# Frontiers of Optoelectronics

 Front. Optoelectron.    2019, Vol. 12 Issue (3) : 229-248     https://doi.org/10.1007/s12200-019-0901-x
 REVIEW ARTICIE
Review on partially coherent vortex beams
Jun ZENG1, Rong LIN2,3, Xianlong LIU2, Chengliang ZHAO1, Yangjian CAI1,2()
1. School of Physical Science and Technology, Soochow University, Suzhou 215006, China
2. Shandong Provincial Engineering and Technical Center of Light Manipulations & Shandong Provincial Key Laboratory of Optics and Photonic Device, School of Physics and Electronics, Shandong Normal University, Jinan 250014, China
3. College of Physics and Electronic Engineering, Heze University, Heze 274015, China
 Download: PDF(9863 KB)   HTML Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
 Abstract Ever since vortex beams were proposed, they are known for owning phase singularity and carrying orbital angular momentum (OAM). In the past decades, coherent optics developed rapidly. Vortex beams have been extended from fully coherent light to partially coherent light, from scalar light to vector light, from integral topological charge (TC) to fractional TC. Partially coherent vortex beams have attracted tremendous interest due to their hidden correlation singularity and unique propagation properties (e.g., beam shaping, beam rotation and self-reconstruction). Based on the sufficient condition for devising a genuine correlation function of partially coherent beam, partially coherent vortex beams with nonconventional correlation functions (i.e., non-Gaussian correlated Schell-model functions) were introduced recently. This timely review summarizes basic concepts, theoretical models, generation and propagation of partially coherent vortex beams. Corresponding Authors: Yangjian CAI Just Accepted Date: 07 March 2019   Online First Date: 30 May 2019    Issue Date: 16 September 2019
 Cite this article: Jun ZENG,Rong LIN,Xianlong LIU, et al. Review on partially coherent vortex beams[J]. Front. Optoelectron., 2019, 12(3): 229-248. URL: http://journal.hep.com.cn/foe/EN/10.1007/s12200-019-0901-x http://journal.hep.com.cn/foe/EN/Y2019/V12/I3/229
 Fig.1  Wave front of spiral structure. (a) and (b) Wave front of right hand spiral structure with topological charge l = 1 and 3; (c) and (d) Wave front of left hand spiral structure with topological charge l = -1 and -3 Fig.2  Intensity and phase of Gaussian vortex beam with different l at the source plane. (a) and (d) l = 3; (b) and (e) l = -3; (c) and (f) l = 1.5 Fig.3  Phase of edge dislocation Fig.4  (a) Modulus and (b) contours of constant phase of the spectral degree of coherence (correlation function) of a partially coherent beam with vortex phase superposed by LG01 and LG11 model beams [131] Fig.5  Intensity (a−c) and cross correlation functions (d−f) of a partially coherent vortex beam with l = 1 in the far-field plane with different coherence lengths [133] Fig.6  Experimental setup for generating a Gaussian Schell-model vortex beam [94]. NDF, neutral density filter; RGGD, rotating ground-glass disk; GAF, Gaussian amplitude filter; SPP, spiral phase plate; L1, L2, lenses Fig.7  (a) Experimental setup for generating a LGpl beam [139]; (b) experimental setup for generating a partially coherent fractional vortex beam [120]. NDF, neutral density filter; BE, beam expander; RM, reflecting mirror; L1, L2, L3, thin lenses; PC1, personal computers; RGGD, rotating ground-glass disk; GAF, Gaussian amplitude filter; SLM, spatial light modulator; CA, circular aperture; BS, beam splitter; CGH, computer-generated holograms; CCD: charge-coupled device Fig.8  Experimental setup for generating a Laguerre-Gaussian correlated Schell-model vortex beam [113]. BE, beam expander; SLM, spatial light modulator; CA, circular aperture; RGGD, rotating ground-glass disk; GAF, Gaussian amplitude filter; L1, L2, thin lenses; SPP, spiral phase plate;PC1, personal computers Fig.9  Experimental setup for generating a vector partially coherent vortex beam with uniform state of polarization [115]. (a) Without antidiagonal elements; (b) with antidiagonal elements. NDF1, NDF2, neutral density filters; L1, L2, thin lenses; RGGD1, RGGD2, rotating ground-glass disks; PBS, polarization beam splitter; GAF, Gaussian amplitude filter; SPP, spiral phase plate; HP, half-wave plate; M1, M2, reflecting mirrors Fig.10  Experimental setup for generating a partially coherent radially polarized vortex beam [117]. M, reflecting mirror; BE, beam expander; L1, L2, thin lenses; RGGD, rotating ground-glass disk; GAF, Gaussian amplitude filter; RPC, radially polarized convertor; SPP, spiral phase plate Fig.11  Intensity distribution and the corresponding cross line (y = 0) of focused Gaussian Schell-model vortex beam in the focal plane for different values of initial coherence length $σ g$ [94] Fig.12  Intensity distribution and the corresponding cross line (y = 0) of a focused partially coherent radially polarized vortex beam in the focal plane for different values of the topological charge m [117] Fig.13  Intensity distribution and the corresponding cross line (y = 0) of an electromagnetic Gaussian Schell-model beam without vortex phase and an electromagnetic Gaussian Schell-model vortex beam in the focal plane for different values of the initial degree of polarization [115] Fig.14  Normalized intensity distributions of a PCIV beam (l = 1) and a PCFV beam (l = 1.5) focused by a thin lens at several propagation distances [120] Fig.15  Intensity distribution and its x- and y-components of a focused partially coherent radially polarized vortex beam with l = 0 in the x-y plane at several propagation distances. The green solid curve denotes the cross line (y = 0) [117] Fig.16  Intensity distribution and its x- and y-components of a focused partially coherent radially polarized vortex beam with l = 2 in the x-y plane at several propagation distances. The green solid curve denotes the cross line (y = 0) [117] Fig.17  Intensity distribution and its x- and y-components of a focused partially coherent radially polarized vortex beam with l = -2 in the x-y plane at several propagation distances. The green solid curve denotes the cross line (y = 0) [117] Fig.18  Normalized average intensity distribution of a partially coherent LG0l beam after passing through a couple of cylindrical lenses at different propagation distances [141] Fig.19  Normalized intensity distribution of a focused partially coherent LGpl beam with p = 1 and l = 1 obstructed by a sector shaped opaque obstacle with center angle a at several propagation distances [102] Fig.20  Modulus of the degree of coherence of a focused partially coherent LGpl beam with p = 1 and l = 1 obstructed by a sector shaped opaque obstacle with center angle a at several propagation distances [102] Fig.21  Modulus of the degree of coherence of a focused partially coherent LGpl beam with p = 1 and l = 1 obstructed by a sector shaped opaque obstacle with center angle a = 90° in the focal plane for different values of initial coherence length [102]