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%).