透射光束的Goos-H(?)nchen效应及其机制
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摘要
GH(Goos-H?nchen)效应这个传统的问题近些年来受到学术界的广泛关注,一方面是受超光速问题研究的推动,另一方面是这个效应在光学传感、光开关和集成光学等微光学领域具有潜在的应用。我们知道,传统意义上的GH效应是指在电介质界面上的全反射光束相对于几何反射光束在侧向上的一个微小的位移,通常认为它与光疏介质中的倏逝场密切相关。最近的研究工作表明,在不涉及倏逝场的电介质板透射过程中也会产生GH位移,并且这个位移还可以是反向的。本文研究的目的旨在揭示透射GH位移的机制,并在实验上测量这个位移。
论文第一部分为绪论。首先简单介绍了国内外对于GH效应研究的历史和现状。其次介绍了GH位移理论分析的两种常用方法——稳态相位法和能流法,同时列举了GH位移的实验测量及应用。最后阐述了本论文研究的主要内容。
论文第二部分首先利用透射系数的一阶近似(稳态相位理论)研究了有限光束穿过空气中薄介质板后透射光束的GH位移,发现其具有共振增强效应,给出了该位移取负值时光束入射角及介质板的厚度所需满足的必要条件。其次利用透射系数的二阶近似发现了实际透射光束存在GH位移、角偏转、束腰宽度的修正及焦点的纵向移动这四种非几何光学效应,并且GH位移和角偏转依赖于光束的束腰宽度。接着我们对高斯光束穿过介质板后的GH位移进行了数值模拟,其结果与稳态相位理论结果十分吻合。最后利用微波实验装置首次观测到了穿过薄介质板后透射微波束的反向GH位移,并且实验结果与理论结果吻合得很好。
论文第三部分对有限光束穿过薄介质板后透射光束GH位移的机制给出了一种物理解释,即有限光束在薄介质板中会经历多次反射,实际透射光束的GH位移正是来源于介质板中经多次反射后所形成的各个出射光束在出射端的相干叠加,所以透射光束的GH位移来源于光束的重构,而不是透射光束形变的结果。其次在数学和物理上给出了透射光束不产生形变时对光束入射角以及薄介质板厚度的限制条件。最后利用高斯型入射光束对透射光束的重构进行了数值分析,结果表明:在满足上述限制条件的情况下,重构的实际透射光束可产生反向的GH位移;当不满足上述限制条件时,重构的实际透射光束与几何透射光束相比会产生严重的形变,所以此时再讨论透射光束的GH位移已经没有意义了。本部分内容为研究有限光束在微结构中的透射现象提供了理论依据。
论文第四部分首先利用传输矩阵法计算了有限光束穿过周期性多层结构后的透射系数,随后利用稳态相位理论研究了有限光束穿过周期性多层结构后透射光束的GH位移和透射率,并以折射率分布为( n1 n2)5n1的11层膜系为例进行了详细分析。结果表明:透射光束的GH位移依赖于周期性结构的有效厚度、介质折射率以及光束入射角,并且在由常规材料所组成的周期性结构中,该位移可正可负,同时具有共振增强效应,数值可达入射波长的几十倍。在特定条件下,此种周期性多层结构将对入射的各种偏振光实现全角全透射。最后我们利用高斯光束进行了数值模拟,结果表明由稳态相位法所得到的近似结果对于实际光束是有效的。本部分内容是单层膜结构到多层膜结构的推广。
论文第五部分是总结与展望。首先概述了本论文的主要研究内容与成果,其次结合当前的研究热点指出下一步的研究方向。
The fundamental topic of the GH (Goos-H?nchen) effect has attracted increasing interest recent years because of two important aspects. On the one hand, the GH effect can be analogous to the tunneling delay in research of superluminal phenomenon which is the controversial issue of the frontiers; on the other hand, the GH effect is claimed to be applicable to optical microstructure such as optical sensors, optical switches, and integrated optics devices. However, the conventional concept of the GH effect simply refers to the small lateral displacement of the totally reflected beam at a dielectric interface from the position predicted by geometrical reflection, and is considered closely related to the evanescent field in the optical less dense medium. Our recent work has demonstrated that the GH displacement will also take place when a beam transmits through a thin dielectric slab. This GH displacement can be negative as well as positive and has no concern with the evanescent field. The aim of this Ph. D. dissertation is to investigate the properties and mechanism of the transmission GH displacement and to perform experimental measurements of the displacement. The main contents involved in this dissertation are as follows:
The first chapter is the introduction. Firstly, the history and current researches on GH effect are briefly reviewed. Secondly, the main two approaches employed to discuss the GH displacement theoretically are introduced as the stationary phase approach and the energy-flux approach, respectively. We illustrate the experimental measurements about the GH displacement and its applications. Lastly, the primary contents discussed in this dissertation are stressed.
