部分相干部分偏振光束的特性和应用研究
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摘要
本文首先对部分相干部分偏振光束的特性进性了研究，研究的基本方法是互相干函数(相干矩阵元)传输的直接衍射积分方法和矢量光束的BCP矩阵处理方法。
对GSM光束任意缝宽的双缝衍射进行了计算，用衍射的方法直观地分析了杨氏双缝实验屏上相干性，即相干参数对条纹可见度影响，并同时分析了双缝的遮拦比对条纹可见度的影响。
分析了GSM光束经加不同方向偏振片的双缝的衍射，对衍射场中的相干性和偏振特性进行了分析。直观地说明了杨氏双缝实验的条纹可见度与双光束的偏振角度的关系，得到了光束不同偏振成分间的相干性差别。
对GSM光束和PGSM光束经尺寸有限的偏振光栅(PG)衍射后，衍射场的偏振特性进行了分析。得出了GSM光束和PGSM光束经偏振光栅衍射后，偏振度分布都是非均匀的，且受偏振光栅尺寸和周期影响的关系。
详细分析了PGSM光束的焦移特性。在透镜前加偏振片后，根据不同的偏振片透振方向得到了PGSM光束焦移与PGSM光束的偏振状态、相干参数比α_1／α_2的关系。说明光束的矢量性会影响其聚焦性质。在θ=θ°和α_1=α_2=α时，PGSM光束的焦移特性与GSM光束的焦移特性相同。
本文还对部分相干部分偏振光束的应用进行了探讨。用模拟退火优化算法，对GSM光束的位相恢复进行了探讨。得到了该算法用于GSM光束位相恢复设计的经验和位相恢复的初步结果。
最后，对相干参数的测量方法进行了讨论和设计。可测量的相干参数为
四J；I大学博士学位论文 摘要
光束的时间相干函数、相干长度、相干度的绝对值、平均相干度以及平均横
向相干长度。对矢量光束的偏振度和相干矩阵元的测量也做了方法讨论。
In this dissertation, the properties of paYtially coherent and partially
polarized light are studied based on the beam coherence --polarization (BCP)
matrix approach and propagation law of mutual intensity .The models of beams
studied in the works are Gaussian Schell-model (GSM) beams and partially
polarized Gaussian Schell-model (PGSM) beams.
The irriadiance distribution at the observation screen of Young's experiment is
ana1yzed. The YOung's experiment is treated as a two-slit diffraction
phenomenon .The dependence of irradiance distribution on the parameter of GSM
beams and slit size (obscure ratio) is studied.
The intensity and polarization changes of partia1ly coherent and partially
polarized light in Young's experiment are studied. Detailed mathematical
fOrmulations and numerical results are given to illustrate the dependence of the
intensity distribtltion and degree of polarization of the light at the observational
screen on the coherence property of the incident light and the orientation of
polarizers. The more general applicable advantage of the method is pointed out.
The polarization properties of GSM beams and PGSM beams passing through a
po1arization grating (PG) are studied where the finite size of the PG is considered.
The degree of polarization P fOr GSM and PGSM beams in passing through PGs
changes upon propagation and is llonunifOrm across the transversal cross
section.lt has been fOund that the finite number of the period and trucation of the
PG affect the behavior of the P and the variation of the P for PGSM beams is
dependent on the ratio aI / a2.
A detailed study of the focal shift of PGSM beams is made. It is found that
apart from the Fresnel number and trucation parameter, the focal shift of PGSM
beams depends on the angle of polarizer and tl1e ratio aI / a2.
The phase optimization for use with GSM beam is discussed. The simulated
annealing process is app1ied for the calculation of the diffractive phase (DPE)
I I 1
element. The optical resconstruction of the DPE is modeled by the convolution of a coherent diffraction pattern and the far-field intensity distribution of GSM beam .
The methods of measuring the coherent parameters are discussed which include temporal coherence function, coherence length, the degree of coherence, the global degree of coherence and the average transverse coherence length .The measurements for the degree of polarization and the element of mutual matrix are also presented .
对GSM光束任意缝宽的双缝衍射进行了计算，用衍射的方法直观地分析了杨氏双缝实验屏上相干性，即相干参数对条纹可见度影响，并同时分析了双缝的遮拦比对条纹可见度的影响。
分析了GSM光束经加不同方向偏振片的双缝的衍射，对衍射场中的相干性和偏振特性进行了分析。直观地说明了杨氏双缝实验的条纹可见度与双光束的偏振角度的关系，得到了光束不同偏振成分间的相干性差别。
对GSM光束和PGSM光束经尺寸有限的偏振光栅(PG)衍射后，衍射场的偏振特性进行了分析。得出了GSM光束和PGSM光束经偏振光栅衍射后，偏振度分布都是非均匀的，且受偏振光栅尺寸和周期影响的关系。
详细分析了PGSM光束的焦移特性。在透镜前加偏振片后，根据不同的偏振片透振方向得到了PGSM光束焦移与PGSM光束的偏振状态、相干参数比α_1／α_2的关系。说明光束的矢量性会影响其聚焦性质。在θ=θ°和α_1=α_2=α时，PGSM光束的焦移特性与GSM光束的焦移特性相同。
本文还对部分相干部分偏振光束的应用进行了探讨。用模拟退火优化算法，对GSM光束的位相恢复进行了探讨。得到了该算法用于GSM光束位相恢复设计的经验和位相恢复的初步结果。
最后，对相干参数的测量方法进行了讨论和设计。可测量的相干参数为
四J；I大学博士学位论文 摘要
光束的时间相干函数、相干长度、相干度的绝对值、平均相干度以及平均横
向相干长度。对矢量光束的偏振度和相干矩阵元的测量也做了方法讨论。
In this dissertation, the properties of paYtially coherent and partially
polarized light are studied based on the beam coherence --polarization (BCP)
matrix approach and propagation law of mutual intensity .The models of beams
studied in the works are Gaussian Schell-model (GSM) beams and partially
polarized Gaussian Schell-model (PGSM) beams.
