随机电磁光束经像散透镜后磁场的光谱Stokes奇点
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摘要
利用交叉谱密度函数的传输公式,以部分相干刃型位错光束为例,推导出随机电磁光束磁场通过像散透镜传输后的解析表达式.使用光谱Stokes参数,详细讨论了光谱Stokes场的奇点变化规律.结果表明,随机电磁光束磁场通过透镜后的传输过程中,存在光谱s12,s23和s31奇点.改变刃型位错的离轴量、斜率、空间相关长度等光束参数以及随着传输距离的变化,会有磁场光谱Stokes奇点的移动、产生和湮没,也会有V点的产生和C点旋向性的反转.此外,还与电场的光谱Stokes奇点做了比较.
Much interest has been aroused in the polarization singularities. A new technique for metrology called singular Stokes polarimetry based on the detection of polarization singularities has been recently developed and used to detect deformations and displacements of samples on a submicron scale, to measure the topology of polarized speckle field and to study the biomedicine as well. The polarization singularities have been extensively studied theoretically, numerically and experimentally. However, most of the studiesare restricted within the frameworks of the fully coherent wave-fields.By using the spectral Stokes parameters introduced by Korotkova and Wolf [Korotkova O, Wolf E 2005 Opt. Lett. 30198], Yan and Lü [Yan H, Lü B 2009 Opt. Lett. 34 1933] have extended the concept of the polarization singularities from fully coherent beams to partially coherent beams. On the other hand, Hajnal [Hajnal J V 1990 Proc. R. Soc.Lond. A 430 413] studied the electric and magnetic polarization singularities in free-space propagation experimentally with microwaves and confirmed that the electric and magnetic polarization singularities are not coincident in general.In this paper, taking the partially coherent edge dislocation beam for example, the explicit magnetic propagation expression for stochastic electromagnetic beam through an astigmatic lens is derived based on the representation of cross-spectral density matrix propagation. Using the spectral Stokes parameters the magnetic spectral singularities are studied in detail. It is shown that there exist magnetic spectral s12, s23 and s31singularities of stochastic electromagnetic beams through an astigmatic lens. The magnetic spectral Stokes singularities correspond to the zero points of complex Stokes fields sij= 0. s12 singularity corresponds to the circular polarization(C-point) of partially coherent beam, and s3 > 0(s3< 0) means right-(left-) handedness, where the orientations of the major and minor axes of the polarization ellipse become undefined. s23 and s31singularities must be located on L-lines, where the handedness of the polarization ellipse is undetermined(linear polarization). By suitably varying a control parameter, such as off-axis distance, slope of edge dislocation, spatial correlation length, and astigmatic coefficient or propagation distance, the motion, creation,and annihilation of magnetic spectral Stokes singularities may appear. It has been shown that a pair of C-points with equal but opposite topological charges and with similar handedness may be created or annihilated. The V point and handedness reversal of C point may take place. Compared with the electric spectral Stokes singularities of stochastic electromagnetic beams, the positions are not the same, and the left- and right-handedness spaces do not coincide. The results obtained in this paper would be useful for an in-depth understanding of polarization singularities of stochastic electromagnetic beams.
