Ukrainian Journal of Physical Optics

2023 Volume 24, Issue 1

ISSN 1816-2002 (Online), ISSN 1609-1833 (Print)

Optical vector vortices generated with circularly planar and circularly hybrid nematic cells

1Dudok T., 1Skab I., 1Mys O., Krupych O., 3Nastishin Yu. A., 4Kurochkin O., 4Nazarenko V., 3Ryzhov Ye., 3Chernenko A. D. and 1Vlokh R.

1O. G. Vlokh Institute of Physical Optics, 23 Dragomanov Street, 79005 Lviv, Ukraine
2Ivan Franko National University of Lviv, Faculty of Electronics and Computer Technologies, Department of Optoelectronics and Information Technologies, 107 Tarnavskyi Street, 79017 Lviv, Ukraine
3Hetman Petro Sahaidachnyi National Army Academy, 32 Heroes of Maidan Street, 79012 Lviv, Ukraine
4Institute of Physics, National Academy of Sciences of Ukraine, Kyiv 03028, Ukraine


Among the variety of optical elements used for the generation of vector and vortex light beams, liquid-crystal cells containing topological defects deserve a special attention. Nowadays, they represent one of the most popular techniques because of simplicity of their preparation. In this work we study optical singularities of the laser beams passing through a cell with a circular planar alignment of its director on both substrates, a so-called CC-cell. The other subject is a CH-cell with a circular planar alignment on one substrate and a homeotropic (i.e., perpendicular to the substrate plane) alignment on the opposite substrate. The CC- and CH-cells are characterized optically with both polarization optical microscopy and imaging polarimetry. The optical singularities of the object beams passing through these cells are visualized by means of their interference with quasi-spherical and quasi-plane-wave reference Gaussian beams. For the CC-cells, one expects formation of the defects with the topological strength q=+1 on the surfaces. Due to an effect of escape into a third dimension, a singular director distribution does not propagate through the bulk. While reviewing the literature on the applications of liquid-crystal disclinations for generating the singular beams, we have found that the escape of the director into the third dimension is usually ignored for integer-strength disclinations. We also analyze in detail how the escape into the third dimension manifests itself when the light propagates through the CC-cells. For the case of CH-cells, we find that the optical patterns obtained with the polarization optical microscopy, the imaging polarimetry and the interference techniques indicate that the circular symmetry of a sample structure is essentially broken.

Keywords: liquid crystals, optical vortices, topological defects, optical indicatrix, optical phase difference

