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.
Similar content being viewed by others
References
Nye J, Berry M. Dislocations in wave trains. Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 1974, 336(1605): 165–190
Soskin M, Vasnetsov M. Singular optics. Progress in Optics, 2001, 42(4): 219–276
Gbur G, Tyson R K. Vortex beam propagation through atmospheric turbulence and topological charge conservation. Journal of the Optical Society of America A, Optics, Image Science, and Vision, 2008, 25(1): 225–230
Zhen B, Hsu C W, Lu L, Stone A D, Soljačić M. Topological nature of optical bound states in the continuum. Physical Review Letters, 2014, 113(25): 257401
Flossmann F, Schwarz U, Maier M. Propagation dynamics of optical vortices in Laguerre-Gaussian beams. Optics Communications, 2005, 250(4–6): 218–230
Zhu K, Zhou G, Li X, Zheng X, Tang H. Propagation of Bessel-Gaussian beams with optical vortices in turbulent atmosphere. Optics Express, 2008, 16(26): 21315–21320
Schwarz U, Sogomonian S, Maier M. Propagation dynamics of phase dislocations embedded in a Bessel light beam. Optics Communications, 2002, 208(4–6): 255–262
Orlov S, Regelskis K, Smilgevičius V, Stabinis A. Propagation of Bessel beams carrying optical vortices. Optics Communications, 2002, 209(1–3): 155–165
Yang Y, Dong Y, Zhao C, Cai Y. Generation and propagation of an anomalous vortex beam. Optics Letters, 2013, 38(24): 5418–5421
Vaity P, Rusch L. Perfect vortex beam: Fourier transformation of a Bessel beam. Optics Letters, 2015, 40(4): 597–600
Li P, Zhang Y, Liu S, Ma C, Han L, Cheng H, Zhao J. Generation of perfect vectorial vortex beams. Optics Letters, 2016, 41(10): 2205–2208
Paterson C. Atmospheric turbulence and orbital angular momentum of single photons for optical communication. Physical Review Letters, 2005, 94(15): 153901
Thidé B, Then H, Sjöholm J, Palmer K, Bergman J, Carozzi T D, Istomin Y N, Ibragimov N H, Khamitova R. Utilization of photon orbital angular momentum in the low-frequency radio domain. Physical Review Letters, 2007, 99(8): 087701
Grier D G. A revolution in optical manipulation. Nature, 2003, 424(6950): 810–816
O’Neil A T, Padgett M J. Axial and lateral trapping efficiency of Laguerre-Gaussian modes in inverted optical tweezers. Optics Communications, 2001, 193(1–6): 45–50
Ng J, Lin Z, Chan C T. Theory of optical trapping by an optical vortex beam. Physical Review Letters, 2010, 104(10): 103601
Wang X, Rui G, Gong L, Gu B, Cui Y. Manipulation of resonant metallic nanoparticle using 4Pi focusing system. Optics Express, 2016, 24(21): 24143–24152
Chen J, Wan C, Kong L J, Zhan Q. Tightly focused optical field with controllable photonic spin orientation. Optics Express, 2017, 25(16): 19517–19528
Molina-Terriza G, Torres J P, Torner L. Twisted photons. Nature Physics, 2007, 3(5): 305–310
Bozinovic N, Yue Y, Ren Y, Tur M, Kristensen P, Huang H, Willner A E, Ramachandran S. Terabit-scale orbital angular momentum mode division multiplexing in fibers. Science, 2013, 340(6140): 1545–1548
Vaziri A, Pan J W, Jennewein T, Weihs G, Zeilinger A. Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum. Physical Review Letters, 2003, 91(22): 227902
Gu Y, Gbur G. Measurement of atmospheric turbulence strength by vortex beam. Optics Communications, 2010, 283(7): 1209–1212
Li X, Tai Y, Zhang L, Li H, Li L. Characterization of dynamic random process using optical vortex metrology. Applied Physics B, Lasers and Optics, 2014, 116(4): 901–909
Tamburini F, Anzolin G, Umbriaco G, Bianchini A, Barbieri C. Overcoming the rayleigh criterion limit with optical vortices. Physical Review Letters, 2006, 97(16): 163903
Yu W, Ji Z, Dong D, Yang X, Xiao Y, Gong Q, Xi P, Shi K. Superresolution deep imaging with hollow Bessel beam STED microscopy. Laser & Photonics Reviews, 2016, 10(1): 147–152