The irriadiance distribution at the observation screen of Young's experiment is
ana1yzed. The YOung's experiment is treated as a two-slit diffraction
phenomenon .The dependence of irradiance distribution on the parameter of GSM
beams and slit size (obscure ratio) is studied.
The intensity and polarization changes of partia1ly coherent and partially
polarized light in Young's experiment are studied. Detailed mathematical
fOrmulations and numerical results are given to illustrate the dependence of the
intensity distribtltion and degree of polarization of the light at the observational
screen on the coherence property of the incident light and the orientation of
polarizers. The more general applicable advantage of the method is pointed out.
The polarization properties of GSM beams and PGSM beams passing through a
po1arization grating (PG) are studied where the finite size of the PG is considered.
The degree of polarization P fOr GSM and PGSM beams in passing through PGs
changes upon propagation and is llonunifOrm across the transversal cross
section.lt has been fOund that the finite number of the period and trucation of the
PG affect the behavior of the P and the variation of the P for PGSM beams is
dependent on the ratio aI / a2.
A detailed study of the focal shift of PGSM beams is made. It is found that
apart from the Fresnel number and trucation parameter, the focal shift of PGSM
beams depends on the angle of polarizer and tl1e ratio aI / a2.
The phase optimization for use with GSM beam is discussed. The simulated
annealing process is app1ied for the calculation of the diffractive phase (DPE)
I I 1
element. The optical resconstruction of the DPE is modeled by the convolution of a coherent diffraction pattern and the far-field intensity distribution of GSM beam .
The methods of measuring the coherent parameters are discussed which include temporal coherence function, coherence length, the degree of coherence, the global degree of coherence and the average transverse coherence length .The measurements for the degree of polarization and the element of mutual matrix are also presented .
引文
[1] Peter P .,Hans J. ,et al., Measuring the coherence function of continuous-wave laser by a photorefractive grating method ,Appl. Opt. ,38(3) 516
[2] 赵凯华，钟锡华，《光学》，北京大学出版社1982
[3] M. Born,E.Wolf, Principales of Optics, 7th edition, Cambrigdge University Press 1999
[4] L. Mandel ,E. Wolf ,Optical coherence and quantum optics ,Cambridge University Press 1995
[5] L. Peixiang ,F. Ernst, et al. ,Spatial coherence of prepulse-induced neonlike X-ray lasers Phys. Rev. A 58,628-635(1998)
[6] D. Velaskas ,K. Jarashiunas, et al. ,Coherence length measurement of laser pulses, Appl. Pis'maZh. Teor. Fiz. 1,708-711(1975)
[7] H. J .Eichler ,U. Klein, et al. ,Coherence time measurement of picpicsecond pulses bya light-induced grating method ,Appl. Phys .21,215-219(1986)
[8] R. E. Burge, G. E. Slark ,et al. ,J. Opt. Soc. Am. B 14,2742(1997)
[9] J. E. Trebes, K. A. Nugent, et al. ,Phys. Rev. Lett. 68,588(1992)
[10] W. Chen.,S. Wang et al. ,1990Conference on Laser and Electro-optics, Technical Digest Series Vol. 7(Optical Society of America, Washington, DC, 1990) ,p.282
[11] M. J. Baastians, Local-frequency description of optical signals and systems, research report of the Eindhoven University of Technology Netherlands, ISBN 90-6144-191-9,1988
[12] R. Castaneda, On spatial coherence beams, Optik 109,77-83,1998
[2] 赵凯华，钟锡华，《光学》，北京大学出版社1982
[3] M. Born,E.Wolf, Principales of Optics, 7th edition, Cambrigdge University Press 1999
[4] L. Mandel ,E. Wolf ,Optical coherence and quantum optics ,Cambridge University Press 1995
[5] L. Peixiang ,F. Ernst, et al. ,Spatial coherence of prepulse-induced neonlike X-ray lasers Phys. Rev. A 58,628-635(1998)
[6] D. Velaskas ,K. Jarashiunas, et al. ,Coherence length measurement of laser pulses, Appl. Pis'maZh. Teor. Fiz. 1,708-711(1975)
[7] H. J .Eichler ,U. Klein, et al. ,Coherence time measurement of picpicsecond pulses bya light-induced grating method ,Appl. Phys .21,215-219(1986)
[8] R. E. Burge, G. E. Slark ,et al. ,J. Opt. Soc. Am. B 14,2742(1997)
[9] J. E. Trebes, K. A. Nugent, et al. ,Phys. Rev. Lett. 68,588(1992)
[10] W. Chen.,S. Wang et al. ,1990Conference on Laser and Electro-optics, Technical Digest Series Vol. 7(Optical Society of America, Washington, DC, 1990) ,p.282
[11] M. J. Baastians, Local-frequency description of optical signals and systems, research report of the Eindhoven University of Technology Netherlands, ISBN 90-6144-191-9,1988
[12] R. Castaneda, On spatial coherence beams, Optik 109,77-83,1998