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Analysis of surface scattering characteristics of ultra-smooth optical components in gravitational wave detection system
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摘要
在引力波探测系统中，超光滑光学元件表面散射特性对高精度引力波测量至关重要。本文针对超光滑光学元件，建立了一种能快速准确地分析和预测其表面散射特性的非傍轴标量散射模型Generalized Beckmann-Kirchhoff (GBK)。在此基础上，研究了入射角度、散射方位角对P偏振和S偏振入射光的角分辨散射分布的影响，以及入射角度、散射方位角、自相关长度、斜率、截止频率以及表面粗糙度等因素对不同表面统计分布特征下的角分辨散射分布的影响。研究结果可为引力波探测系统中超光滑光学元件的加工、系统杂散光的产生及抑制等提供参考。
Abstract
In gravitational-wave detection systems, the surface scattering properties of ultra-smooth optical components play a crucial role in achieving high-precision gravitational-wave measurements. To analyze and predict the surface scattering properties of ultra-smooth optical components accurately and rapidly, a non-paraxial scalar scattering model, the Generalized Beckmann-Kirchhoff (GBK) model, was built up. On this basis, the influences of both the incident angle and the scattering azimuth angle on the angular resolved scattering distributions of both P-polarized and S-polarized incident light were investigated. Under different statistical distribution characteristics of optical surfaces, the effects of incident angle, azimuth angle, autocorrelation length, slope, cut-off frequency, and surface roughness on the scattering angle resolution distribution were analyzed. The research results can provide useful references for the manufacturing of ultra-smooth optical components and the generation and mitigation of stray light in gravitational-wave detection systems.
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Overview
Overview: In gravitational-wave detection systems, achieving a backscatter of space-borne telescopes below 10-10 or even lower is crucial to meet the design requirements. The scattering of ultra-smooth optical elements is the primary of stray light in gravitational-wave detection systems, significantly impacting high-precision gravitational-wave detection. To address this, a non-paraxial scalar scattering model, Generalized Beckmann-Kirchhoff (GBK), is proposed to analyze and predict the surface scattering characteristics of ultra-smooth optical elements in gravitational-wave detection systems. The GBK model is developed based on the Modified Beckmann-Kirchhoff (MBK) scalar scattering model, incorporating the power spectral density (PSD) function extracted from the MBK scalar scattering model and utilizing the Rayleigh–Rice (RR) vector scattering model as a standard for fitting. Comparative analyses between the GBK scalar scattering model and the RR vector scattering model under different conditions (surface roughness, incidence angle and autocorrelation length) validate the accuracy of the GBK scalar scattering model. Furthermore, the relationships between polarization angle resolved scattering (ARS) and scattering angles of isotropic elements at different incident angles, as well as the variations of different polarization ARS with scattering azimuth angles, are investigated. On this basis, this work focuses on the scattering characteristics of ultra-smooth optical element surfaces with different statistical distribution characteristics, including Gaussian, fractal, and Cauchy-Lorenz distributions. The influences of different statistical distributions of element surface, along with parameters such as incidence angle, scattering azimuth angle, autocorrelation length, slope, cut-off frequency and surface roughness, on the ARS distribution are quantitatively analyzed. The findings reveal significant variations in the scattering of P-polarized light compared to S-polarized light. With different statistical distributions of element surface, the ARS distributions consistently peak at the specular reflection. As the incidence angle, scattering azimuth angle and slope increase, the peak value of the ARS distribution gradually decreases and the width of the ARS distribution broadens. Additionally, an increase in autocorrelation length, cut-off frequency, and surface roughness leads to a rise in the peak value and narrower width of the ARS distribution. In the context of space gravitational-wave detection systems, particular attention must be paid to both the peak value and the width of the ARS distribution. The results can provide valuable references for the manufacturing of ultra-smooth optical elements and the generation and suppression of stray light in gravitational-wave detection systems.
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图 2 不同条件下角分辨散射分布。(a)不同表面粗糙度；(b)不同入射角度；(c)不同自相关长度
Figure 2. Distributions of angle resolved scattering under different conditions. (a) Different surface roughness; (b) Different incidence angles; (c) Different autocorrelation lengths
图 3 各向同性光学元件偏振ARS与散射角之间的关系。(a) S光的偏振散射特性；(b) P光的偏振散射特性
Figure 3. Relationships between polarization ARS and scattering angles of isotropic optical elements. (a) Scattering characteristics ofS-polarization light; (b) Scattering characteristics of P-polarization light
图 4 四种偏振状态下，偏振ARS与散射方位角之间的关系。(a) 平行偏振；(b) 交叉偏振
Figure 4. Relationships between polarization ARS and scattering azimuth angles in four polarization states. (a) Parallel polarization; (b) Cross polarization
图 5 不同入射角度下，偏振ARS与散射方位角的关系。(a) θi= 15°；(b) θi= 30°；(c) θi= 45°；(d) θi= 60°
Figure 5. Relationships between polarization ARS and scattering azimuth angles at different incident angles. (a) θi= 15°; (b) θi= 30°; (c) θi= 45°; (d) θi= 60°
图 6 在高斯统计分布下，ARS与四种不同参数的关系。(a) 入射角度；(b) 散射方位角；(c) 自相关长度；(d) 表面粗糙度
Figure 6. Relationships between ARS and four different parameters under the Gaussian statistical distribution. (a) Incidence angle; (b) Scattering azimuth angle; (c) Autocorrelation length; (d) Surface roughness
图 7 在分形统计分布下ARS与四种不同参数的关系。(a) 入射角度；(b) 散射方位角；(c) 斜率；(d) 表面粗糙度
Figure 7. Relationships between ARS and four different parameters under the fractal statistical distribution. (a) Incidence angle; (b) Scattering azimuth angle; (c) Slope; (d) Surface roughness
图 8 在柯西-洛伦兹统计分布下，ARS与四种不同参数的关系。(a) 入射角度；(b) 散射方位角；(c) 截止频率；(d) 表面粗糙度
Figure 8. Relationships between ARS and four different parameters under the Cauchy-Lorenz statistical distribution. (a) Incidence angle; (b) Scattering azimuth angle; (c) Cut-off frequency; (d) Surface roughness
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