In the second chapter, we first investigate the GH displacement of a light beam transmitting through a thin dielectric slab in vacuum by the first-order approximation of the transmission coefficient, i.e., the stationary phase approach. It is shown that the GH displacement can be resonantly enhanced. Necessary conditions for the displacement to be backward are advanced by considering the restrictions on the incidence angle and the slab thickness. Secondly, with the help of the second-order approximation of the transmission coefficient, we find that the actual transmitted light beam undergoes four non-geometrical effects, including GH displacement, angular deflection, width modification and longitudinal focal shift when compared with the results predicted by geometrical optics. The GH displacement and the angular deflection are shown to be dependent on the width of the beam waist. Thirdly, numerical simulations of the GH displacement for a Gaussian-shaped light beam transmitting through the dielectric slab are performed. The numerical results agree well with the theoretical ones. Lastly, we made experiments to observe the backward (negative) GH displacement of the microwave beam transmitting through thin slabs. The experimental results are in good agreement with the theoretical ones.
In the third chapter, firstly, we give a physical explanation for the mechanism of the GH displacement of a light beam transmitting through a thin dielectric slab configuration. From the view of the multiple reflections inside the slab, we find that the actual transmitted beam with the GH displacement originates from the coherent interference between the successive transmitted constituents that arise from the multiple reflections inside the slab. We conclude that the GH displacement of the transmitted beam is produced by the mechanism of reshaping, rather than the distortion of the transmitted beam. Secondly, the physical restriction on the incidence angle and thickness of the slab for the transmitted beam maintaining well the shape of the incident beam is advanced mathematically. Lastly, numerical analysis of the reshaping of the transmitted beam has been given by Gaussian-shaped incident beam. It is shown that we can obtain the reshaping actual transmitted beam with negative displacement when the restriction conditions are satisfied; otherwise, it is meaningless to discuss the displacement of the transmitted beam due to the serve distortion of the beam profile. The problems investigated in this chapter form the theoretical basis of the discussion on the beam transmitting through optical microstructures.
In the fourth chapter, at first, we work out the transmission coefficient of a light beam transmitting through the periodic multiple layer structure by transfer matrix approach, and consequently we investigate the transmittivity and the GH displacement of the transmitted beam by stationary phase approach. As an example, we give a detail analysis on an 11 layer structure with the refractive index in the form of ( n1 n2)5n1. We find that the GH displacement of the transmitted beam is dependent on the effective thickness of the periodic configuration, the refractive index of the medium and the incidence angle of the light beam. It is shown that the displacement can be negative as well as positive in the periodic configuration made up of general materials. The magnitude of the displacement can be of one or two orders of wavelength at transmission resonance. Under specific conditions, such periodic multiple layer structure permits omnidirectional total transmission for incident light with all kinds of polarization states. At last, the numerical simulations for Gaussian-shaped beam are made to demonstrate the validity of the stationary phase approach. The contents discussed here can be identified as the generalization of the discussion from the single layer structure to multiple layer structure.
In the last chapter, I summarize the main contents and achievements in the dissertation with brief discussions on further research direction.
论文第一部分为绪论。首先简单介绍了国内外对于GH效应研究的历史和现状。其次介绍了GH位移理论分析的两种常用方法——稳态相位法和能流法,同时列举了GH位移的实验测量及应用。最后阐述了本论文研究的主要内容。
论文第二部分首先利用透射系数的一阶近似(稳态相位理论)研究了有限光束穿过空气中薄介质板后透射光束的GH位移,发现其具有共振增强效应,给出了该位移取负值时光束入射角及介质板的厚度所需满足的必要条件。其次利用透射系数的二阶近似发现了实际透射光束存在GH位移、角偏转、束腰宽度的修正及焦点的纵向移动这四种非几何光学效应,并且GH位移和角偏转依赖于光束的束腰宽度。接着我们对高斯光束穿过介质板后的GH位移进行了数值模拟,其结果与稳态相位理论结果十分吻合。最后利用微波实验装置首次观测到了穿过薄介质板后透射微波束的反向GH位移,并且实验结果与理论结果吻合得很好。
论文第三部分对有限光束穿过薄介质板后透射光束GH位移的机制给出了一种物理解释,即有限光束在薄介质板中会经历多次反射,实际透射光束的GH位移正是来源于介质板中经多次反射后所形成的各个出射光束在出射端的相干叠加,所以透射光束的GH位移来源于光束的重构,而不是透射光束形变的结果。其次在数学和物理上给出了透射光束不产生形变时对光束入射角以及薄介质板厚度的限制条件。最后利用高斯型入射光束对透射光束的重构进行了数值分析,结果表明:在满足上述限制条件的情况下,重构的实际透射光束可产生反向的GH位移;当不满足上述限制条件时,重构的实际透射光束与几何透射光束相比会产生严重的形变,所以此时再讨论透射光束的GH位移已经没有意义了。本部分内容为研究有限光束在微结构中的透射现象提供了理论依据。
论文第四部分首先利用传输矩阵法计算了有限光束穿过周期性多层结构后的透射系数,随后利用稳态相位理论研究了有限光束穿过周期性多层结构后透射光束的GH位移和透射率,并以折射率分布为( n1 n2)5n1的11层膜系为例进行了详细分析。结果表明:透射光束的GH位移依赖于周期性结构的有效厚度、介质折射率以及光束入射角,并且在由常规材料所组成的周期性结构中,该位移可正可负,同时具有共振增强效应,数值可达入射波长的几十倍。在特定条件下,此种周期性多层结构将对入射的各种偏振光实现全角全透射。最后我们利用高斯光束进行了数值模拟,结果表明由稳态相位法所得到的近似结果对于实际光束是有效的。本部分内容是单层膜结构到多层膜结构的推广。
论文第五部分是总结与展望。首先概述了本论文的主要研究内容与成果,其次结合当前的研究热点指出下一步的研究方向。
