Coherence modulation and topological charge measurement
of vortex field

doi:10.3969/j.issn.1007-5461.2022.02.004

Abstract

Abstract: Vortex field is a kind of special structured light field with spiral wavefront, which is widely used in optical micromanipulation, large-capacity optical communication and super-resolution imaging due to its physical properties such as phase singularity, orbital angular momentum and central dark core structure. By modulating the traditional physical dimensions of vortex field (amplitude, polarization andfrequency), the novel vortex fields with richer modes and wider application can be obtained. In addition, there is a very important regulation dimension of vortex field, that is coherence. Recently, researchers have obtained a novel type of vortex field, namely partially coherent vortex beam, by adjusting the coherence of vortex beam. Compared with fully coherent vortex beam, partially coherent vortex beam has more advantages in some fields, such as higher disturbance resistance to turbulent atmosphere, richer beam shaping, higher self-reconstruction ability and stronger particles trapping ability. In this paper, the research progress of the partially coherent integer vortex beams and the partially coherent fractional vortex beams in recent years is reviewed, and the theoretical model, generation method, transmission characteristics, topological charge measurement and application of partially coherent vortex beam are described in detail.

Key words: physical optics, singularity optics, vortex field, coherence modulation, partially coherent; topological charge measurement

CLC Number:

TN011

WANG Zhuoyi, ZENG Jun, ZHANG Hao, LU Xingyuan, ZHAO Chengliang∗, CAI Yangjian, ∗. Coherence modulation and topological charge measurement of vortex field[J]. Chinese Journal of Quantum Electronics, 2022, 39(2): 225-250.