Beijersbergen M W, Allen L, Van der Veen H, Woerdman J. Astigmatic laser mode converters and transfer of orbital angular momentum. Optics Communications, 1993, 96(1–3): 123–132
Arlt J, Dholakia K. Generation of high-order Bessel beams by use of an axicon. Optics Communications, 2000, 177(1–6): 297–301
Beijersbergen M, Coerwinkel R, Kristensen M, Woerdman J. Helical-wavefront laser beams produced with a spiral phaseplate. Optics Communications, 1994, 112(5–6): 321–327
Heckenberg N R, McDuff R, Smith C P, White A G. Generation of optical phase singularities by computer-generated holograms. Optics Letters, 1992, 17(3): 221–223
Matsumoto N, Ando T, Inoue T, Ohtake Y, Fukuchi N, Hara T. Generation of high-quality higher-order Laguerre-Gaussian beams using liquid-crystal-on-silicon spatial light modulators. Journal of the Optical Society of America A, Optics, Image Science, and Vision, 2008, 25(7): 1642–1651
Marrucci L, Manzo C, Paparo D. Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media. Physical Review Letters, 2006, 96(16): 163905
Chen P, Ji W, Wei B Y, Hu W, Chigrinov V, Lu Y Q. Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates. Applied Physics Letters, 2015, 107(24): 241102
Machavariani G, Lumer Y, Moshe I, Meir A, Jackel S. Efficient extracavity generation of radially and azimuthally polarized beams. Optics Letters, 2007, 32(11): 1468–1470
Naidoo D, Roux F S, Dudley A, Litvin I, Piccirillo B, Marrucci L, Forbes A. Controlled generation of higher-order Poincaré sphere beams from a laser. Nature Photonics, 2016, 10(5): 327–332
Cai X, Wang J, Strain M J, Johnson-Morris B, Zhu J, Sorel M, O’Brien J L, Thompson M G, Yu S. Integrated compact optical vortex beam emitters. Science, 2012, 338(6105): 363–366
Fang X, Yang G, Wei D, Wei D, Ni R, Ji W, Zhang Y, Hu X, Hu W, Lu Y Q, Zhu S N, Xiao M. Coupled orbital angular momentum conversions in a quasi-periodically poled LiTaO3 crystal. Optics Letters, 2016, 41(6): 1169–1172
Wu Y, Ni R, Xu Z, Wu Y, Fang X, Wei D, Hu X, Zhang Y, Xiao M, Zhu S. Tunable third harmonic generation of vortex beams in an optical superlattice. Optics Express, 2017, 25(25): 30820–30826
Leach J, Keen S, Padgett M J, Saunter C, Love G D. Direct measurement of the skew angle of the Poynting vector in a helically phased beam. Optics Express, 2006, 14(25): 11919–11924
Berkhout G C, Beijersbergen M W. Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects. Physical Review Letters, 2008, 101(10): 100801
Sztul H I, Alfano R R. Double-slit interference with Laguerre-Gaussian beams. Optics Letters, 2006, 31(7): 999–1001
Hickmann J M, Fonseca E J, Soares W C, Chávez-Cerda S. Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum. Physical Review Letters, 2010, 105(5): 053904
de Araujo L E, Anderson M E. Measuring vortex charge with a triangular aperture. Optics Letters, 2011, 36(6): 787–789
Guo C S, Yue S J, Wei G X. Measuring the orbital angular momentum of optical vortices using a multipinhole plate. Applied Physics Letters, 2009, 94(23): 231104
Vinu R V, Singh R K. Determining helicity and topological structure of coherent vortex beam from laser speckle. Applied Physics Letters, 2016, 109(11): 111108
Prabhakar S, Kumar A, Banerji J, Singh R P. Revealing the order of a vortex through its intensity record. Optics Letters, 2011, 36(22): 4398–4400
Zhao P, Li S, Feng X, Cui K, Liu F, Zhang W, Huang Y. Measuring the complex orbital angular momentum spectrum of light with a mode-matching method. Optics Letters, 2017, 42(6): 1080–1083
Dudley A, Litvin I A, Forbes A. Quantitative measurement of the orbital angular momentum density of light. Applied Optics, 2012, 51(7): 823–833