The fundamental topic of the GH (Goos-H?nchen) effect has attracted increasing interest recent years because of two important aspects. On the one hand, the GH effect can be analogous to the tunneling delay in research of superluminal phenomenon which is the controversial issue of the frontiers; on the other hand, the GH effect is claimed to be applicable to optical microstructure such as optical sensors, optical switches, and integrated optics devices. However, the conventional concept of the GH effect simply refers to the small lateral displacement of the totally reflected beam at a dielectric interface from the position predicted by geometrical reflection, and is considered closely related to the evanescent field in the optical less dense medium. Our recent work has demonstrated that the GH displacement will also take place when a beam transmits through a thin dielectric slab. This GH displacement can be negative as well as positive and has no concern with the evanescent field. The aim of this Ph. D. dissertation is to investigate the properties and mechanism of the transmission GH displacement and to perform experimental measurements of the displacement. The main contents involved in this dissertation are as follows:
The first chapter is the introduction. Firstly, the history and current researches on GH effect are briefly reviewed. Secondly, the main two approaches employed to discuss the GH displacement theoretically are introduced as the stationary phase approach and the energy-flux approach, respectively. We illustrate the experimental measurements about the GH displacement and its applications. Lastly, the primary contents discussed in this dissertation are stressed.
In the second chapter, we first investigate the GH displacement of a light beam transmitting through a thin dielectric slab in vacuum by the first-order approximation of the transmission coefficient, i.e., the stationary phase approach. It is shown that the GH displacement can be resonantly enhanced. Necessary conditions for the displacement to be backward are advanced by considering the restrictions on the incidence angle and the slab thickness. Secondly, with the help of the second-order approximation of the transmission coefficient, we find that the actual transmitted light beam undergoes four non-geometrical effects, including GH displacement, angular deflection, width modification and longitudinal focal shift when compared with the results predicted by geometrical optics. The GH displacement and the angular deflection are shown to be dependent on the width of the beam waist. Thirdly, numerical simulations of the GH displacement for a Gaussian-shaped light beam transmitting through the dielectric slab are performed. The numerical results agree well with the theoretical ones. Lastly, we made experiments to observe the backward (negative) GH displacement of the microwave beam transmitting through thin slabs. The experimental results are in good agreement with the theoretical ones.
In the third chapter, firstly, we give a physical explanation for the mechanism of the GH displacement of a light beam transmitting through a thin dielectric slab configuration. From the view of the multiple reflections inside the slab, we find that the actual transmitted beam with the GH displacement originates from the coherent interference between the successive transmitted constituents that arise from the multiple reflections inside the slab. We conclude that the GH displacement of the transmitted beam is produced by the mechanism of reshaping, rather than the distortion of the transmitted beam. Secondly, the physical restriction on the incidence angle and thickness of the slab for the transmitted beam maintaining well the shape of the incident beam is advanced mathematically. Lastly, numerical analysis of the reshaping of the transmitted beam has been given by Gaussian-shaped incident beam. It is shown that we can obtain the reshaping actual transmitted beam with negative displacement when the restriction conditions are satisfied; otherwise, it is meaningless to discuss the displacement of the transmitted beam due to the serve distortion of the beam profile. The problems investigated in this chapter form the theoretical basis of the discussion on the beam transmitting through optical microstructures.
In the fourth chapter, at first, we work out the transmission coefficient of a light beam transmitting through the periodic multiple layer structure by transfer matrix approach, and consequently we investigate the transmittivity and the GH displacement of the transmitted beam by stationary phase approach. As an example, we give a detail analysis on an 11 layer structure with the refractive index in the form of ( n1 n2)5n1. We find that the GH displacement of the transmitted beam is dependent on the effective thickness of the periodic configuration, the refractive index of the medium and the incidence angle of the light beam. It is shown that the displacement can be negative as well as positive in the periodic configuration made up of general materials. The magnitude of the displacement can be of one or two orders of wavelength at transmission resonance. Under specific conditions, such periodic multiple layer structure permits omnidirectional total transmission for incident light with all kinds of polarization states. At last, the numerical simulations for Gaussian-shaped beam are made to demonstrate the validity of the stationary phase approach. The contents discussed here can be identified as the generalization of the discussion from the single layer structure to multiple layer structure.
In the last chapter, I summarize the main contents and achievements in the dissertation with brief discussions on further research direction.
引文
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