Statistical properties of a radially polarized twisted Gaussian Schell-model beam in a uniaxial crystal

Abstract We derive the analytical formulas for the elements of the cross-spectral density matrix of a radially polarized partially coherent beam with a twist phase named radially polarized twisted Gaussian Schell-model (RPTGSM) beam propagating in a uniaxial crystal, and explore the statistical properties, such as the intensity distribution, the degree of polarization (DOP) and the state of polarization (SOP) of such beam in a uniaxial crystal with the help of the derived formulas. It is found that the statistical properties of a RPTGSM beam are closely related with the twist phase and the anisotropy of the uniaxial crystal, e.g. the twist phase leads to the rotation of the intensity, DOP and SOP distributions, and the anisotropy of the uniaxial crystal leads to the asymmetry distributions of these statistical properties. Our results will be useful for designing light field with prescribed intensity, DOP and SOP distributions, and may be useful in optical manipulations and free-space optical communications.

[1]  K. Sundar,et al.  Twisted Gaussian Schell-model beams. II. Spectrum analysis and propagation characteristics , 1993 .

[2]  K. Sundar,et al.  Twisted Gaussian Schell-model beams. I. Symmetry structure and normal-mode spectrum , 1993 .

[3]  R. Simon,et al.  Twisted Gaussian Schell-model beams , 1993 .

[4]  A. Friberg,et al.  Interpretation and experimental demonstration of twisted Gaussian Schell-model beams , 1994 .

[5]  L. Mandel,et al.  Optical Coherence and Quantum Optics , 1995 .

[6]  Kathleen S. Youngworth,et al.  Focusing of high numerical aperture cylindrical-vector beams. , 2000, Optics express.

[7]  J. Stamnes,et al.  Transmission of a two-dimensional Gaussian beam into a uniaxial crystal. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[8]  T G Brown,et al.  Longitudinal field modes probed by single molecules. , 2001, Physical review letters.

[9]  J. Movilla,et al.  Orbital angular momentum of partially coherent beams. , 2001, Optics letters.

[10]  Q. Zhan,et al.  Focus shaping using cylindrical vector beams. , 2002, Optics express.

[11]  G. Cincotti,et al.  Propagation of cylindrically symmetric fields in uniaxial crystals. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[12]  E. Wolf.  Unified theory of coherence and polarization of random electromagnetic beams , 2003 .

[13]  Claudio Palma,et al.  Optical propagation in uniaxial crystals orthogonal to the optical axis: paraxial theory and beyond. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[14]  G Leuchs,et al.  Sharper focus for a radially polarized light beam. , 2003, Physical review letters.

[15]  E. Wolf,et al.  Changes in the state of polarization of a random electromagnetic beam on propagation , 2005 .

[16]  Yangjian Cai,et al.  Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere , 2006 .

[17]  Kathleen S. Youngworth,et al.  Dark-field imaging with cylindrical-vector beams. , 2006, Applied optics.

[18]  P. Meystre.  Introduction to the Theory of Coherence and Polarization of Light , 2007 .

[19]  Dean Brown,et al.  Partially correlated azimuthal vortex illumination: coherence and correlation measurements and effects in imaging. , 2008, Optics express.

[20]  D. J. Liu,et al.  Propagation of partially polarized, partially coherent beams in uniaxial crystals orthogonal to the optical axis , 2009 .

[21]  Q. Zhan.  Cylindrical vector beams: from mathematical concepts to applications , 2009 .

[22]  O. Korotkova,et al.  Twist phase-induced polarization changes in electromagnetic Gaussian Schell-model beams , 2009 .

[23]  Zhongxiang Zhou,et al.  Generalized Stokes parameters of stochastic electromagnetic beams propagating through uniaxial crystals orthogonal to the optical axis , 2009 .

[24]  Olga Korotkova,et al.  Radiation force of scalar and electromagnetic twisted Gaussian Schell-model beams. , 2009, Optics express.

