Suppression of higher diffraction orders using quasiperiodic array of rectangular holes with large size tolerance
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摘要: 传统光栅的基础研究和应用研究进展一直备受关注。然而，高阶衍射污染使传统光栅获得的光谱纯度受到严重影响。为了抑制高阶衍射贡献，人们提出了许多单级或准单级光栅的设计方案，但它们对高阶衍射的抑制效果不可避免地受到加工精度的限制。提出了一种准周期矩形孔阵列光栅，通过优化矩形孔的概率密度分布函数，获得了比以往设计更大的加工误差宽容度。对这种光栅的衍射特性进行了分析研究。理论计算表明，即使孔径相对误差超过20%，光栅也可以完全抑制二阶、三阶和四阶衍射，五阶衍射效率与一阶衍射效率之比小于0.01%，大大降低了对加工精度的要求。Abstract: Advances in basic and applied research of conventional grating have been attracting much attention from optical engineering community. However, the higher orders diffraction contamination degrades the spectral purity obtained by conventional gratings seriously. Many designs of single-order or quasi-single-order gratings have been proposed to suppress higher-order diffraction contributions, however, their inhibitive effects on the higher order diffractions are restrained by the processing accuracy unavoidably. In this paper, we propose a grating that incorporates a quasi-periodical array of rectangular holes, and achieves larger tolerance of processing errors compared with the previously designed gratings by optimizing the probability density distribution function of the holes. This paper describes an analytical study of the diffraction property of this grating. Theoretical calculations reveal that the grating completely suppresses the 2nd, 3rd, and 4th orders diffractions, and the ratio of the 5th order diffraction efficiency to that of the 1st is as low as 0.01% even if relative errors for hole sizes exceed 20%, which greatly decreases the required processing accuracy.
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Key words:
- single-order diffraction grating /
- X-ray /
- spectrometer /
- tolerance of processing errors
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Figure 1. Schematic of the distribution of holes in the array: from δ-function to arbitrary positive function
${\mathit{\Gamma}} \left( {{\xi _n},{\eta _n}} \right)$ 
Figure 2. (a) Design for a quasi-periodical hole array: in each lattice (d×d square), a rectangular hole with side lengths of d/6 and d is positioned randomly on the ξn axis and has a trapezoidal distribution profile shown in (b)
Figure 3. Comparison between far-field diffraction patterns of a quasi-periodical array shown in Fig. 2 when H＝L＝100 and a periodic grating with a duty cycle of 1∶5 and 201 periods
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