随机电磁光束时空域传输特性的一些研究
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摘要
相干性和偏振性是光束的两个重要特性,自从1994年James首先发现部分相干电磁光束在自由空间传播时其偏振度会发生变化以来,相干性和偏振性被认为是相互关联的。最近,Wolf提出用2×2阶交叉光谱密度矩阵来描写空间-频率域中的随机电磁光束,建立了表征部分相干部分偏振电磁光束相干性和偏振性的统一理论。随后,国内外的研究人员对随机电磁光束进行了大量的研究。部分相干、部分偏振的电磁光束被广泛的应用于非线性光学、大气激光光通信、惯性约束核聚变、光学成像等领域。本文在理论上研究了随机电磁光束在光学谐振腔中的传输特性,分析了光腔参数对光束相干、偏振、光谱特性的影响。从空间—时间域出发研究了随机电磁脉冲光束的时空耦合条件,分析了时空耦合特性对脉冲光束偏振特性的影响。具体各章内容为：
第一章,分别综述了激光光束传输变换理论的发展历史,部分相干光的研究背景,偏振光学理论的历史与进展。概述了本论文的研究目的、内容和创新点。
第二章,介绍了一些光传输理论基础：光传输的衍射理论,矩阵光学相关内容,部分相干光的张量处理方法,偏振光学理论。
第三章,利用张量的方法处理随机电磁光束在高斯型光学谐振腔中的传输问题。特别分析了光束在谐振腔内传输过程中的偏振度演化特性。结果显示偏振度的演化趋势不仅依赖于光束的初始参数,还依赖于光腔的结构参数。分析表明稳定腔和非稳腔内光束的偏振度演化趋势有很大区别。
第四章,基于Stokes参数与相干偏振统一理论的联系,分析了随机电磁光束的偏振态在高斯光腔中的演化特性,给出Stokes参数和偏振椭圆的表达式。结果显示偏振特性相关参数在传输过程呈现振荡还是呈现单调变化与光腔参数有关。此外,随着传输周期数N的增大,偏振特性在空间的横向分布将不再均匀,而是逐渐趋于高斯型。
第五章,研究了随机电磁光束的高斯型光腔内传输时光谱的演化特性。分析表明随机电磁光束在光腔中的频移特性主要取决于光束的初始偏振度和光腔参数。光束光谱在轴上点发生蓝移,轴外点发生红移。此外,分析得到了光束相对频移量与初始偏振度无关的条件。
第六章,提出了时空耦合的随机电磁脉冲光束模型,采用6×6阶矩阵对此脉冲光束进行描述,分析了脉冲光束产生时空耦合的条件。研究了时空耦合的随机电磁脉冲通过反射光栅后传输特性,结果表明脉冲光束的偏振度演化特性不仅依赖于光栅结构,而且由于时空耦合效应的存在,偏振度的演化与脉冲光束的时间空间特性有密切的联系。
Coherence and polarization are two important characteristics of optical beam. In1994, James first demonstrated that the degree of polarization of partially coherent optical beam would been varying when the beam propagating in free space. Since then, the coherence and polarization have been consider correlative. The2×2matrix of cross spectral density has been used to describe random electromagnetic beams(REMBs) in spatio-frequency domain by E. Wolf. The unified theory of coherence and polarization has been built. Then the research of REMBs has attracted people's widespread attention. The partially coherent and partially polarized beam has been widely applied in nonlinear optics, free-space optical communications, inertial confinement fusion by laser, and optical imaging. This thesis focuses on the studies on the propagation property of REMBs in optical resonator and the analysis of the affecting of REMBs'coherence, polarization and spectrum by resonator parameter. Furthermore, the condition of spatio-temporal coupling of random electromagnetic pulsed beams(REMPBs) has been studied in spatio-temporal domain. The affecting of polarized characteristic of pulsed beams by the spatio-temporal coupling is analyzed. The contents of this thesis are as follows:
In Chapter1, the history of light propagation and transformation theory, the background of the research on partially coherent light and the progresses in polarized light theory are reviewed. The purpose, main content and originality of this paper are presented.
