变折射率体全息光栅衍射特性分析方法与制作工艺研究
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摘要
体全息光栅以其较高的衍射效率、良好的波长和角度选择性、低噪声，且对偏振状态、温度变化不敏感等优势逐渐成为近年来颇具竞争力的分光元件，已成为光谱分析、天文观测、数据存储、光纤通讯等领域关注的热点。然而，复杂的处理工艺往往使体全息光栅出现条纹间距变化、调制分布不均等偏离理想状态的现象，导致其技术指标与设计值不符，影响其应用效果。因此，研究非均匀混合调制轮廓的潜像光栅衍射效率计算方法，建立非均匀膨胀和收缩下变栅距光栅模型，分析非理想体全息光栅的衍射特性以指导体全息光栅制作工艺十分重要。
基于此，本文对变折射率体全息光栅衍射特性分析方法与制作工艺进行了研究，并对其在PGP成像光谱仪中的应用进行了探索。具体研究工作如下：
第一，提出一种既兼顾位相与振幅调制又引入衰减分布的异相光栅衍射效率计算方法。引入介电常数与吸收常数随膜层厚度非均匀变化函数，重构衍射光振幅的二阶微分耦合波方程。详细分析了记录过程中平均吸收常数、吸收调制度、衰减系数、相移量和几何分层等参数对光栅衍射特性的影响。为厚膜光栅在记录过程中提供了一种有效的衍射效率严格算法。
第二，引入膨胀因子随光栅胶层厚度的变化函数研究在非均匀膨胀和收缩情况下反射体全息光栅的衍射特性。通过推导平均折射率和折射率调制度的解析表达式，分析了平均折射率和折射率调制度在衰减分布时对光栅角度和波长选择特性的影响程度，考察了膨胀因子以定值、线性函数、非线性函数变化时光栅的衍射特性，并给出了胶层厚度及光栅周期与曝光和未曝光区域膨胀因子的函数关系。解决了反射体全息光栅在非均匀膨胀与收缩下折射率参量变化问题。
第三，设计并研制了一种可见光波段高衍射效率的透射体全息光栅。对体全息光栅结构参数进行了分析优化，给出详细制作流程、工艺条件参数及关键技术控制方法，经过角度和波长选择性测试，结果满足设计要求。
第四，作为体全息光栅的具体应用，提出了PGP整体化设计方法，并开发了计算PGP整体衍射效率的分析软件。通过阐述棱镜与光栅的分光原理，给出了棱镜与光栅各项结构参数对PGP模块衍射特性的影响，以及在光栅基底与记录材料的折射率不同时PGP的衍射特性，讨论了光栅布拉格波长的漂移特性。据此设计了一种在400nm-1000nm波段范围内衍射效率高于50%的PGP分光模块，解决了棱镜与光栅匹配问题，实现了PGP整体化设计、整体化分析。
Volume holographic grating is becoming a more competitive dispersion opticalelement, due to its unique and desirable properties, such as high diffraction efficiency,high wavelength and angle selectivity, low noise, relatively low dependence onpolarization angle and temperature. Volume holographic grating has received muchmore attention in spectral analysis, astronomical observation, data storage and fiberoptic communication. However, practical gratings tend to deviate from the idealconditions during complicated technological processes, for instance, variable fringespace, non-uniform modulation distribution and so on, which lead to the technicalindexes deviated from the value of the design. Thus, constructing diffractionefficiency calculation method for non-uniform mixed modulation grating, andestablishing the model of varied-line-spacing grating caused by swelling or shrinking,are very necessary for analyzing diffraction characteristics of the non-ideal gratingand guiding the process of grating fabrication.
Given these problems, the analysis methods for the diffraction characteristics of varied-refractive-index volume holographic grating, the fabricating technologies,and the application in PGP imaging spectroscopy are researched thoroughly in thispaper.
First, a method for calculating diffraction efficiencies of attenuated grating andmixed phase-amplitude grating with a phase difference is presented. Coupled-waveequations about the amplitudes of internal diffraction waves are reconstructed, byassuming that the relative permittivity and absorption as a function of film thickness.Diffraction characteristics changing with the parameters during recording processare investigated in detail, including absorption constant, absorption modulation, andattenuation coefficient, phase difference between the phase and absorption grating,and the sub-regions. It is a useful and rigorous method for thick gratings analysis.
Second, diffraction characteristics of reflection volume holographic grating atnon-uniform swelling and shrinking are analyzed, by introducing a function betweenswelling factor and film thickness. The expressions of average refractive index andthe modulation are derived to discuss the influences on angular and wavelengthselectivity. Accordingly, the efficiency curves are given not only when the swellingfactor is expressed as a constant, a linear or a nonlinear function, but also the case inwhich the swelling factors are unequal at the exposure area and the unexposed area.The method can solve the problem which the index varies along the depth.
Third, a transmission grating with high diffraction efficiency at the visiblespectral coverage is developed. Parameters optimization, manufacturing flow,technological parameters and controlling method are given, the result is satisfiedwith design requirements, though testing the angle and wavelength selectivity.
