Optimal Design of Wide Angle Diffractive Optical Element
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摘要: 为进一步研究入射角度的增大对衍射光学元件（diffractive optical element, DOE）衍射效率及微结构高度等参数的影响，分析了入射角度和周期宽度对带宽积分平均衍射效率的影响。基于扩展标量衍射理论，建立了DOE的微结构高度与入射角度和周期宽度的数学模型，提出了工作在一定入射角度范围内，基于复合带宽积分平均衍射效率（comprehensive polychromatic integral diffraction efficiency, CPIDE）最大化实现设计波长和微结构高度等结构参数的优化设计方法。以工作在红外波段的DOE为例进行分析。结果表明：当相对周期宽度为20，入射角度范围为0°~40°时，该DOE的CPIDE为94.15%，微结构高度为1.3396 μm。该设计方法可以实现广角DOE的优化设计。Abstract: The influence of the incident angle on the diffraction efficiency and microstructure height of the diffractive optical element (DOE) was analyzed to further study the influence of the incident angle and period width on the polychromatic integral diffraction efficiency (PIDE). Based on the extended scalar diffraction theory (ESDT), a mathematical model of the relationship among the microstructure height, incident angle, and period width of the DOE was established. An optimal design method for structural parameters, such as the design wavelength and microstructure height, was proposed based on maximizing the comprehensive PIDE (CPIDE) within a certain range of incident angles. A DOE operating within the infrared waveband was considered as an example. The results indicate that when the relative period width is 20 and the incidence angle range is 0° to 40°, the CPIDE of the DOE is 94.15%, and the microstructure height is 1.3396 μm. This design method can realize the optimal design of a wide-angle DOE.
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图 2 正入射时的PIDE与波长的关系
Figure 2. Relationship between PIDE and wavelength at normal incidence
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图 7 衍射效率与波长关系的对比
Figure 7. Comparison of the relationship between diffraction efficiency and wavelength
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图 8 一定周期宽度时的PIDE与入射角度和波长的关系
Figure 8. PIDE versus incident angle and wavelength at a certain period width
表 1 微结构高度与周期宽度的关系
Table 1 Relationship between microstructure height and period width
Incident angle/(°) Period width /λ 5 10 20 30 ∞ 0 1.3758 1.3734 1.3728 1.3727 1.3726 20 1.3579 1.3463 1.3411 1.3395 1.3365 40 1.2689 1.2511 1.2430 1.2404 1.2355 60 1.1266 1.1076 1.0988 1.0960 1.0907 
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表 2 基于带宽积分平均衍射效率最大化确定的结构参数
Table 2 Structural parameters determined by maximum PIDE
Parameters Incident angle/° 0 20 40 60 Maximum PIDE/% 94.47 94.47 94.48 94.50 Design wavelength/μm 1.7399 1.7298 1.7220 1.7182 Microstructure height/μm 1.3724 1.3360 1.2350 1.0904
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表 3 基于带宽积分平均衍射效率最大化确定的结构参数
Table 3 Structural parameters determined by maximum CPIDE
Parameters Incident angle range/° 0-20 0-40 0-60 Design wavelength/μm 1.73 1.72 1.72 Design angle/° 8.25 16 24 Microstructure height/μm 1.3615 1.3396 1.3142 CPIDE/% 94.45 94.15 92.67
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