Zhou H L, Fu D Z, Dong J J, Zhang P, Chen D X, Cai X L, Li F L, Zhang X L. Orbital angular momentum complex spectrum analyzer for vortex light based on the rotational Doppler effect. Light, Science & Applications, 2017, 6(4): e16251
Basistiy I, Soskin M, Vasnetsov M. Optical wavefront dislocations and their properties. Optics Communications, 1995, 119(5–6): 604–612
Lee W, Yuan X C, Dholakia K. Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step. Optics Communications, 2004, 239(1–3): 129–135
Berry M. Optical vortices evolving from helicoidal integer and fractional phase steps. Journal of Optics A, Pure and Applied Optics, 2004, 6(2): 259–268
Gbur G. Fractional vortex Hilbert’s hotel. Optica, 2016, 3(3): 222–225
Tao S H, Lee W M, Yuan X C. Dynamic optical manipulation with a higher-order fractional bessel beam generated from a spatial light modulator. Optics Letters, 2003, 28(20): 1867–1869
Fang Y, Lu Q, Wang X, Zhang W, Chen L. Fractional-topological-charge-induced vortex birth and splitting of light fields on the submicron scale. Physical Review A, 2017, 95(2): 023821
Molchan M A, Doktorov E V, Vlasov R A. Propagation of vector fractional charge Laguerre-Gaussian light beams in the thermally nonlinear moving atmosphere. Optics Letters, 2010, 35(5): 670–672
Vasylkiv Y, Skab I, Vlokh R. Crossover regime of optical vortices generation via electro-optic nonlinearity: the problem of optical vortices with the fractional charge generated by crystals. Journal of the Optical Society of America A, Optics, Image Science, and Vision, 2014, 31(9): 1936–1945
Yang Y, Zhu X, Zeng J, Lu X, Zhao C, Cai Y. Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation. Nanophotonics, 2018, 7(3): 677–682
Oemrawsingh S S R, de Jong J A, Ma X, Aiello A, Eliel E R, ’t Hooft G W, Woerdman J P. High-dimensional mode analyzers for spatial quantum entanglement. Physical Review A, 2006, 73(3): 032339
Guo C S, Yu Y N, Hong Z. Optical sorting using an array of optical vortices with fractional topological charge. Optics Communications, 2010, 283(9): 1889–1893
Tao S, Yuan X C, Lin J, Peng X, Niu H. Fractional optical vortex beam induced rotation of particles. Optics Express, 2005, 13(20): 7726–7731
Situ G, Pedrini G, Osten W. Spiral phase filtering and orientation-selective edge detection/enhancement. Journal of the Optical Society of America A, Optics, Image Science, and Vision, 2009, 26(8): 1788–1797
Strohaber J, Boran Y, Sayrac M, Johnson L, Zhu F, Kolomenskii A, Schuessler H. Nonlinear mixing of optical vortices with fractional topological charge in Raman sideband generation. Journal of Optics, 2017, 19(1): 015607
Ni R, Niu Y, Du L, Hu X, Zhang Y, Zhu S. Topological charge transfer in frequency doubling of fractional orbital angular momentum state. Applied Physics Letters, 2016, 109(15): 151103
Born M, Wolf E. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. 7nd ed. Cambridge: Cambridge University Press, 1999
Wolf E. New theory of partial coherence in the space-frequency domain. Part I: spectra and cross spectra of steady-state sources. Journal of the Optical Society of America, 1982, 72(3): 343–351
Wolf E. New theory of partial coherence in the space-frequency domain. Part II: steady-state fields and higher-order correlations. Journal of the Optical Society of America A, Optics and Image Science, 1986, 3(1): 76–85
Wolf E. Invariance of the spectrum of light on propagation. Physical Review Letters, 1986, 56(13): 1370–1372
Gori F. Collett-Wolf sources and multimode lasers. Optics Communications, 1980, 34(3): 301–305
Carter W H, Wolf E. Coherence and radiometry with quasihomogeneous planar sources. Journal of the Optical Society of America, 1977, 67(6): 785–796
Gori F. Mode propagation of the field generated by Collett-Wolf Schell-model sources. Optics Communications, 1983, 46(3–4): 149–154