In Chapter2, the basic theory of light propagation, such as theory optical diffraction, matrix optics, the tensor method of partially coherent optics and theory of polarized optics, are introduced.
In Chapter3, The interaction of an electromagnetic Gaussian Schell-model (EGSM) beam with a Gaussian cavity is analyzed. In particular, the evolution of the degree of polarization of the EGSM beam is investigated. The results show that the behavior of the degree of polarization depends on both the statistical properties of the source that generate the EGSM beam and on the parameters of the cavity.
In Chapter4, On the basis of the unified theory of coherence and polarization we investigate the behavior of the state of polarization of a stochastic electromagnetic beam in the Gaussian cavity. Both formulations in terms of Stokes parameters and in terms of polarization ellipse are given. We show that the state of polarization stabilizes, except in the case of a lossless cavity, after several passages between the mirrors and might exhibit monotonic or oscillatory behavior depending on the parameters of the resonator. We also find that an initially uniformly polarized beam remains non-uniformly polarized even for large number of passages between the mirrors of the cavity.
In Chapter5, Evolution of the spectral shift of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam in a Gaussian cavity is investigated in detail. It is shown that the spectral shift of the EGSM beam in a Gaussian cavity is mainly determined by the degree of polarization of the initial beam and the parameters of the cavity. The blue shift occurs at the on-axis point, while the red shift can occur at the off-axis points. The condition under which the relative spectral shift is independent of the degree of polarization of the initial beam is analyzed.
In Chapter6, Matrix optics is applied to a class of random, in time and space, electromagnetic pulsed beam-like (REMPB) radiation interacting with linear optical elements. A6x6order matrix describing transformation of a six-dimensional state vector including four spatial and two temporal positions within the field is used to derive conditions for spatio-temporal coupling. An example is included which deals with a spatio-temporal coupling in a typical REMPB on reflection from a reflecting grating. Electromagnetic nature of such interaction is explored via considering dependence of the degree of polarization of the reflected REMPB on its source and on the structure of the grating.
第一章,分别综述了激光光束传输变换理论的发展历史,部分相干光的研究背景,偏振光学理论的历史与进展。概述了本论文的研究目的、内容和创新点。
第二章,介绍了一些光传输理论基础：光传输的衍射理论,矩阵光学相关内容,部分相干光的张量处理方法,偏振光学理论。
第三章,利用张量的方法处理随机电磁光束在高斯型光学谐振腔中的传输问题。特别分析了光束在谐振腔内传输过程中的偏振度演化特性。结果显示偏振度的演化趋势不仅依赖于光束的初始参数,还依赖于光腔的结构参数。分析表明稳定腔和非稳腔内光束的偏振度演化趋势有很大区别。
第四章,基于Stokes参数与相干偏振统一理论的联系,分析了随机电磁光束的偏振态在高斯光腔中的演化特性,给出Stokes参数和偏振椭圆的表达式。结果显示偏振特性相关参数在传输过程呈现振荡还是呈现单调变化与光腔参数有关。此外,随着传输周期数N的增大,偏振特性在空间的横向分布将不再均匀,而是逐渐趋于高斯型。
第五章,研究了随机电磁光束的高斯型光腔内传输时光谱的演化特性。分析表明随机电磁光束在光腔中的频移特性主要取决于光束的初始偏振度和光腔参数。光束光谱在轴上点发生蓝移,轴外点发生红移。此外,分析得到了光束相对频移量与初始偏振度无关的条件。
第六章,提出了时空耦合的随机电磁脉冲光束模型,采用6×6阶矩阵对此脉冲光束进行描述,分析了脉冲光束产生时空耦合的条件。研究了时空耦合的随机电磁脉冲通过反射光栅后传输特性,结果表明脉冲光束的偏振度演化特性不仅依赖于光栅结构,而且由于时空耦合效应的存在,偏振度的演化与脉冲光束的时间空间特性有密切的联系。
Coherence and polarization are two important characteristics of optical beam. In1994, James first demonstrated that the degree of polarization of partially coherent optical beam would been varying when the beam propagating in free space. Since then, the coherence and polarization have been consider correlative. The2×2matrix of cross spectral density has been used to describe random electromagnetic beams(REMBs) in spatio-frequency domain by E. Wolf. The unified theory of coherence and polarization has been built. Then the research of REMBs has attracted people's widespread attention. The partially coherent and partially polarized beam has been widely applied in nonlinear optics, free-space optical communications, inertial confinement fusion by laser, and optical imaging. This thesis focuses on the studies on the propagation property of REMBs in optical resonator and the analysis of the affecting of REMBs'coherence, polarization and spectrum by resonator parameter. Furthermore, the condition of spatio-temporal coupling of random electromagnetic pulsed beams(REMPBs) has been studied in spatio-temporal domain. The affecting of polarized characteristic of pulsed beams by the spatio-temporal coupling is analyzed. The contents of this thesis are as follows:
