Objective The diffractive optical element (DOE) possesses unique characteristics, such as negative dispersion and athermalization, which distinguish it from traditional refractive lenses. DOE is extensively utilized in various applications, including imaging, beam shaping, and 3D displays. It plays a significant role in the miniaturization of imaging optical systems and their engineering applications. Previous studies utilizing vector analysis and the extended scalar diffraction theory (ESDT) have demonstrated a more accurate calculation of the shading effect's impact on the reduction of diffraction efficiency at normal incidence. However, these studies did not address the influence of substrate materials at large-angle incidence on diffraction efficiency. This paper presents a technique for selecting substrate materials for the DOE based on ESDT. This method is essential for advancing the theoretical examination of the multilayer diffractive optical element (MLDOE) at high incident angles, particularly in the design of refractive-diffractive hybrid systems that incorporate diffraction elements with small period widths.

Methods Based on the ESDT, a theoretical model was proposed to describe the relationship between the microstructure height and the period width of the DOE, taking into account the substrate material and the angle of incidence (Eq.6). A method for selecting the substrate material for the DOE, based on the ESDT at oblique incidence, was proposed (Eq.8). An analysis was conducted using a MLDOE operating in the MWIR-LWIR dual band as an illustrative example.

Results and Discussions As illustrated in Fig.3, there is a significant contrast between the outcomes of SDT and ESDT. The results of SDT remain unaffected by the width of the microstructure period, whereas the outcomes of ESDT fluctuate based on this width. Figure 4 demonstrates the variation in polychromatic integral diffraction efficiency (PIDE) of ESDT with respect to angle under different period widths. It is evident from Fig.4 that, according to ESDT, there are discrepancies in the simulation results of diffraction efficiency for varying period widths. The outcomes of extended scalar diffraction theory are contingent upon the width of the microstructure period. The differences in diffraction efficiency for various substrate material combinations, as determined by ESDT, are presented in Fig.6 and Tab.1 for different period widths. As shown in Fig.6, the substrate material AMTIR1-ZNS exhibits the least variation in diffraction efficiency across all period widths, while the material combination GE-ZNS produces the greatest variation in diffraction efficiency across the same range. Consequently, AMTIR1-ZNS emerges as the most suitable substrate material combination for the MWIR-LWIR dual band.

Conclusions This paper validates the accuracy and reliability of the rapid selection method for substrate materials based on ESDT. This design approach and its findings can serve as a valuable guide for designing MLDOE in dual-band infrared optical systems. Furthermore, this analytical method and its conclusions provide theoretical guidance for the optimal design of DOE operating at different incident angles.