Gori F, Guattari G, Padovani C. Modal expansion for J o-correlated Schell-model sources. Optics Communications, 1987, 64(4): 311–316
Gori F, Guattari G, Palma C, Padovani C. Observation of optical redshifts and blueshifts produced by source correlations. Optics Communications, 1988, 67(1): 1–4
Ricklin J C, Davidson F M. Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication. Journal of the Optical Society of America A, Optics, Image Science, and Vision, 2002, 19(9): 1794–1802
Ricklin J C, Davidson F M. Atmospheric optical communication with a Gaussian Schell beam. Journal of the Optical Society of America A, Optics, Image Science, and Vision, 2003, 20(5): 856–866
Kato Y, Mima K, Miyanaga N, Arinaga S, Kitagawa Y, Nakatsuka M, Yamanaka C. Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression. Physical Review Letters, 1984, 53(11): 1057–1060
Beléndez A, Carretero L, Fimia A. The use of partially coherent light to reduce the efficiency of silver halide noise gratings. Optics Communications, 1993, 98(4–6): 236–240
Cai Y, Zhu S Y. Ghost imaging with incoherent and partially coherent light radiation. Physical Review E, 2005, 71(5): 056607
Zhao C, Cai Y, Lu X, Eyyuboğlu H T. Radiation force of coherent and partially coherent flat-topped beams on a Rayleigh particle. Optics Express, 2009, 17(3): 1753–1765
Zhang J F, Wang Z Y, Cheng B, Wang Q Y, Wu B, Shen X X, Zheng L L, Xu Y F, Lin Q. Atom cooling by partially spatially coherent lasers. Physical Review A., 2013, 88(2): 023416
Zubairy M S, McIver J K. Second-harmonic generation by a partially coherent beam. Physical Review A, 1987, 36(1): 202–206
Cai Y, Peschel U. Second-harmonic generation by an astigmatic partially coherent beam. Optics Express, 2007, 15(23): 15480–15492
van Dijk T, Fischer D G, Visser T D, Wolf E. Effects of spatial coherence on the angular distribution of radiant intensity generated by scattering on a sphere. Physical Review Letters, 2010, 104(17): 173902
Ding C, Cai Y, Korotkova O, Zhang Y, Pan L. Scattering-induced changes in the temporal coherence length and the pulse duration of a partially coherent plane-wave pulse. Optics Letters, 2011, 36(4): 517–519
Kermisch D. Partially coherent image processing by laser scanning. Journal of the Optical Society of America, 1975, 65(8): 887–891
Gori F, Santarsiero M, Borghi R, Vicalvi S. Partially coherent sources with helicoidal modes. Optica Acta, 1998, 45(3): 539–554
Gbur G, Visser T D, Wolf E. ‘Hidden’ singularities in partially coherent wavefields. Journal of Optics A Pure & Applied Optics, 2004, 6(5): S239–S242
Visser T D, Gbur G, Wolf E. Effect of the state of coherence on the three-dimensional spectral intensity distribution near focus. Optics Communications, 2002, 213(1–3): 13–19
Bouchal Z, Perina J. Non-diffracting beams with controlled spatial coherence. Optica Acta, 2002, 49(10): 1673–1689
Gbur G, Visser T D. Coherence vortices in partially coherent beams. Optics Communications, 2003, 222(1–6): 117–125
Ponomarenko S A. A class of partially coherent beams carrying optical vortices. Journal of the Optical Society of America A, Optics, Image Science, and Vision, 2001, 18(1): 150–156
Maleev I D, Palacios D M, Marathay A S, Swartzlander G AJr. Spatial correlation vortices in partially coherent light: theory. Journal of the Optical Society of America B, Optical Physics, 2004, 21(11): 1895–1900
Jeng C C, Shih M F, Motzek K, Kivshar Y. Partially incoherent optical vortices in self-focusing nonlinear media. Physical Review Letters, 2004, 92(4): 043904
van Dijk T, Visser T D. Evolution of singularities in a partially coherent vortex beam. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 2009, 26(4): 741–744
Wang F, Zhu S, Cai Y. Experimental study of the focusing properties of a Gaussian Schell-model vortex beam. Optics Letters, 2011, 36(16): 3281–3283