References

[1] Berry, Michael.A Half-century of Physical Asymptotics and Other Diversions: Selected Works by Michael Berry [M]. World Scientific, 1974: 6-31。
[2]Coullet P, Gil L, Rocca F.Optical vortices[J].Optics Communications, 1989, 73(5):403-408
[3]Allen L, Beijersbergen M W, Spreeuw R J C, et al.Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes[J].Physical review A, 1992, 45(11):8185-8189
[4]Guo C, Yu Y, Hong Z.Optical sorting using an array of optical vortices with fractional topological charge[J].Optics communications, 2010, 283(9):1889-18930
[5]Dong M, Jiang D, Luo N, et al.Trapping two types of Rayleigh particles using a focused partially coherent anomalous vortex beam[J].Applied Physics B-Lasers and Optics, 2019, 125(4):1-8
[6]Zhao C L, Cai Y J, Lu X H, et al.Radiation force of coherent and partially coherent flat-topped beams on a Rayleigh particle[J].Optics Express, 2009, 17(3):1753-1765
[7]Liang C, Monfared Y E, Liu X, et al.Optimizing illumination’s complex coherence state for overcoming Rayleigh’s resolution limit[J].Chinese Optics Letters, 2021, 19(5):052601-052601
[8]Li Y, Cui Z, Han Y, et al.Channel capacity of orbital-angular-momentum-based wireless communication systems with partially coherent elegant Laguerre–Gaussian beams in oceanic turbulence[J].Journal of the Optical Society of America A, 2019, 36(4):471-477
[9]Peng J, Zhang L, Zhang K, et al.Channel capacity of OAM based FSO communication systems with partially coherent Bessel–Gaussian beams in anisotropic turbulence[J][J].Optics Communications, 2018, 418(1):32-36
[10]Gori F, Santarsiero M, Borghi R, et al.Partially coherent sources with helicoidal modes[J].Journal of Modern Optics, 1998, 45(3):539-554
[11] Wolf E.Introduction to the Theory of Coherence and Polarization of Light[M]. Cambridge University Press, 2007.174-194.
[12]Gori F, Guattari G, Padovani C.Bessel-gauss beams[J].Optics communications, 1987, 64(6):491-495
[13]Durnin J, Miceli J J, Eberly J H.Diffraction-Free Beams[J].Physical Review Letters, 1987, 58(15):1499-1501
[14]Wang F, Zhu S J, Cai Y J.Experimental study of the focusing properties of a Gaussian Schell-model vortex beam[J].Optics Letters, 2011, 36(16):3281-3283
[15]Chen Y H, Wang F, Zhao C L, et al.Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam[J].Optics Express, 2014, 22(5):5826-5838
[16]Zhang Y T, Liu L, Zhao C L, et al.Multi-Gaussian Schell-model vortex beam[J].Physics Letters A, 2014, 378(9):750-754
[17]Peng X F, Lu X Y, Liu X L, et al.Generation and Propagation of a Hermite-Gaussian Correlated Schell-Model LG(0l) Beam[J].Applied Sciences-Basel, 2019, 9(3):1-19
[18]Cai Y, Chen Y, Wang F.Generation and propagation of partially coherent beams with nonconventional correlation functions: a review [Invited][J].Journal of the Optical Society of America A, 2014, 31(9):2083-2096
[19]Deschamps J, Courjon D, Bulabois J.Gaussian Schell-model sources: an example and some perspectives[J].Journal of the Optical Society of America, 1983, 73(3):256-261
[20]Brandao P A, Cavalcanti S B.Topological charge identification of partially coherent light diffracted by a triangular aperture[J].Physics Letters A, 2016, 380(47):4013-4017
[21]Zhao C L, Dong Y, Wang Y M, et al.Experimental generation of a partially coherent Laguerre-Gaussian beam[J].Applied Physics B-Lasers and Optics, 2012, 109(2):345-349
[22]Zhao C, Wang F, Dong Y, et al.Effect of spatial coherence on determining the topological charge of a vortex beam[J].Applied Physics Letters, 2012, 101(26):261104-261104
[23]Liu X, Wu T, Liu L, et al.Experimental determination of the azimuthal and radial mode orders of a partially coherent LGpl beam[J].Chinese Optics Letters, 2017, 15(3):030002-030002
[24]Chen T C, Lu X Y, Zeng J, et al.Young's double-slit experiment with a partially coherent vortex beam[J].Optics Express, 2020, 28(25):38106-38114
[25]Wolf E.New theory of partial coherence in the space–frequency domainPart I: spectra and cross spectra of steady-state sources[J].Journal of the Optical Society of America A, 1982, 72(3):343-351
