基于张量方法研究部分相干光和部分偏振光在大气湍流中的传输特性
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摘要
光场的相干、偏振和光谱特性是现代光学的重要研究内容,对现代光学理论和激光技术的发展具有重要意义。本论文采用简便有效的张量方法避免了大量耗时的积分运算,从部分相干光在大气湍流中的传输理论出发,深入研究了部分相干光和部分偏振的电磁光束在大气湍流中的传输特性和光谱变化。具体研究内容与成果归纳如下：
(1)基于空间-频率域中的交叉谱密度函数传输理论,研究了扭曲的各向异性的高斯-谢尔模型(TAGSM)光束和椭圆高斯光束(EGB)在大气湍流中传输时的频谱移动特性。通过数值计算和理论分析表明：不满足“定标律”的光束在大气湍流中传输时的频谱移动是由于光束的相干诱导和大气湍流共同作用引起的；通过调控光源的扭曲参数、相干特性以及光斑大小,可以调制光束在大气湍流种传输时的频谱移动大小以及光谱跃迁位置。所得结论对光谱实验和高精度光谱测量具有理论参考价值。部分相干光通过大气湍流中的光谱变化可望在光互连、光通信等方面获得应用。
从工程应用角度考虑,研究了TAGSM光束的光束参数、离轴TAGSM光束的离轴参数在大气湍流中传输时的变换规律以及具有各种对称形状的部分相干的空心光束(DHB)在大气湍流中的传输变换特性。
(2)推导了相干合成和非相干合成的径向分布的部分相干平顶光束(FTB)阵列在大气湍流中的传输时的张量形式的解析表达式,并研究了阵列光束的光强和复相干度模的分布。研究表明：大气湍流和光束阵列的单元光束之间的相关性是影响光束阵列传输特性的两大因素；由于大气湍流的影响,阵列光束远距离传输后退化为高斯光束,复相干度模的分布起始于高斯分布,终止于高斯分布,空间相干性会随着传输距离的增大变差。所得结论对部分空间相干光阵列的大气传输相关工作有实际应用意义。
(3)基于各向异性的随机电磁高斯-谢尔模型(EGSM)光束,提出了具有扭曲特性的各向异性的随机电磁高斯-谢尔模型(ETAGSM)光束的数学-物理模型,基于部分相干偏振统一理论研究了有无光阑限制的随机电磁光束在大气湍流中传输的光谱特性。研究发现：近距离传输时,主要受到光阑衍射的作用,远距离处主要受大气湍流的作用；通过调制光阑孔径参数、光源扭曲参数以及光源相干性参数等可以调制ETAGSM光束在大气湍流中传输时的光谱特性的分布情况。
本文通过理论分析所得的研究成果对探索和研究部分相干光和部分偏振光在激光空间技术中的应用具有重要的理论及应用价值。研究激光在大气湍流中传输特性,在激光雷达、激光制导、激光通讯等应用领域具有重要意义。
The coherence, polarization and spectral properties of light field are main topics in the laser optics, which play an important role in development of the modern optics theory and laser technologies. Starting from the propagation law of partially coherent light, I present in this dissertation the research results on the propagation and the spectral characteristics of the partially coherent light and the partially coherent partially polarized light propagating in turbulent atmosphere by use of convenient and effective tensor method. The main works of this paper are lasted as follows:
(1)Start from the propagation law of the cross-spectral density function in the space-frequency domain, the spectral changes of the partially coherent twist anisotropic Gaussian-Schell model(TAGSM) beam and elliptical Gaussian beam(EGB) propagating in turbulent atmosphere are investigated. Nummerical calculations and analysis shows that: the spectral changes of pratially coherent beam which dosen't follow "the scalling low" propagating in turbulent atmosphere are induced by the coherence of the source beam and the diffraction of the turbulent atmosphere; we can modulate the value of the relative spectral changes and the spectral switch through modulating the degree of twist property, the coherence, the spot width of partially coherent beams. The results obtained in this paper would be useful for spectral experiments and the high-precision spectral measurements. The spectral changes of partially coherent beams propagating in turbulent atmosphere would be hopefully applied to the optical interconnection and optical communication, etc.
