# Nonparaxial Propagation Properties of Specially Correlated Radially Polarized Beams in Free Space
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[PERSON]  
4 School of Physical Science and Technology, Soochow University, Suzhou 215006, China; [EMAIL_ADDRESS] (Y.D. ); [EMAIL_ADDRESS] (Y.C. )1  
[PERSON]  
4 School of Physical Science and Technology, Soochow University, Suzhou 215006, China; [EMAIL_ADDRESS] (Y.D. ); [EMAIL_ADDRESS] (Y.C. )1  
[PERSON]  
4 School of Physical Science and Technology, Soochow University, Suzhou 215006, China; [EMAIL_ADDRESS] (Y.D. ); [EMAIL_ADDRESS] (Y.C. )1  
[PERSON]  
4 School of Physical Science and Technology, Soochow University, Suzhou 215006, China; [EMAIL_ADDRESS] (Y.D. ); [EMAIL_ADDRESS] (Y.C. )1  
[PERSON]  
4 School of Physical Science and Technology, Soochow University, Suzhou 215006, China; [EMAIL_ADDRESS] (Y.D. ); [EMAIL_ADDRESS] (Y.C. )1  
[PERSON]  
4 School of Physical Science and Technology, Soochow University, Suzhou 215006, China; [EMAIL_ADDRESS] (Y.D. ); [EMAIL_ADDRESS] (Y.C. )1  
[PERSON]  
4 School of Physical Science and Technology, Soochow University, Suzhou 215006, China; [EMAIL_ADDRESS] (Y.C. )1  
[PERSON]  
4 School of Physical Science and Technology, Soochow University, Suzhou 215006, China; [EMAIL_ADDRESS] (Y.D. ); [EMAIL_ADDRESS] (Y.C. )1  
[PERSON]  
4 School of Physical Science and Technology, Soochow University, Suzhou 215006, China; [EMAIL_ADDRESS] (Y.D. ); [EMAIL_ADDRESS] (Y.C. )1  
[PERSON]  
4 School of Physical Science and Technology, Soochow University, Suzhou 215006, China; [EMAIL_ADDRESS] (Y.D. ); [EMAIL_ADDRESS] (Y.C. )1  
[PERSON]  
4 School of Physical Science and Technology, Sooch University, Suzhou 215006, China; [EMAIL_ADDRESS] (Y.D. ); [EMAIL_ADDRESS] (Y.C. )1  
[PERSON]  
4 School of Physical Science and Technology, Soochow University, Suzhou 215006, China; [EMAIL_ADDRESS] (Y.C. )1  
[PERSON]  
4 School of Physical Science and Technology, Soochow University, Suzhou 215006, China; [EMAIL_ADDRESS] (Y.C. )1  
[PERSON]  
4 School of Physical Science and Technology, Soochow University, Suzhou 215006, China; [EMAIL_ADDRESS] (Y.C. )1  
[PERSON]  
4 School of Physical Science and Technology, Soochow University, Suzhou 215006, China; [EMAIL_ADDRESS] (Y.C. )1  
[PERSON]  
4 School of Physical Science and Technology, Soochow University, Suzhou 215006, China; yikouniao@163. PCRP beam were revealed in reference [13] and have modulated significantly the statistical properties in interference experiments with a PCRP beam [14]. More recently, various kinds of partially coherent beams with nonconventional spatial correlation functions were introduced and generated [15; 16; 17; 18; 19; 20; 21; 22] owing to the development of appropriate conditions for devising genuine correlation functions [23; 24; 25; 26]. Such partially coherent beams with engineered correlation functions exhibit many unusual properties during propagation. They can find rich potential applications in laser beam shaping, optical imaging, optical trapping, and free-space optical communications [27; 28; 29; 30; 31; 32; 33; 34; 35; 36]. Among them, a typical class of partially coherent vector beams, i.e., special correlated radially polarized (SCRP) beam, was theoretically introduced and experimentally generated in [21]. Different from the PCRP beam which is fully polarized at source and depolarized on propagation, an SCRP beam is unpolarized at source and becomes more polarized during propagation. Further, for the SCRP beam, a very pure radial polarization state can be generated in the far field (or the focal plane). It was also demonstrated that by tailoring the spatial correlation function, the paraxial propagation properties of an SCRP beam in free space and turbulent atmosphere can be modulated [21; 37]. Recently, we discovered that the paraxial SCRP beam exhibits super-strong self-reconstruction of its intensity profile and polarization state upon scattering from an opaque obstacle [38], which is anticipated to be used in image transfer in turbid media.