[26]Chen X, Li J, Rafsanjani S M H, et al.Synthesis of I-m-Bessel correlated beams via coherent modes[J].Optics Letters, 2018, 43(15):3590-3593
[27]Wang F, Lv H, Chen Y, et al.Three modal decompositions of Gaussian Schell-model sources: comparative analysis[J].Optics Express, 2021, 29(19):29676-29689
[28]Yang Y J, Zhu X L, Zeng J, et al.Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation[J].Nanophotonics, 2018, 7(3):677-682
[29]Perez-Garcia B, Yepiz A, Hernandez-Aranda R I, et al.Digital generation of partially coherent vortex beams[J].Optics Letters, 2016, 41(15):3471-3474
[30]Ostrovsky A S, García-García J, Rickenstorff-Parrao C, et al.Partially coherent diffraction-free vortex beams with a Bessel-mode structure[J].Optics Letters, 2017, 42(24):5182-5185
[31]Stoklasa B, Motka L, Rehacek J, et al.Wavefront sensing reveals optical coherence[J].Nature communications, 2014, 5(1):1-7
[32]Vaughan J M, Willetts D V.Interference properties of a light beam having a helical wave surface[J].Optics Communications, 1979, 30(3):263-267
[33]Berkhout G C G, Beijersbergen M W.Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects[J].Physical review letters, 2008, 101(10):100801-100801
[34]Mourka A, Baumgartl J, Shanor C, et al.Visualization of the birth of an optical vortex using diffraction from a triangular aperture[J].Optics Express, 2011, 19(7):5760-5771
[35]Guo C S, Yue S J, Wei G X.Measuring the orbital angular momentum of optical vortices using a multipinhole plate[J].Applied Physics Letters, 2009, 94(23):231104-231104
[36]Prabhakar S, Kumar A, Banerji J, et al.Revealing the order of a vortex through its intensity record[J].Optics Letters, 2011, 36(22):4398-4400
[37]Zhao P, Li S, Feng X, et al.Measuring the complex orbital angular momentum spectrum of light with a mode-matching method[J].Optics letters, 2017, 42(6):1080-1083
[38]Yang Y, Chen M, Mazilu M, et al.Effect of the radial and azimuthal mode indices of a partially coherent vortex field upon a spatial correlation singularity[J].New Journal of Physics, 2013, 15(11):113053-113053
[39]Lu X Y, Zhao C L, Shao Y F, et al.Phase detection of coherence singularities and determination of the topological charge of a partially coherent vortex beam[J][J].Applied Physics Letters, 2019, 114(20):201106-201106
[40]Wang T, Pu J X, Chen Z Y.Beam-spreading and topological charge of vortex beams propagating in a turbulent atmosphere[J].Optics Communications, 2009, 282(7):1255-1259
[41]Sztul H I, Alfano R R.Double-slit interference with Laguerre-Gaussian beams[J].Optics Letters, 2006, 31(7):999-1001
[42]Basistiy I V, Soskin M S, Vasnetsov M V.Optical wavefront dislocations and their properties[J].Optics Communications, 1995, 119(5-6):604-612
[43]Berry M V.Optical vortices evolving from helicoidal integer and fractional phase steps[J].Journal of Optics A: Pure and Applied Optics, 2004, 6(2):259-268
[44]Lee W M, Yuan X C, Dholakia K.Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step[J].Optics Communications, 2004, 239(1-3):129-135
[45]Gao J, Zhu Y, Wang D, et al.Bessel–Gauss photon beams with fractional order vortex propagation in weak non-Kolmogorov turbulence[J].Photonics Research, 2016, 4(2):30-34
[46]Gbur G.Fractional vortex Hilbert’s hotel[J].Optica, 2016, 3(3):222-225
[47]Yang Y, Zhu X, Zeng J, et al.Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation[J].Nanophotonics, 2018, 7(3):677-682
[48]Oemrawsingh S R, Aiello A, Eliel E R, et al.How to observe high-dimensional two-photon entanglement with only two detectors[J].Physical review letters, 2004, 92(21):217901-217901
[49]Calvo G F, Picón A, Bramon A.Measuring two-photon orbital angular momentum entanglement[J].Physical Review A, 2007, 75(1):012319-012319
[50]Tao S H, Yuan X C, Lin J, et al.Fractional optical vortex beam induced rotation of particles[J].Optics Express, 2005, 13(20):7726-7731
[51]Tkachenko G, Chen M, Dholakia K, et al.Is it possible to create a perfect fractional vortex beam?[J].Optica, 2017, 4(3):330-333
[52]Chen L, Lei J, Romero J.Quantum digital spiral imaging[J].Light: Science & Applications, 2014, 3(3):e153-e153