Takeing into the consideration of the technology application, the propagation properties of the beams parameters of TAGSM beam, the decentered parameter of decentered TAGSM beam and partially coherent dark hollow beams(DHBs) propagating in turbulent atmosphere have been investigated.
(2)Analytical expressions of the radial partially coherent flat-topped beam (FTB) array propagating in turbulent atmosphere are derived firstly, where the correlated superposition and uncorrelated superposition are considered. Detailed numerical calculations illustrate the distribution of normalized average intensity and the the modulus of the complex degree of coherence of radial FTB array propagating in turbulent atmosphere. It is shown that the atmospheric turbulence and the correlation of each beamlet are two main factors which affect the propagation of array beams. Because of the influence of the turbulent atmosphere, the normalized average intensity distribution of the correlated and uncorrelated case propagating in turbulent atmosphere tends to Gaussian shape;the distribution of the modulus of the complex degree of coherence of radial FTB array beam starts and ends as Gaussian distribution which resembles the average intensity profile. The spatial coherence of correlated or uncorrelated radial FTB array becomes worse with increasing z in turbulent atmosphere. The results obtained would be useful for partially coherent array beam propagating in atmosphere.
(3) Based on the isotropic electromagnetic Gaussian-Schell model beam, we introduced the mathematical physics model of stochastic electromagnetic twist anisotropic Gaussian-Schell model (ETAGSM) beam by use of the tensor method. Based on the unified theory of coherence and polariziation, the analytical propagation expressions for the cross-spectral density matrix of ETAGSM beams with aperture or not propagating in turbulent atmosphere are derived, which permits us to study the spectral properties of ETAGSM beams with aperture or not. Detailed numerical caculations show that:the affection of the aperture on the spectral properties of the stochastic ETAGSM beam is obvious in the near field; while in the far field, the atmospheric turbulence plays an important role; we can modulate the distribution the spectral degree of polarization of stochastic ETAGSM beams propagating in turbulent atmosphere through modulating the parameters of aperture, the twist property and the coherence of the source beams.
The results obtained in this paper would be useful for studying the propagation of partially coherent beams and partially polarized beam propagating through turbulent atmosphere. This thesis emphasizes on the research of the theory and of the laser beam propagation in the atmosphere, which experiments are of great importance in the areas of laser radar, laser missile-guidance and communication etc.
(1)基于空间-频率域中的交叉谱密度函数传输理论,研究了扭曲的各向异性的高斯-谢尔模型(TAGSM)光束和椭圆高斯光束(EGB)在大气湍流中传输时的频谱移动特性。通过数值计算和理论分析表明：不满足“定标律”的光束在大气湍流中传输时的频谱移动是由于光束的相干诱导和大气湍流共同作用引起的；通过调控光源的扭曲参数、相干特性以及光斑大小,可以调制光束在大气湍流种传输时的频谱移动大小以及光谱跃迁位置。所得结论对光谱实验和高精度光谱测量具有理论参考价值。部分相干光通过大气湍流中的光谱变化可望在光互连、光通信等方面获得应用。
从工程应用角度考虑,研究了TAGSM光束的光束参数、离轴TAGSM光束的离轴参数在大气湍流中传输时的变换规律以及具有各种对称形状的部分相干的空心光束(DHB)在大气湍流中的传输变换特性。
(2)推导了相干合成和非相干合成的径向分布的部分相干平顶光束(FTB)阵列在大气湍流中的传输时的张量形式的解析表达式,并研究了阵列光束的光强和复相干度模的分布。研究表明：大气湍流和光束阵列的单元光束之间的相关性是影响光束阵列传输特性的两大因素；由于大气湍流的影响,阵列光束远距离传输后退化为高斯光束,复相干度模的分布起始于高斯分布,终止于高斯分布,空间相干性会随着传输距离的增大变差。所得结论对部分空间相干光阵列的大气传输相关工作有实际应用意义。
(3)基于各向异性的随机电磁高斯-谢尔模型(EGSM)光束,提出了具有扭曲特性的各向异性的随机电磁高斯-谢尔模型(ETAGSM)光束的数学-物理模型,基于部分相干偏振统一理论研究了有无光阑限制的随机电磁光束在大气湍流中传输的光谱特性。研究发现：近距离传输时,主要受到光阑衍射的作用,远距离处主要受大气湍流的作用；通过调制光阑孔径参数、光源扭曲参数以及光源相干性参数等可以调制ETAGSM光束在大气湍流中传输时的光谱特性的分布情况。
本文通过理论分析所得的研究成果对探索和研究部分相干光和部分偏振光在激光空间技术中的应用具有重要的理论及应用价值。研究激光在大气湍流中传输特性,在激光雷达、激光制导、激光通讯等应用领域具有重要意义。
The coherence, polarization and spectral properties of light field are main topics in the laser optics, which play an important role in development of the modern optics theory and laser technologies. Starting from the propagation law of partially coherent light, I present in this dissertation the research results on the propagation and the spectral characteristics of the partially coherent light and the partially coherent partially polarized light propagating in turbulent atmosphere by use of convenient and effective tensor method. The main works of this paper are lasted as follows:
