用于激光光束整形的衍射光学元件设计
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摘要
近年来,激光技术已经广泛应用到工业、农业、医药卫生、国防和科学研究等国民经济各个领域,目前已经很难找到不应用激光技术的领域和部门了。然而激光光束的某些特性使得它的进一步广泛应用受到了限制。例如:激光束的光强呈高斯分布而不是均匀分布,它的传播路径是双曲线而不是直线,这些特性在某种程度上限制了它的应用。为了扩展激光的应用领域,提高激光技术的应用水平,就需要对激光束进行整形,以适应不同场合的要求。
衍射光学元件具有体积小、重量轻、易复制、造价低、衍射效率高、设计自由度多、材料可选性宽、色散性能独特等优点,并能实现传统光学器件难以完成的微小、阵列、集成及任意波面变换等新功能,在激光光束整形方面有着广泛的应用前景。
本文详细论述了用于激光光束整形的衍射光学元件设计基础理论和优化算法,并围绕三种设计模型,即标量模型、矢量模型和光线模型对衍射光学元件的优化设计展开深入研究,重点开展了基于标量模型的优化算法改进,基于矢量模型的亚波长衍射光学元件优化设计以及基于光线模型,借助ZEMAX软件设计模拟圆锥镜光学特性的透镜圆锥镜和实现长焦深、小焦斑的衍射光学元件等研究工作。具体内容包括:
1.基于标量设计模型,提出了GSGA混合算法、平滑修正法和模糊控制迭代算法设计用于光束整形的衍射光学元件,计算机设计结果表明了这些算法的有效性。特别是模糊控制迭代算法,它将模糊控制理论应用到衍射光学元件的设计中,通过模糊决策智能地选择优化路径,从而基本克服了算法易陷入局部最优的问题。
2.对具有非周期结构的亚波长衍射光学元件设计展开研究。基于Mansuripur的矢量衍射模型,提出矢量模糊控制迭代算法设计用于光束整形的亚波长衍射光学元件。通过对设计结果的分析、比较、讨论以及借助时域有限差分法的进一步分析,验证了方法的有效性。而且,针对Mansuripur矢量衍射模型中某些假设条件过于主观,提出了改进方案。重新推导衍射公式,建立改进的矢量模型,并基于改进模型设计了亚波长衍射元件。
3.在光线理论模型的基础上,采用ZEMAX软件对模拟圆锥镜光学特性的透镜圆锥镜和实现长焦深、小焦斑的衍射光学元件设计展开研究。通过合理设计目标函数,编写所需的外部扩展程序,并借助软件自身的优化能力完成了元件的设计任务,在设计过程中,为了平衡轴上光强分布均匀和主光斑大小不变这两个不兼容的条件,提出了加权的方法设计目标函数,取得了别人满意的设计结果。
Recently, laser technology has been widely applied in many fields, such as industry, agriculture, medical and health, national defense, and scientific research. It is difficult to find a field which is not connected with the laser technology. However, some properties of laser beams limit its further application. For example, its intensity distribution is Gaussian profile, not uniform one. And propagation path is hyperbolic line, not straight line. In order to extend the application field and improve application level of laser technology, it is very necessary to shape laser beams for meeting the demands of different occasions.
Diffractive optical elements have many advantages, such as small size, light weight, replicating easily, low cost, high diffraction efficiency, many design variables, wide range of optional materials, peculiar chromatic dispersion performances, and so on. Therefore they can implement some new functions, for example microminiatrue, array, integration and arbitrary wave transformation, which are difficult for traditional optical elements to realize. Diffractive optical elements have wide application prospect in laser beam shaping.
Design methods of diffractive optical elements for beam shaping are investigated in this dissertation, which mainly include the improvement of algorithms based on scalar model, the design of sub-wavelength diffractive optical elements based on vector model, and the design of lens axicon for simulating the axicon performance and diffractive optical elements for achieving long depth of focus and small spot by ZEMAX. The main works contained in this dissertation are as follows:
1. The GSGA hybrid algorithm, the profile-smoothing algorithm, and fuzzy control iterative algorithm are proposed for designing diffractive optical elements for laser beam shaping in the scalar domain. Computer-designed results show the validity of those algorithms. Especially fuzzy control iterative algorithm, applying the fuzzy control theory to design DOE, can intellectively choose the optimization path by fuzzy decision, which will enable it to avoid being trapped into local optimum solution.
2. The design of finite aperture aperiodic sub-wavelength DOEs is studied. Based on Mansuripur's vector diffractive model, vector fuzzy control iterative algorithm is put forward for the designing of sub-wavelength DOEs for beam shaping. To validate the method, the design results are discussed and the FDTD is further used. Moreover, because the assumption in the Mansuripur's model is somewhat subject, an improved scheme is proposed. The updated vector diffraction formula is deduced, a revised model is built and a sub-wavelength diffractive optical element is designed.