Yang Y, Chen M, Mazilu M, Mourka A, Liu Y D, Dholakia K. Effect of the radial and azimuthal mode indices of a partially coherent vortex field upon a spatial correlation singularity. New Journal of Physics, 2013, 15(11): 113053
Qin Z, Tao R, Zhou P, Xu X, Liu Z. Propagation of partially coherent Bessel-Gaussian beams carrying optical vortices in non-Kolmogorov turbulence. Optics & Laser Technology, 2014, 56(33): 182–188
Zhang Z, Fan H, Xu H F, Qu J, Huang W. Three-dimensional focus shaping of partially coherent circularly polarized vortex beams using a binary optic. Journal of Optics, 2015, 17(6): 065611
Singh R K, Sharma A M, Senthilkumaran P. Vortex array embedded in a partially coherent beam. Optics Letters, 2015, 40(12): 2751–2754
Liu D, Wang Y, Yin H. Evolution properties of partially coherent flat-topped vortex hollow beam in oceanic turbulence. Applied Optics, 2015, 54(35): 10510–10516
Cheng M, Guo L, Li J, Huang Q, Cheng Q, Zhang D. Propagation of an optical vortex carried by a partially coherent Laguerre-Gaussian beam in turbulent ocean. Applied Optics, 2016, 55(17): 4642–4648
Zhang Y, Ma D, Zhou Z, Yuan X. Research on partially coherent flat-topped vortex hollow beam propagation in turbulent atmosphere. Applied Optics, 2017, 56(10): 2922–2926
Liu X, Peng X, Liu L, Wu G, Zhao C, Wang F, Cai Y. Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle. Applied Physics Letters, 2017, 110(18): 181104
Stahl C S D, Gbur G. Partially coherent vortex beams of arbitrary order. Journal of the Optical Society of America A, Optics, Image Science, and Vision, 2017, 34(10): 1793–1799
Liu D, Yin H, Wang G, Wang Y. Propagation of partially coherent Lorentz-Gauss vortex beam through oceanic turbulence. Applied Optics, 2017, 56(31): 8785–8792
Ostrovsky A S, García-García J, Rickenstorff-Parrao C, Olvera-Santamaría M A. Partially coherent diffraction-free vortex beams with a Bessel-mode structure. Optics Letters, 2017, 42(24): 5182–5185
Gori F, Santarsiero M. Devising genuine spatial correlation functions. Optics Letters, 2007, 32(24): 3531–3533
Gori F, Ramirezsanchez V, Santarsiero M, Shirai T. On genuine cross-spectral density matrices. Journal of Optics A, 2009, 11(8): 085706
Chen Y, Liu L, Wang F, Zhao C, Cai Y. Elliptical Laguerre-Gaussian correlated Schell-model beam. Optics Express, 2014, 22(11): 13975–13987
Tong Z, Korotkova O. Electromagnetic nonuniformly correlated beams. Journal of the Optical Society of America A, Optics, Image Science, and Vision, 2012, 29(10): 2154–2158
Lajunen H, Saastamoinen T. Non-uniformly correlated partially coherent pulses. Optics Express, 2013, 21(1): 190–195
Sahin S, Korotkova O. Light sources generating far fields with tunable flat profiles. Optics Letters, 2012, 37(14): 2970–2972
Zhang Y, Liu L, Zhao C, Cai Y. Multi-Gaussian Schell-model vortex beam. Physics Letters A, 2014, 378(9): 750–754
Chen Y, Wang F, Zhao C, Cai Y. Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam. Optics Express, 2014, 22(5): 5826–5838
Liu H, Chen D, Xia J, Lü Y, Zhang L, Pu X. Influences of uniaxial crystal on partially coherent multi-Gaussian Schell-model vortex beams. Optical Engineering (Redondo Beach, Calif.), 2016, 55(11): 116101
Liu X, Wang F, Liu L, Zhao C, Cai Y. Generation and propagation of an electromagnetic Gaussian Schell-model vortex beam. Journal of the Optical Society of America A, Optics, Image Science, and Vision, 2015, 32(11): 2058–2065
Zhang Y, Pan L, Cai Y. Propagation of Correlation Singularities of a Partially Coherent Laguerre-Gaussian Electromagnetic Beam in a Uniaxial Crystal. IEEE Photonics Journal, 2017, 9(4): 1–13
Guo L, Chen Y, Liu X, Liu L, Cai Y. Vortex phase-induced changes of the statistical properties of a partially coherent radially polarized beam. Optics Express, 2016, 24(13): 13714–13728