Much interest has been aroused in the polarization singularities. A new technique for metrology called singular Stokes polarimetry based on the detection of polarization singularities has been recently developed and used to detect deformations and displacements of samples on a submicron scale, to measure the topology of polarized speckle field and to study the biomedicine as well. The polarization singularities have been extensively studied theoretically, numerically and experimentally. However, most of the studiesare restricted within the frameworks of the fully coherent wave-fields.By using the spectral Stokes parameters introduced by Korotkova and Wolf [Korotkova O, Wolf E 2005 Opt. Lett. 30198], Yan and Lü [Yan H, Lü B 2009 Opt. Lett. 34 1933] have extended the concept of the polarization singularities from fully coherent beams to partially coherent beams. On the other hand, Hajnal [Hajnal J V 1990 Proc. R. Soc.Lond. A 430 413] studied the electric and magnetic polarization singularities in free-space propagation experimentally with microwaves and confirmed that the electric and magnetic polarization singularities are not coincident in general.In this paper, taking the partially coherent edge dislocation beam for example, the explicit magnetic propagation expression for stochastic electromagnetic beam through an astigmatic lens is derived based on the representation of cross-spectral density matrix propagation. Using the spectral Stokes parameters the magnetic spectral singularities are studied in detail. It is shown that there exist magnetic spectral s12, s23 and s31singularities of stochastic electromagnetic beams through an astigmatic lens. The magnetic spectral Stokes singularities correspond to the zero points of complex Stokes fields sij= 0. s12 singularity corresponds to the circular polarization(C-point) of partially coherent beam, and s3 > 0(s3< 0) means right-(left-) handedness, where the orientations of the major and minor axes of the polarization ellipse become undefined. s23 and s31singularities must be located on L-lines, where the handedness of the polarization ellipse is undetermined(linear polarization). By suitably varying a control parameter, such as off-axis distance, slope of edge dislocation, spatial correlation length, and astigmatic coefficient or propagation distance, the motion, creation,and annihilation of magnetic spectral Stokes singularities may appear. It has been shown that a pair of C-points with equal but opposite topological charges and with similar handedness may be created or annihilated. The V point and handedness reversal of C point may take place. Compared with the electric spectral Stokes singularities of stochastic electromagnetic beams, the positions are not the same, and the left- and right-handedness spaces do not coincide. The results obtained in this paper would be useful for an in-depth understanding of polarization singularities of stochastic electromagnetic beams.
引文
[1]Nye J F,Hajnal J V 1987 Proc.R.Soc.Lond.A 409 21
[2]Soskin M S,Vasnetsov M V 2001 Prog.Opt.42 219
[3]Nye J F 1999 Natural Focusing and the Fine Structure of Light(UK:IOP Publishing,Bristol)pp373–381
[4]Berry M V,Dennis M R 2001 Proc.R.Soc.Lond.A457 141
[5]Konukhov A I,Melnikov L A 2001 J.Opt.B 3 S139
[6]Freund I 2001 Opt.Lett.26 1996