[53]Situ G, Warber M, Pedrini G, et al.Phase contrast enhancement in microscopy using spiral phase filtering[J].Optics Communications, 2010, 283(7):1273-1277
[54]Wang J, Zhang W, Qi Q, et al.Gradual edge enhancement in spiral phase contrast imaging with fractional vortex filters[J].Scientific reports, 2015, 5(1):1-6
[55]Zeng J, Liu X L, Wang F, et al.Partially coherent fractional vortex beam[J].Optics Express, 2018, 26(21):26830-26844
[56]Zeng J, Liang C H, Wang H Y, et al.Partially coherent radially polarized fractional vortex beam[J].Optics Express, 2020, 28(8):11493-11513
[57]Young T.XIV. An account of some cases of the production of colours,not hitherto described[J][J].Philosophical Transactions of the Royal Society of London, 1802, 92(0):387-397
[58]Zernike F.The concept of degree of coherence and its application to optical problems[J].Physica, 1938, 5(8):785-795
[59]Cai Y J, Chen C Y.Paraxial propagation of a partially coherent Hermite-Gaussian beam through aligned and misaligned ABCD optical systems[J].Journal of the Optical Society of America a-Optics Image Science and Vision, 2007, 24(8):2394-2401
[60]Lin Q, Cai Y J.Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams[J].Optics Letters, 2002, 27(4):216-218
[61]Schleich W P.Optical Coherence and Quantum Optics,by LMandel,EWolf[J].Science, 1996, 272(5270):1897-1898
[62]Palacios D M, Maleev I D, Marathay A S, et al.Spatial correlation singularity of a vortex field[J].Physical review letters, 2004, 92(14):143905-143905
[63]Wang F, Cai Y, Korotkova O.Partially coherent standard and elegant Laguerre-Gaussian beams of all orders[J].Optics express, 2009, 17(25):22366-22379
[64]Wang T, Pu J, Chen Z.Propagation of partially coherent vortex beams in a turbulent atmosphere[J].Optical Engineering, 2008, 47(3):036002-036002
[65]Wang F, Cai Y, Eyyuboglu H T, et al.Average Intensity and Spreading of Partially Coherent Standard and Elegant Laguerre-Gaussian Beams in Turbulent Atmosphere[J][J].Progress in Electromagnetics Research-Pier, 2010, 103(0):33-56
[66]Soskin M S, Gorshkov V N, Vasnetsov M V, et al.Topological charge and angular momentum of light beams carrying optical vortices[J].Physical Review A, 1997, 56(5):4064-4075
[67]Bogatyryova G V, Fel' de C V, Polyanskii P V, et al.Partially coherent vortex beams with a separable phase[J].Optics Letters, 2003, 28(11):878-880
[68]Gbur G, Visser T D.Coherence vortices in partially coherent beams[J].Optics Communications, 2003, 222(1-6):117-125
[69]Swartzlander G A, Schmit J.Temporal correlation vortices and topological dispersion[J].Physical Review Letters, 2004, 93(9):093901-093901
[70]Siegman A E.Hermite-Gaussian Functions of Complex Argument as Optical-Beam Eigenfunctions[J].Journal of the Optical Society of America, 1973, 63(9):1093-1094
[71]Takenaka T, Yokota M, Fukumitsu O.Propagation of light beams beyond the paraxial approximation[J].Journal of the Optical Society of America A, 1985, 2(6):826-829
[72]Zauderer E.Complex Argument Hermite-Gaussian and Laguerre-Gaussian Beams[J].Journal of the Optical Society of America a-Optics Image Science and Vision, 1986, 3(4):465-469
[73]Saghafi S, Sheppard C J R.Near field and far field of elegant Hermite-Gaussian and Laguerre-Gaussian modes[J].Journal of Modern Optics, 1998, 45(10):1999-2009
[74]Berry M V, Balazs N L.Nonspreading wave packets[J].American Journal of Physics, 1979, 47(3):264-267
[75]Siviloglou G A, Christodoulides D N.Accelerating finite energy Airy beams[J].Optics Letters, 2007, 32(8):979-981
[76]Sahin S, Korotkova O.Light sources generating far fields with tunable flat profiles[J].Optics Letters, 2012, 37(14):2970-2972
[77]Korotkova O, Sahin S, Shchepakina E.Multi-Gaussian Schell-model beams[J].Journal of the Optical Society of America A, 2012, 29(10):2159-2164
[78]Liang C, Wang F, Liu X, et al.Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry[J].Optics Letters, 2014, 39(4):769-772
[79]Gori F, Santarsiero M.Devising genuine spatial correlation functions[J].Optics Letters, 2007, 32(24):3531-3533