Zhao C, Cai Y. Trapping two types of particles using a focused partially coherent elegant Laguerre-Gaussian beam. Optics Letters, 2011, 36(12): 2251–2253
Liu X, Shen Y, Liu L, Wang F, Cai Y. Experimental demonstration of vortex phase-induced reduction in scintillation of a partially coherent beam. Optics Letters, 2013, 38(24): 5323–5326
Zeng J, Liu X, Wang F, Zhao C, Cai Y. Partially coherent fractional vortex beam. Optics Express, 2018, 26(21): 26830–26844
Perez-Garcia B, Yepiz A, Hernandez-Aranda R I, Forbes A, Swartzlander G A. Digital generation of partially coherent vortex beams. Optics Letters, 2016, 41(15): 3471–3474
Liu R, Wang F, Chen D, Wang Y, Zhou Y, Gao H, Zhang P, Li F. Measuring mode indices of a partially coherent vortex beam with Hanbury Brown and Twiss type experiment. Applied Physics Letters, 2016, 108(5): 051107
Pires H D, Woudenberg J, van Exter M P. Measurements of spatial coherence of partially coherent light with and without orbital angular momentum. Journal of the Optical Society of America A, Optics, Image Science, and Vision, 2010, 27(12): 2630–2637
Pires H D, Woudenberg J, van Exter M P. Measurement of the orbital angular momentum spectrum of partially coherent beams. Optics Letters, 2010, 35(6): 889–891
Zhao C, Wang F, Dong Y, Han Y, Cai Y. Effect of spatial coherence on determining the topological charge of a vortex beam. Applied Physics Letters, 2012, 101(26): 261104
Yang Y, Mazilu M, Dholakia K. Measuring the orbital angular momentum of partially coherent optical vortices through singularities in their cross-spectral density functions. Optics Letters, 2012, 37(23): 4949–4951
Escalante A Y, Perezgarcia B, Hernandezaranda R I, Swartzlander G A. Determination of angular momentum content in partially coherent beams through cross correlation measurements. In: Proceedings of SPIE Laser Beam Shaping. SPIE, 2013, 884302
Kotlyar V V, Almazov A A, Khonina S N, Soifer V A, Elfstrom H, Turunen J. Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate. Journal of the Optical Society of America A, Optics, Image Science, and Vision, 2005, 22(5): 849–861
Wang F, Cai Y, Korotkova O. Partially coherent standard and elegant Laguerre-Gaussian beams of all orders. Optics Express, 2009, 17(25): 22366–22379
Dennis M R, O’Holleran K, Padgett M J. Chapter 5 Singular Optics: Optical Vortices and Polarization Singularities. Progress in Optics, 2009, 53: 293–363
Bogatyryova G V, Fel’de C V, Polyanskii P V, Ponomarenko S A, Soskin M S, Wolf E. Partially coherent vortex beams with a separable phase. Optics Letters, 2003, 28(11): 878–880
Mandel L, Wolf E. Optical Coherence and Quantum Optics. Cambridge: Cambridge University Press, 2001, 1–1194
Palacios D M, Maleev I D, Marathay A S, Swartzlander G AJr. Spatial correlation singularity of a vortex field. Physical Review Letters, 2004, 92(14): 143905
Wolf E. Introduction to the Theory of Coherence and Polarization of Light. Cambridge: Cambridge University Press, 2007
Cai Y, Chen Y, Wang F. Generation and propagation of partially coherent beams with nonconventional correlation functions: a review. Journal of the Optical Society of America A, Optics, Image Science, and Vision, 2014, 31(9): 2083–2096
Ren Y X, Lu R D, Gong L. Tailoring light with a digital micromirror device. Annalen der Physik, 2015, 527(7–8): 447–470
De Santis P, Gori F, Guattari G, Palma C. An example of a Collett-Wolf source. Optics Communications, 1979, 29(3): 256–260
Ostrovsky A S, García E H. Modulation of spatial coherence of optical field by means of liquid crystal light modulator. Revista Mexicana de Física, 2005, 51(5): 442–446
Liu X, Wu T, Liu L, Zhao C, Cai Y. Experimental determination of the azimuthal and radial mode orders of a partially coherent LGpl beam. Chinese Optics Letters, 2017, 15(3): 030002–030006