[7]Freund I 2002 Opt.Commun.201 251
[8]Mokhun A I,Soskin M S,Freund I 2002 Opt.Lett.27995
[9]Freund I,Mokhun A I,Soskin M S,Angelsky O V,Mokhun I I 2002 Opt.Lett.27 545
[10]Angelsky O,Mokhun A,Mokhun I,Soskin M 2002 Opt.Commun.207 57
[11]Angelsky O V,Mokhum I I,Mokhum A I 2002 Phys.Rev.E 65 036602
[12]Soskin M S,Denisenko V,Freund I 2003 Opt.Lett.281475
[13]Flossmann F,Schwarz U T,Maier M,Dennis M R 2005Phys.Rev.Lett.95 253901
[14]Schoonover R W,Visser T D 2006 Opt.Express 14 5733
[15]Dennis M R 2008 Opt.Lett.33 2572
[16]Felde C V,Chernyshov A A,Bogatyryova G V,Polyanskii P V,Soskin M S 2008 JETP Lett.88 418
[17]Chernyshov A A,Felde C V,Bogatyryova H V,Polyanskii P V,Soskin M S 2009 J.Opt.A:Pure Appl.Opt.11 094010
[18]Yan H,LüB 2009 Opt.Lett.34 1933
[19]Soskin M S,Denisenko V G,Egorov R I 2004 Proc.of SPIE 5458 79
[20]Bliokh K Y,Niv A,Kleiner V 2008 Opt.Express 16 695
[21]Korotkova O,Wolf E 2005 Opt.Lett.30 198
[22]Luo Y M,LüB D 2010 J.Opt.12 115703
[23]Hajnal J V 1990 Proc.R.Soc.Lond.A 430 413
[24]Berry M V 2004 J.Opt.A:Pure Appl.Opt.6 475
[25]Luo Y M,LüB D,Tang B H,Zhu Y 2012 Acta Phys.Sin.61 134202(in Chinese)[罗亚梅,吕百达,唐碧华,朱渊2012物理学报61 134202]
[26]Luo Y M,Gao Z H,Tang B H,LüB D 2013 J.Opt.Soc.Am.A 30 1646
[27]Liu L H,LüW Y,Yang C,Mai C J,Chen D P 2015Acta Phys.Sin.64 034208(in Chinese)[刘李辉,吕炜煜,杨超,麦灿基,陈德鹏2015物理学报64 034208]
[28]Wolf E 2007 Introduction to the Theory of Coherence and Polarization of Light(Cambridge:Cambridge University Press)pp174–201
[29]Freund I,Shvartsman N 1994 Phys.Rev.A 50 5164
[2]Soskin M S,Vasnetsov M V 2001 Prog.Opt.42 219
[3]Nye J F 1999 Natural Focusing and the Fine Structure of Light(UK:IOP Publishing,Bristol)pp373–381
[4]Berry M V,Dennis M R 2001 Proc.R.Soc.Lond.A457 141
[5]Konukhov A I,Melnikov L A 2001 J.Opt.B 3 S139
[6]Freund I 2001 Opt.Lett.26 1996
[7]Freund I 2002 Opt.Commun.201 251
[8]Mokhun A I,Soskin M S,Freund I 2002 Opt.Lett.27995
[9]Freund I,Mokhun A I,Soskin M S,Angelsky O V,Mokhun I I 2002 Opt.Lett.27 545
[10]Angelsky O,Mokhun A,Mokhun I,Soskin M 2002 Opt.Commun.207 57
[11]Angelsky O V,Mokhum I I,Mokhum A I 2002 Phys.Rev.E 65 036602
[12]Soskin M S,Denisenko V,Freund I 2003 Opt.Lett.281475
[13]Flossmann F,Schwarz U T,Maier M,Dennis M R 2005Phys.Rev.Lett.95 253901
[14]Schoonover R W,Visser T D 2006 Opt.Express 14 5733
[15]Dennis M R 2008 Opt.Lett.33 2572
[16]Felde C V,Chernyshov A A,Bogatyryova G V,Polyanskii P V,Soskin M S 2008 JETP Lett.88 418
[17]Chernyshov A A,Felde C V,Bogatyryova H V,Polyanskii P V,Soskin M S 2009 J.Opt.A:Pure Appl.Opt.11 094010
[18]Yan H,LüB 2009 Opt.Lett.34 1933
[19]Soskin M S,Denisenko V G,Egorov R I 2004 Proc.of SPIE 5458 79
[20]Bliokh K Y,Niv A,Kleiner V 2008 Opt.Express 16 695
[21]Korotkova O,Wolf E 2005 Opt.Lett.30 198
[22]Luo Y M,LüB D 2010 J.Opt.12 115703
[23]Hajnal J V 1990 Proc.R.Soc.Lond.A 430 413
[24]Berry M V 2004 J.Opt.A:Pure Appl.Opt.6 475
[25]Luo Y M,LüB D,Tang B H,Zhu Y 2012 Acta Phys.Sin.61 134202(in Chinese)[罗亚梅,吕百达,唐碧华,朱渊2012物理学报61 134202]
[26]Luo Y M,Gao Z H,Tang B H,LüB D 2013 J.Opt.Soc.Am.A 30 1646
[27]Liu L H,LüW Y,Yang C,Mai C J,Chen D P 2015Acta Phys.Sin.64 034208(in Chinese)[刘李辉,吕炜煜,杨超,麦灿基,陈德鹏2015物理学报64 034208]
[28]Wolf E 2007 Introduction to the Theory of Coherence and Polarization of Light(Cambridge:Cambridge University Press)pp174–201
[29]Freund I,Shvartsman N 1994 Phys.Rev.A 50 5164