(1)Start from the propagation law of the cross-spectral density function in the space-frequency domain, the spectral changes of the partially coherent twist anisotropic Gaussian-Schell model(TAGSM) beam and elliptical Gaussian beam(EGB) propagating in turbulent atmosphere are investigated. Nummerical calculations and analysis shows that: the spectral changes of pratially coherent beam which dosen't follow "the scalling low" propagating in turbulent atmosphere are induced by the coherence of the source beam and the diffraction of the turbulent atmosphere; we can modulate the value of the relative spectral changes and the spectral switch through modulating the degree of twist property, the coherence, the spot width of partially coherent beams. The results obtained in this paper would be useful for spectral experiments and the high-precision spectral measurements. The spectral changes of partially coherent beams propagating in turbulent atmosphere would be hopefully applied to the optical interconnection and optical communication, etc.
Takeing into the consideration of the technology application, the propagation properties of the beams parameters of TAGSM beam, the decentered parameter of decentered TAGSM beam and partially coherent dark hollow beams(DHBs) propagating in turbulent atmosphere have been investigated.
(2)Analytical expressions of the radial partially coherent flat-topped beam (FTB) array propagating in turbulent atmosphere are derived firstly, where the correlated superposition and uncorrelated superposition are considered. Detailed numerical calculations illustrate the distribution of normalized average intensity and the the modulus of the complex degree of coherence of radial FTB array propagating in turbulent atmosphere. It is shown that the atmospheric turbulence and the correlation of each beamlet are two main factors which affect the propagation of array beams. Because of the influence of the turbulent atmosphere, the normalized average intensity distribution of the correlated and uncorrelated case propagating in turbulent atmosphere tends to Gaussian shape;the distribution of the modulus of the complex degree of coherence of radial FTB array beam starts and ends as Gaussian distribution which resembles the average intensity profile. The spatial coherence of correlated or uncorrelated radial FTB array becomes worse with increasing z in turbulent atmosphere. The results obtained would be useful for partially coherent array beam propagating in atmosphere.
(3) Based on the isotropic electromagnetic Gaussian-Schell model beam, we introduced the mathematical physics model of stochastic electromagnetic twist anisotropic Gaussian-Schell model (ETAGSM) beam by use of the tensor method. Based on the unified theory of coherence and polariziation, the analytical propagation expressions for the cross-spectral density matrix of ETAGSM beams with aperture or not propagating in turbulent atmosphere are derived, which permits us to study the spectral properties of ETAGSM beams with aperture or not. Detailed numerical caculations show that:the affection of the aperture on the spectral properties of the stochastic ETAGSM beam is obvious in the near field; while in the far field, the atmospheric turbulence plays an important role; we can modulate the distribution the spectral degree of polarization of stochastic ETAGSM beams propagating in turbulent atmosphere through modulating the parameters of aperture, the twist property and the coherence of the source beams.
The results obtained in this paper would be useful for studying the propagation of partially coherent beams and partially polarized beam propagating through turbulent atmosphere. This thesis emphasizes on the research of the theory and of the laser beam propagation in the atmosphere, which experiments are of great importance in the areas of laser radar, laser missile-guidance and communication etc.
引文
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