[80]Gori F, Ramírez-Sánchez V, Santarsiero M, et al.On genuine cross-spectral density matrices[J].Journal of Optics A: Pure and Applied Optics, 2009, 11(8):085706-085706
[81]Martínez-Herrero R, Mejías P M, Gori F.Genuine cross-spectral densities and pseudo-modal expansions[J].Optics Letters, 2009, 34(9):1399-1401
[82]Martínez-Herrero R, Mejías P M.Elementary-field expansions of genuine cross-spectral density matrices[J].Optics Letters, 2009, 34(15):2303-2305
[83]Dong Y M, Wang F, Zhao C L, et al.Effect of spatial coherence on propagation,tight focusing,and radiation forces of an azimuthally polarized beam[J].Physical Review A, 2012, 86(1):013840-013840
[84]Wang F, Cai Y, Dong Y, et al.Experimental generation of a radially polarized beam with controllable spatial coherence[J].Applied Physics Letters, 2012, 100(5):051108-051108
[85]Nie Z Q, Shi G, Li D Y, et al.Tight focusing of a radially polarized Laguerre-Bessel-Gaussian beam and its application to manipulation of two types of particles[J].Physics Letters A, 2015, 379(9):857-863
[86]Guo L N, Chen Y H, Liu X L, et al.Vortex phase-induced changes of the statistical properties of a partially coherent radially polarized beam[J].Optics Express, 2016, 24(13):13714-13728
[87] Goodman J W.Statistical optics[M]. John Wiley & Sons, 2015.
[88]Wang F, Wu G, Liu X, et al.Experimental measurement of the beam parameters of an electromagnetic Gaussian Schell-model source[J].Optics Letters, 2011, 36(14):2722-2724
[89]Wang F, Cai Y.Experimental generation of a partially coherent flat-topped beam[J].Optics Letters, 2008, 33(16):1795-1797
[90]Farina J D, Narducci L M, Collett E.Generation of highly directional beams from a globally incoherent source[J].Optics Communications, 1980, 32(2):203-208
[91]He Q, Turunen J, Friberg A T.Propagation and imaging experiments with Gaussian Schell-model beams[J].Optics communications, 1988, 67(4):245-250
[92]Carter W H, Bertolotti M.An analysis of the far-field coherence and radiant intensity of light scattered from liquid crystals[J].Journal of the Optical Society of America A, 1978, 68(3):329-333
[93]Ostrovsky A S, Garcia-Garcia J, Rickenstorff-Parrao C, et al.Partially coherent diffraction-free vortex beams with a Bessel-mode structure[J].Optics Letters, 2017, 42(24):5182-5185
[94] Mandel L, Wolf E.Optical coherence and quantum optics[M]. Cambridge university press, 1995.
[95]Wang F, Liu X L, Yuan Y S, et al.Experimental generation of partially coherent beams with different complex degrees of coherence[J].Optics Letters, 2013, 38(11):1814-1816
[96]Zhu X, Wang F, Zhao C, et al.Experimental realization of dark and antidark diffraction-free beams[J].Optics Letters, 2019, 44(9):2260-2263
[97]Wolf E.New spectral representation of random sources and of the partially coherent fields that they generate[J].Optics Communications, 1981, 38(1):3-6
[98]Wolf E.New theory of partial coherence in the space–frequency domainPart I: spectra and cross spectra of steady-state sources[J].Journal of the Optical Society of America A, 1982, 72(3):343-351
[99]Starikov A, Wolf E.Coherent-mode representation of Gaussian Schell-model sources and of their radiation fields[J].Journal of the Optical Society of America A, 1982, 72(7):923-928
[100]Basu S, Hyde M W, Xiao X, et al.Computational approaches for generating electromagnetic Gaussian Schell-model sources[J].Optics express, 2014, 22(26):31691-31707
[101]Tong R, Dong Z, Chen Y, et al.Fast calculation of tightly focused random electromagnetic beams: controlling the focal field by spatial coherence[J].Optics Express, 2020, 28(7):9713-9727
[102] Liu X, Liu L, Chen Y, et al.Partially coherent vortex beam: from theory to experiment[J].Vortex Dynamics and Optical Vortices, 2017: , 2017, 1(1):275-296
[103]Dong M, Lu X Y, Zhao C L, et al.Measuring topological charge of partially coherent elegant Laguerre-Gaussian beam[J].Optics Express, 2018, 26(25):33035-33043
[104] Cui S W, Chen Z Y, Pu J X.Generation and propagation of partially coherent vortex beams[J].Chinese Optics Letters, 2014, 5(1):77-80
