部分相干刃型位错光束的谱Stokes奇点
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摘要
利用交叉谱密度函数的传输公式,推导出部分相干刃型位错光束在自由空间中传输的解析表达式.结合谱Stokes参数,详细讨论了其Stokes场的奇点变化规律.结果表明,部分相干刃型位错光束在自由空间传输过程中存在谱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,会有谱Stokes奇点的移动、产生和湮没,也会有V点的产生和C点旋性的反转.
The polarization singularities in vector wavefields have been extensively studied analytically and experimentally.The polarization singularities can be analyzed by using electromagnetic theory or Stokes parameters, or be described in terms of complex Stokes scalar fields. In some practical applications, partially coherent beams have more advantages than fully coherent beams. Recently, the concept of the polarization singularities has been extended from fully coherent beams to partially coherent beams. In this paper, using the representation of cross-spectral density matrix propagation,the explicit propagation expressions for the partially coherent edge dislocation beams are derived in free space, and based on the spectral Stokes parameters the spectral singularities are studied in detail. It is shown that there exist spectral s12, s23 and s31singularities of partially coherent edge dislocation beams in free-space propagation. s12 singularities correspond to circular polarization(C-points) of the partially coherent edge dislocation beams, 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 s31 singularities must be located on L-lines, where the handedness of the polarization ellipse is undetermined(linear polarization). The motion, creation and annihilation of spectral Stokes singularities may appear in the variation of a controlling parameter, such as off-axis distance, slope of edge dislocation, spatial correlation length, or in the variation of the propagation distance. By suitably varying the spatial correlation length or propagation distance the V-point,the handedness reversal of C-point, creation and annihilation for a pair of oppositely charged spectral singularities take place. The creation and annihilation occur for a pair of s12 singularities with opposite topological charge but same handedness. The critical points of the controlling parameters and propagation distance, at which pairs of different spectral singularities annihilate, are not the same. The collision of the C-point and L-line results in a V-point(vector singularity), which is unstable. A small perturbation leads to the handedness reversal. At such a point the state of polarization is undetermined and the degree of polarization P = 0. The results obtained in this paper would be useful for a deep understanding of polarization singularities of stochastic electromagnetic beams.
The polarization singularities in vector wavefields have been extensively studied analytically and experimentally.The polarization singularities can be analyzed by using electromagnetic theory or Stokes parameters, or be described in terms of complex Stokes scalar fields. In some practical applications, partially coherent beams have more advantages than fully coherent beams. Recently, the concept of the polarization singularities has been extended from fully coherent beams to partially coherent beams. In this paper, using the representation of cross-spectral density matrix propagation,the explicit propagation expressions for the partially coherent edge dislocation beams are derived in free space, and based on the spectral Stokes parameters the spectral singularities are studied in detail. It is shown that there exist spectral s12, s23 and s31singularities of partially coherent edge dislocation beams in free-space propagation. s12 singularities correspond to circular polarization(C-points) of the partially coherent edge dislocation beams, 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 s31 singularities must be located on L-lines, where the handedness of the polarization ellipse is undetermined(linear polarization). The motion, creation and annihilation of spectral Stokes singularities may appear in the variation of a controlling parameter, such as off-axis distance, slope of edge dislocation, spatial correlation length, or in the variation of the propagation distance. By suitably varying the spatial correlation length or propagation distance the V-point,the handedness reversal of C-point, creation and annihilation for a pair of oppositely charged spectral singularities take place. The creation and annihilation occur for a pair of s12 singularities with opposite topological charge but same handedness. The critical points of the controlling parameters and propagation distance, at which pairs of different spectral singularities annihilate, are not the same. The collision of the C-point and L-line results in a V-point(vector singularity), which is unstable. A small perturbation leads to the handedness reversal. At such a point the state of polarization is undetermined and the degree of polarization P = 0. The results obtained in this paper would be useful for a deep understanding of polarization singularities of stochastic electromagnetic beams.
引文
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[4]Luo Y M,Gao Z H,Tang B H,LüB D 2014 Acta Phys.Sin.63 154201(in Chinese)[罗亚梅,高曾辉,唐碧华,吕百达2014物理学报63 154201]
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[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 2008JETP Lett.88 418
[17]Chernyshov A A,Felde Ch V,Bogatyryova H V 2009 J.Opt.A:Pure Appl.Opt.11 094010
[18]Yan H W,LüB D 2009 Opt.Lett.34 1933
[19]Soskin M S,Denisenko V G,Egorov R I 2004 Proc.SPIE5458 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]Wolf E 2007 Introduction to the Theory of Coherence and Polarization of Light(Cambridge:Cambridge University Press)
[23]He D,Yan H,LüB D 2011 Chin.Phys.B 20 014201
[24]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(Bristol:IOP Publishing)
[4]Luo Y M,Gao Z H,Tang B H,LüB D 2014 Acta Phys.Sin.63 154201(in Chinese)[罗亚梅,高曾辉,唐碧华,吕百达2014物理学报63 154201]
[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 2002 Opt.Lett.27545
[10]Angelsky O,Mokhun A,Mokhun I 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 2005 Phys.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 2008JETP Lett.88 418
[17]Chernyshov A A,Felde Ch V,Bogatyryova H V 2009 J.Opt.A:Pure Appl.Opt.11 094010
[18]Yan H W,LüB D 2009 Opt.Lett.34 1933
[19]Soskin M S,Denisenko V G,Egorov R I 2004 Proc.SPIE5458 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]Wolf E 2007 Introduction to the Theory of Coherence and Polarization of Light(Cambridge:Cambridge University Press)
[23]He D,Yan H,LüB D 2011 Chin.Phys.B 20 014201
[24]Freund I,Shvartsman N 1994 Phys.Rev.A 50 5164