In Chapter1, the history of light propagation and transformation theory, the background of the research on partially coherent light and the progresses in polarized light theory are reviewed. The purpose, main content and originality of this paper are presented.
In Chapter2, the basic theory of light propagation, such as theory optical diffraction, matrix optics, the tensor method of partially coherent optics and theory of polarized optics, are introduced.
In Chapter3, The interaction of an electromagnetic Gaussian Schell-model (EGSM) beam with a Gaussian cavity is analyzed. In particular, the evolution of the degree of polarization of the EGSM beam is investigated. The results show that the behavior of the degree of polarization depends on both the statistical properties of the source that generate the EGSM beam and on the parameters of the cavity.
In Chapter4, On the basis of the unified theory of coherence and polarization we investigate the behavior of the state of polarization of a stochastic electromagnetic beam in the Gaussian cavity. Both formulations in terms of Stokes parameters and in terms of polarization ellipse are given. We show that the state of polarization stabilizes, except in the case of a lossless cavity, after several passages between the mirrors and might exhibit monotonic or oscillatory behavior depending on the parameters of the resonator. We also find that an initially uniformly polarized beam remains non-uniformly polarized even for large number of passages between the mirrors of the cavity.
In Chapter5, Evolution of the spectral shift of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam in a Gaussian cavity is investigated in detail. It is shown that the spectral shift of the EGSM beam in a Gaussian cavity is mainly determined by the degree of polarization of the initial beam and the parameters of the cavity. The blue shift occurs at the on-axis point, while the red shift can occur at the off-axis points. The condition under which the relative spectral shift is independent of the degree of polarization of the initial beam is analyzed.
In Chapter6, Matrix optics is applied to a class of random, in time and space, electromagnetic pulsed beam-like (REMPB) radiation interacting with linear optical elements. A6x6order matrix describing transformation of a six-dimensional state vector including four spatial and two temporal positions within the field is used to derive conditions for spatio-temporal coupling. An example is included which deals with a spatio-temporal coupling in a typical REMPB on reflection from a reflecting grating. Electromagnetic nature of such interaction is explored via considering dependence of the degree of polarization of the reflected REMPB on its source and on the structure of the grating.
引文
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6-5. O. Korotkova and E. Wolf, "Effects of linear non-image forming devices on coherence and polarization properties of random electromagnetic beams. Part II. Examples", J. Mod. Opt.52,2673-2685 (2005).
6-6. Q. Lin and Y. Cai, "Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams," Opt. Lett.27,216-218 (2002).
6-7. M. Yao, Y. Cai, H. T. Eyyuboglu, Y. Baykal, and O. Korotkova, "The evolution of the degree of polarization of an electromagnetic Gaussian Schell-model beam in a Gaussian cavity," Opt. Lett.33,2266-2268 (2008).
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