Fourth, as a specific application, integration design method of PGP is provided,and the software is developed with the functions of design, calculation and analysis.The influencing factors on diffraction characteristics of PGP are researched,including the structure parameters of prism and grating, the Bragg wavelengthshifting, and the index of the substrate. A PGP component with wide spectralcoverage from400nm to1000nm is designed, the diffraction efficiency is not less than50%. The method can realize PGP integration design and integration analysis.
基于此，本文对变折射率体全息光栅衍射特性分析方法与制作工艺进行了研究，并对其在PGP成像光谱仪中的应用进行了探索。具体研究工作如下：
第一，提出一种既兼顾位相与振幅调制又引入衰减分布的异相光栅衍射效率计算方法。引入介电常数与吸收常数随膜层厚度非均匀变化函数，重构衍射光振幅的二阶微分耦合波方程。详细分析了记录过程中平均吸收常数、吸收调制度、衰减系数、相移量和几何分层等参数对光栅衍射特性的影响。为厚膜光栅在记录过程中提供了一种有效的衍射效率严格算法。
第二，引入膨胀因子随光栅胶层厚度的变化函数研究在非均匀膨胀和收缩情况下反射体全息光栅的衍射特性。通过推导平均折射率和折射率调制度的解析表达式，分析了平均折射率和折射率调制度在衰减分布时对光栅角度和波长选择特性的影响程度，考察了膨胀因子以定值、线性函数、非线性函数变化时光栅的衍射特性，并给出了胶层厚度及光栅周期与曝光和未曝光区域膨胀因子的函数关系。解决了反射体全息光栅在非均匀膨胀与收缩下折射率参量变化问题。
第三，设计并研制了一种可见光波段高衍射效率的透射体全息光栅。对体全息光栅结构参数进行了分析优化，给出详细制作流程、工艺条件参数及关键技术控制方法，经过角度和波长选择性测试，结果满足设计要求。
第四，作为体全息光栅的具体应用，提出了PGP整体化设计方法，并开发了计算PGP整体衍射效率的分析软件。通过阐述棱镜与光栅的分光原理，给出了棱镜与光栅各项结构参数对PGP模块衍射特性的影响，以及在光栅基底与记录材料的折射率不同时PGP的衍射特性，讨论了光栅布拉格波长的漂移特性。据此设计了一种在400nm-1000nm波段范围内衍射效率高于50%的PGP分光模块，解决了棱镜与光栅匹配问题，实现了PGP整体化设计、整体化分析。
Volume holographic grating is becoming a more competitive dispersion opticalelement, due to its unique and desirable properties, such as high diffraction efficiency,high wavelength and angle selectivity, low noise, relatively low dependence onpolarization angle and temperature. Volume holographic grating has received muchmore attention in spectral analysis, astronomical observation, data storage and fiberoptic communication. However, practical gratings tend to deviate from the idealconditions during complicated technological processes, for instance, variable fringespace, non-uniform modulation distribution and so on, which lead to the technicalindexes deviated from the value of the design. Thus, constructing diffractionefficiency calculation method for non-uniform mixed modulation grating, andestablishing the model of varied-line-spacing grating caused by swelling or shrinking,are very necessary for analyzing diffraction characteristics of the non-ideal gratingand guiding the process of grating fabrication.
Given these problems, the analysis methods for the diffraction characteristics of varied-refractive-index volume holographic grating, the fabricating technologies,and the application in PGP imaging spectroscopy are researched thoroughly in thispaper.
First, a method for calculating diffraction efficiencies of attenuated grating andmixed phase-amplitude grating with a phase difference is presented. Coupled-waveequations about the amplitudes of internal diffraction waves are reconstructed, byassuming that the relative permittivity and absorption as a function of film thickness.Diffraction characteristics changing with the parameters during recording processare investigated in detail, including absorption constant, absorption modulation, andattenuation coefficient, phase difference between the phase and absorption grating,and the sub-regions. It is a useful and rigorous method for thick gratings analysis.
Second, diffraction characteristics of reflection volume holographic grating atnon-uniform swelling and shrinking are analyzed, by introducing a function betweenswelling factor and film thickness. The expressions of average refractive index andthe modulation are derived to discuss the influences on angular and wavelengthselectivity. Accordingly, the efficiency curves are given not only when the swellingfactor is expressed as a constant, a linear or a nonlinear function, but also the case inwhich the swelling factors are unequal at the exposure area and the unexposed area.The method can solve the problem which the index varies along the depth.
Third, a transmission grating with high diffraction efficiency at the visiblespectral coverage is developed. Parameters optimization, manufacturing flow,technological parameters and controlling method are given, the result is satisfiedwith design requirements, though testing the angle and wavelength selectivity.
Fourth, as a specific application, integration design method of PGP is provided,and the software is developed with the functions of design, calculation and analysis.The influencing factors on diffraction characteristics of PGP are researched,including the structure parameters of prism and grating, the Bragg wavelengthshifting, and the index of the substrate. A PGP component with wide spectralcoverage from400nm to1000nm is designed, the diffraction efficiency is not less than50%. The method can realize PGP integration design and integration analysis.
引文
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