[25]  Tomasz Szoplik,et al.  Focusing radially polarized light by a concentrically corrugated silver film without a hole. , 2009, Physical review letters.

[26]  Yangjian Cai,et al.  Second-order statistics of a twisted gaussian Schell-model beam in turbulent atmosphere. , 2010, Optics express.

[27]  D. Zhao,et al.  Propagation of Uniformly Polarized Stochastic Electromagnetic Beams in Uniaxial Crystals , 2010 .

[28]  Amber M. Beckley,et al.  Full Poincaré beams. , 2010, Optics express.

[29]  Yangjian Cai,et al.  Statistical properties of a nonparaxial Gaussian Schell-model beam in a uniaxial crystal. , 2011, Optics express.

[30]  Yangjian Cai,et al.  Statistics properties of a cylindrical vector partially coherent beam. , 2011, Optics express.

[31]  Olga Korotkova,et al.  Experimental generation of a radially polarized beam with controllable spatial coherence , 2012 .

[32]  Yangjian Cai,et al.  Effect of spatial coherence on propagation, tight focusing, and radiation forces of an azimuthally polarized beam , 2012 .

[33]  Yangjian Cai,et al.  Twist phase-induced reduction in scintillation of a partially coherent beam in turbulent atmosphere. , 2012, Optics letters.

[34]  Olga Korotkova,et al.  Beyond the classical Rayleigh limit with twisted light. , 2012, Optics letters.

[35]  Christoph H. Keitel,et al.  Acceleration of proton bunches by petawatt chirped radially polarized laser pulses , 2012 .

[36]  Yangjian Cai,et al.  Coherence and polarization properties of a radially polarized beam with variable spatial coherence. , 2012, Optics express.

[37]  Yangjian Cai,et al.  Experimental study of the scintillation index of a radially polarized beam with controllable spatial coherence , 2013 .

[38]  Yangjian Cai,et al.  Statistical properties of a cylindrical vector partially coherent beam in turbulent atmosphere , 2013 .

[39]  Yangjian Cai,et al.  Second-order moments of an electromagnetic Gaussian Schell-model beam in a uniaxial crystal. , 2014, Journal of the Optical Society of America. A, Optics, image science, and vision.

[40]  Olga Korotkova,et al.  Generation and propagation of a partially coherent vector beam with special correlation functions , 2014 .

[41]  Yangjian Cai,et al.  Orbital angular moment of a partially coherent beam propagating through an astigmatic ABCD optical system with loss or gain. , 2014, Optics letters.

[42]  Yangjian Cai,et al.  Twist phase-induced changes of the statistical properties of a stochastic electromagnetic beam propagating in a uniaxial crystal. , 2015, Optics express.

[43]  F. Gori,et al.  Twisted Gaussian Schell-model beams as series of partially coherent modified Bessel-Gauss beams. , 2015, Optics letters.

[44]  Yangjian Cai,et al.  Generation and propagation of a vector cosine-Gaussian correlated beam with radial polarization. , 2015, Optics express.

[45]  Lina Guo,et al.  Statistical properties of a partially coherent cylindrical vector beam in oceanic turbulence. , 2015, Journal of the Optical Society of America. A, Optics, image science, and vision.

[46]  Lina Guo,et al.  Orbital angular moment of an electromagnetic Gaussian Schell-model beam with a twist phase. , 2015, Optics express.

[47]  Yangjian Cai,et al.  Second-order statistics of a radially polarized cosine-Gaussian correlated Schell-model beam in anisotropic turbulence. , 2016, Optics express.

[48]  Gaofeng Wu.  Propagation properties of a radially polarized partially coherent twisted beam in free space. , 2016, Journal of the Optical Society of America. A, Optics, image science, and vision.

[49]  Lina Guo,et al.  Vortex phase-induced changes of the statistical properties of a partially coherent radially polarized beam. , 2016, Optics express.

[50]  Yangjian Cai,et al.  Vector Hermite-Gaussian correlated Schell-model beam. , 2016, Optics express.