Methodology for determining temperature dependences of the diffraction efficiency of two-layer two-relief microstructures in the framework of a rigorous coupled-wave analysis

Aiming to calculate the diffraction efficiency of diffractive optical elements with a two-layer microstructure and two internal sawtooth reliefs within the framework of the rigorous electromagnetic theory of diffraction, we propose an approach that involves calculating the efficiency of the element as a whole through the efficiency of each zone of the microstructure separately. This approach is a basis for a DE calculation method, which takes into account the normalized area of each zone of a two-layer microstructure, the temperature dependences of the depths of both reliefs and their refractive indices, as well as the local mutual displacement of the microstructure layers due to a difference in the thermal expansion coefficients of their materials. We present a mathematical apparatus of the proposed technique that minimizes the computational complexity and demonstrates its effectiveness by the example of calculating the diffraction efficiency of the diffractive element of an ultra-high-aperture refractive-diffraction athermal dual-band infrared lens. We show that due to variations in the operating temperature (from –40°C to + 60°C), the diffraction efficiency drops by no more than 7% over the entire operating spectral range (3.5 – 5.2 μm; 7.5 – 11.4 μm) with permissible angles of light incidence on the microstucture ranging from –14° to +14°.