3. Base on the ray model, the lens axicon for stimulating axicon performance and diffractive optical elements with long depth of focus and small spot are designed by ZEMAX. The design works are achieved by rationally designing object function, editing the extend programs and depending on the optimization ability of ZEMAX. In the process of design, in order to trade-off the uniform distribution of light intensity on the axis and the spot keeping unchanged, a weighted method of designing object function is proposed, which makes the results more desirable.
衍射光学元件具有体积小、重量轻、易复制、造价低、衍射效率高、设计自由度多、材料可选性宽、色散性能独特等优点,并能实现传统光学器件难以完成的微小、阵列、集成及任意波面变换等新功能,在激光光束整形方面有着广泛的应用前景。
本文详细论述了用于激光光束整形的衍射光学元件设计基础理论和优化算法,并围绕三种设计模型,即标量模型、矢量模型和光线模型对衍射光学元件的优化设计展开深入研究,重点开展了基于标量模型的优化算法改进,基于矢量模型的亚波长衍射光学元件优化设计以及基于光线模型,借助ZEMAX软件设计模拟圆锥镜光学特性的透镜圆锥镜和实现长焦深、小焦斑的衍射光学元件等研究工作。具体内容包括:
1.基于标量设计模型,提出了GSGA混合算法、平滑修正法和模糊控制迭代算法设计用于光束整形的衍射光学元件,计算机设计结果表明了这些算法的有效性。特别是模糊控制迭代算法,它将模糊控制理论应用到衍射光学元件的设计中,通过模糊决策智能地选择优化路径,从而基本克服了算法易陷入局部最优的问题。
2.对具有非周期结构的亚波长衍射光学元件设计展开研究。基于Mansuripur的矢量衍射模型,提出矢量模糊控制迭代算法设计用于光束整形的亚波长衍射光学元件。通过对设计结果的分析、比较、讨论以及借助时域有限差分法的进一步分析,验证了方法的有效性。而且,针对Mansuripur矢量衍射模型中某些假设条件过于主观,提出了改进方案。重新推导衍射公式,建立改进的矢量模型,并基于改进模型设计了亚波长衍射元件。
3.在光线理论模型的基础上,采用ZEMAX软件对模拟圆锥镜光学特性的透镜圆锥镜和实现长焦深、小焦斑的衍射光学元件设计展开研究。通过合理设计目标函数,编写所需的外部扩展程序,并借助软件自身的优化能力完成了元件的设计任务,在设计过程中,为了平衡轴上光强分布均匀和主光斑大小不变这两个不兼容的条件,提出了加权的方法设计目标函数,取得了别人满意的设计结果。
Recently, laser technology has been widely applied in many fields, such as industry, agriculture, medical and health, national defense, and scientific research. It is difficult to find a field which is not connected with the laser technology. However, some properties of laser beams limit its further application. For example, its intensity distribution is Gaussian profile, not uniform one. And propagation path is hyperbolic line, not straight line. In order to extend the application field and improve application level of laser technology, it is very necessary to shape laser beams for meeting the demands of different occasions.
Diffractive optical elements have many advantages, such as small size, light weight, replicating easily, low cost, high diffraction efficiency, many design variables, wide range of optional materials, peculiar chromatic dispersion performances, and so on. Therefore they can implement some new functions, for example microminiatrue, array, integration and arbitrary wave transformation, which are difficult for traditional optical elements to realize. Diffractive optical elements have wide application prospect in laser beam shaping.
Design methods of diffractive optical elements for beam shaping are investigated in this dissertation, which mainly include the improvement of algorithms based on scalar model, the design of sub-wavelength diffractive optical elements based on vector model, and the design of lens axicon for simulating the axicon performance and diffractive optical elements for achieving long depth of focus and small spot by ZEMAX. The main works contained in this dissertation are as follows:
1. The GSGA hybrid algorithm, the profile-smoothing algorithm, and fuzzy control iterative algorithm are proposed for designing diffractive optical elements for laser beam shaping in the scalar domain. Computer-designed results show the validity of those algorithms. Especially fuzzy control iterative algorithm, applying the fuzzy control theory to design DOE, can intellectively choose the optimization path by fuzzy decision, which will enable it to avoid being trapped into local optimum solution.
2. The design of finite aperture aperiodic sub-wavelength DOEs is studied. Based on Mansuripur's vector diffractive model, vector fuzzy control iterative algorithm is put forward for the designing of sub-wavelength DOEs for beam shaping. To validate the method, the design results are discussed and the FDTD is further used. Moreover, because the assumption in the Mansuripur's model is somewhat subject, an improved scheme is proposed. The updated vector diffraction formula is deduced, a revised model is built and a sub-wavelength diffractive optical element is designed.
3. Base on the ray model, the lens axicon for stimulating axicon performance and diffractive optical elements with long depth of focus and small spot are designed by ZEMAX. The design works are achieved by rationally designing object function, editing the extend programs and depending on the optimization ability of ZEMAX. In the process of design, in order to trade-off the uniform distribution of light intensity on the axis and the spot keeping unchanged, a weighted method of designing object function is proposed, which makes the results more desirable.
引文
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