Wang F, Liu X, Yuan Y, Cai Y. Experimental generation of partially coherent beams with different complex degrees of coherence. Optics Letters, 2013, 38(11): 1814–1816
Chen J, Liu X, Yu J, Cai Y. Simultaneous determination of the sign and the magnitude of the topological charge of a partially coherent vortex beam. Applied Physics B, Lasers and Optics, 2016, 122(7): 201
Polyanskii P V. Some current views on singular optics. In: Proceedings of SPIE 6th International Conference on Correlation Optics. SPIE, 2004, 31–41
Soskin M, Boriskina S V, Chong Y, Dennis M R, Desyatnikov A. Singular optics and topological photonics. Journal of Optics, 2017, 19(1): 010401
Acknowledgements
Authors are thankful for the support of the National Natural Science Foundation of China (Grant Nos. 91750201, 11525418, 11774250 and 11804198), Project of the Priority Academic Program Development of Jiangsu Higher Education Institutions.
Author information
Authors and Affiliations
Corresponding author
Additional information
Jun Zeng spent his bachelor time at Hubei University of Arts and Science (Xiangyang, China). He studied at Taiyuan University of Science and Technology (Taiyuan, China) for his Master’s degree in optics from 2013 to 2016. Since September 2017, he became a Ph.D. candidate in School of Physical Science and Technology at Soochow University (Suzhou, China). His research topics include singular optics, atmospheric optics and optical measurement.
Rong Lin spent her bachelor time at Heze University (Heze, China). she received her master’s degree in 2012 from Shandong Normal University (Jinan, China) in 2009. Since September 2012, she became a teacher in College of Physics and Electronic Engineering, Heze University. Since September 2018, she became a Ph.D. candidate in School of Physics and Electronics, Shandong Normal University. Her research topics include optical coherence and nonlinear optics.
Xianlong Liu spent his bachelor time at Yanbian University (Jilin), and got his master’s degree at Soochow University (Jiangsu) in 2013. Latter he became a Ph.D. candidate in School of Physical Science and Technology, Soochow University, and got his doctor’s degree at 2017. He spent a year in Netherland as a Joint Ph.D. student at VU University of Amsterdam in 2017. His research topic includes laser optics, atmospheric optics and optical imaging.
Chengliang Zhao is a professor of School of Physical Science and Technology, Soochow University, China. He received his Ph.D. degree in Physics from Zhejiang University. His research interests include coherent optics, diffractive imaging, phase retrieval and optical tweezers.
Yangjian Cai is a professor of School of Physical Science and Technology, Soochow University, and also a professor of School of Physics and Electronics, Shandong Normal University, China. He received his B.Sc. degree in Physics at Zhejiang University, Ph.D. degree in Physics at Zhejiang University and Ph.D. degree in Electromagnetic theory at Royal Institute of Technology. In 2015, he obtained the National Science Fund for Distinguished Young Scholars. His research interests include optical coherence and polarization, propagation, optical imaging, particle trapping, turbulent atmosphere. He has published over 300 papers in refereed international journals, and he is a topical editor of JOSA A, a topical editor of PhotoniX and an editorial board member of Progress in Optics.
Rights and permissions
About this article
Cite this article
Zeng, J., Lin, R., Liu, X. et al. Review on partially coherent vortex beams. Front. Optoelectron. 12, 229–248 (2019). https://doi.org/10.1007/s12200-019-0901-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12200-019-0901-x