a blazed diffraction grating in reflection under conical incidence. This type of grating is meant to disperse the incident light on one particular diffraction order, and this property is fundamental in spectroscopy. Conventionally, a blazed metallic grating is made of a sawtooth profile designed to work with the ±1st diffraction order in reflection. In this paper, we question this intuitive triangular pattern and look for optimal opto-geometric characteristics using topology optimization based on finite element modelling of Maxwell’s equations. In practical contexts, the grating geometry is mono-periodic, but it is enlightened by a 3D plane wave with a wave vector outside of the plane of invariance. Consequently, this study deals with the resolution of direct and inverse problems using the finite element method in this intermediate state between 2D and 3D: the so-called conical incidence. A multi-wavelength objective is used in order to obtain a broadband blazed effect. Finally, several numerical experiments are detailed. Our numerical results show that it is possible to reach a 98% diffraction efficiency on the −1st diffraction order if the optimization is performed on a single wavelength, and that the reflection integrated over the [400,1500] nm wavelength range can be 29% higher in absolute terms, 56% in relative terms, than that of the sawtooth blazed grating when using a multi-wavelength optimization criterion (from 52% to 81%).
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