[105]Liu X, Peng X, Liu L, et al.Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle[J].Applied Physics Letters, 2017, 110(18):181104-181104
[106]Zeng J, Lu X Y, Liu L X, et al.Simultaneous measurement of the radial and azimuthal mode indices of a higher-order partially coherent vortex beam based on phase detection[J].Optics Letters, 2019, 44(15):3881-3884
[107]Ostrovsky A S, Rickenstorff-Parrao C, Arrizón V.Generation of the perfect optical vortex using a liquid-crystal spatial light modulator[J].Optics Letters, 2013, 38(4):534-536
[108]Wang H, Liu L X, Zhou C D, et al.Vortex beam generation with variable topological charge based on a spiral slit[J].Nanophotonics, 2019, 8(2):317-324
[109]Chen J, Liu X, Yu J, et al.Simultaneous determination of the sign and the magnitude of the topological charge of a partially coherent vortex beam[J].Applied Physics B, 2016, 122(7):1-12
[110] Liao K-S, Chen Z-Y, Pu J-X.Measuring the Topological Charge of Vortex Beams with Young' s Double-Slit Interference Experiment[J].Journal of Huaqiao University (Natural Science), 2009, 6(0):623-627
[111] Yang Y J, Liu Y D.Measuring azimuthal and radial mode indices of a partially coherent vortex field[J].Journal of Optics, 2016, 18(1):015604-015604
[112]Malik M, Murugkar S, Leach J, et al.Measurement of the Orbital Angular Momentum Spectrum of Partially Coherent Fields using Double Angular Slit Interference[J].Physical Review A, 2012, 86(1):063806-063806
[113] Yan Y, Yue Y, Huang H, et al.Multicasting in a spatial division multiplexing system based on optical orbital angular momentum[J].Optics Letters, 2013, 38(19):3930-3933
[114] Zhou H, Dong J, Zhang J, et al.Retrieving orbital angular momentum distribution of light with plasmonic vortex lens[J].Scientific Reports, 2016, 6(1):27265-27265
[115] Zhou H L, Fu D Z, Dong J J, et al.Orbital angular momentum complex spectrum analyzer for vortex light based on the rotational Doppler effect[J], 2017, 006(002): 119-126.[J].Light: Science & Applications, 2017, 6(0):16251-16251
[116]Chen Y H, Wang F, Liu L, et al.Generation and propagation of a partially coherent vector beam with special correlation functions[J].Physical Review A, 2014, 89(1):013801-013801
[117]Liu Z, Yan S, Liu H, et al.Superhigh-resolution recognition of optical vortex modes assisted by a deep-learning method[J].Physical review letters, 2019, 123(18):183902-183902
[118]Yu J, Huang Y, Wang F, et al.Scintillation properties of a partially coherent vector beam with vortex phase in turbulent atmosphere[J].Optics Express, 2019, 27(19):26676-26688
[119]Gu Y, Gbur G.Scintillation of nonuniformly correlated beams in atmospheric turbulence[J].Optics letters, 2013, 38(9):1395-1397
[120]Porat G, Dolev I, Barlev O, et al.Airy beam laser[J].Optics Letters, 2011, 36(20):4119-4121
[121]Lin Y, Seka W, Eberly J H, et al.Experimental Investigation of Bessel Beam Characteristics[J].Applied Optics, 1992, 31(15):2708-2713
[122]Zhu K C, Li S X, Tang Y, et al.Study on the propagation parameters of Bessel-Gaussian beams carrying optical vortices through atmospheric turbulence[J].Journal of the Optical Society of America a-Optics Image Science and Vision, 2012, 29(3):251-257
[123]Peng D, Huang Z, Liu Y, et al.Optical coherence encryption with structured random light[J].PhotoniX, 2021, 2(1):1-15
[124]Peng X, Wang H, Liu L, et al.Self-reconstruction of twisted Laguerre-Gaussian Schell-model beams partially blocked by an opaque obstacle[J].Optics Express, 2020, 28(21):31510-31523
[125]Au?ón J, Nieto-Vesperinas M.Partially coherent fluctuating sources that produce the same optical force as a laser beam[J].Optics letters, 2013, 38(15):2869-2872
[126]Li Y.Light beams with flat-topped profiles[J].Optics letters, 2002, 27(12):1007-1009
[127]Zhao C, Cai Y J O L.Trapping two types of particles using a focused partially coherent elegant Laguerre–Gaussian beam[J],2011,36(12): 2251-2253[J].Optics letters, 2011, 36(12):2251-2253

Coherence modulation and topological charge measurement of vortex field

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