UDC: 535.34, 535.37, 544.25

    1. Schatz M F and Neitzel G P, 2001. Experiments on thermocapillary instabilities. Ann. Rev. Fluid Mech. 33: 93-127. doi:10.1146/annurev.fluid.33.1.93
    2. Forbes A, 2019. Common elements for uncommon light: vector beams with GRIN lenses. Light Sci. Appl. 8: 111. doi:10.1038/s41377-019-0228-9
    3. Rongxuan Wang, Law A C, Garcia D, Shuo Yang and Zhenyu James Kong, 2021. Development of structured light 3D-scanner with high spatial resolution and its applications for additive manufacturing quality assurance. Int. J. Adv. Manuf. Technol. 117: 845-862. doi:10.1007/s00170-021-07780-2
    4. Wuchen Zhang, Deborah A Kosiorek and Amy N Brodeur, 2020. Application of structured-light 3-D scanning to the documentation of plastic fingerprint impressions: A quality comparison with traditional photography. J. Forensic Sci. 65: 784-790. doi:10.1111/1556-4029.14249
    5. Allen L, Beijersbergen M W, Spreeuw R J C and Woerdman J P, 1992. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys. Rev. A. 45: 8185-8189. doi:10.1103/PhysRevA.45.8185
    6. Qiwen Zhan, 2009. Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt. Photon. 1: 1-57. doi:10.1364/AOP.1.000001
    7. Mair A, Vaziri A, Weihs G and Zeilinger A, 2001. Entanglement of the orbital angular momentum states of photons. Nature. 412: 313-316. doi:10.1038/35085529
    8. Leach J, Jack B, Romero J, Jha A K, Yao A M, Franke-Arnold S, Ireland D G, Boyd R W, Barnett S M and Padgett M J, 2010. Quantum correlations in optical angle-orbital angular momentum variables. Science. 329: 662-665. doi:10.1126/science.1190523
    9. Quabis S, Dorn R, Eberler M, Glockl O and Leuchs G, 2000. Focusing light to a tighter spot. Opt. Commun. 179: 1-7. doi:10.1016/S0030-4018(99)00729-4
    10. Youngworth K S and Brown T G, 2000. Focusing of high numerical aperture cylindrical-vector beams. Opt. Express 7: 77-87. doi:10.1364/OE.7.000077
    11. Grier D G, 2003. A revolution in optical manipulation. Nature. 424: 810-816. doi:10.1038/nature01935
    12. Mawet D, Riaud P, Absil O and Surdej J, 2005. Annular groove phase mask coronagraph. Astro. Phys. 633: 1191-1200. doi:10.1086/462409
    13. Liu Y, Cline D and He P, 1999. Vacuum laser acceleration using a radially polarized CO2 laser beam. Nucl. Instrum. Meth. Phys Res. A. 424: 296-303. doi:10.1016/S0168-9002(98)01433-8
    14. Kimura W D, Kim G H, Romea R D, Steinhauer L C, Pogorelsky I V, Kusche K P, Fernow R C, Wang X and Liu Y, 1995. Laser acceleration of relativistic electrons using the inverse Cherenkov effect. Phys. Rev. Lett. 74: 546-549. doi:10.1103/PhysRevLett.74.546
    15. Basistiy V I, Soskin M S and Vasnetsov M V, 1995. Optical wavefront dislocations and their properties. Opt. Commun. 119: 604-612. doi:10.1016/0030-4018(95)00267-C
    16. Long Zhu and Jian Wang, 2014. Arbitrary manipulation of spatial amplitude and phase using phase-only spatial light modulators. Sci. Rep. 4: 7441. doi:10.1038/srep07441
    17. Long Zhu and Jian Wang, 2019. A review of multiple optical vortices generation: methods and applications. Front. Optoelectron. 12: 52-68. doi:10.1007/s12200-019-0910-9
    18. Beijersbergen M W, Coerwinkel R P C, Kristensen M and Woerdman J P, 1994. Helical-wavefront laser beams produced with a spiral phaseplate. Opt. Commun. 112: 321-327. doi:10.1016/0030-4018(94)90638-6
    19. Stalder M and Schadt M, 1996. Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters. Opt. Lett. 21: 1948-1950. doi:10.1364/OL.21.001948
    20. Zhi-Xiang Li, Ya-Ping Ruan, Peng Chen, Jie Tang, Wei Hu, Ke-Yu Xia and Yan-Qing Lu, 2021. Liquid crystal devices for vector vortex beams manipulation and quantum information applications [Invited]. Chin. Opt. Lett. 19: 112601. doi:10.3788/COL202119.112601
    21. Skab I, Vasylkiv Y, Savaryn V and Vlokh R, 2011. Optical anisotropy induced by torsion stresses in LiNbO3 crystals: appearance of an optical vortex. J. Opt. Soc. Amer. A. 28: 633-640. doi:10.1364/JOSAA.28.000633
    22. Skab I, Vasylkiv Yu, Smaga I and Vlokh R, 2011. Spin-to-orbital momentum conversion via electro-optic Pockels effect in crystals. Phys. Rev. A. 84: 043815. doi:10.1103/PhysRevA.84.043815
    23. Skab I, Vasylkiv Yu, Vlokh R, 2012. Induction of optical vortex in the crystals subjected to bending stresses. Appl. Opt. 51: 5797-5805 . doi:10.1364/AO.51.005797
    24. Niv A, Biener G, Kleiner V and Hasman E, 2004. Propagation-invariant vectorial Bessel beams obtained by use of quantized Pancharatnam-Berry phase optical elements. Opt. Lett. 29: 238-240. doi:10.1364/OL.29.000238
    25. Niv A, Biener G, Kleiner V and Hasman E, 2005. Rotating vectorial vortices produced by space-variant subwavelength gratings. Opt. Lett. 30: 2933-2935. doi:10.1364/OL.30.002933
    26. Niv A, Biener G, Kleiner V, Hasman E, 2006. Manipulation of the Pancharatnam phase in vectorial vortices. Opt. Express. 14: 4208-4220. doi:10.1364/OE.14.004208
    27. Oron R, Blit S, Davidson N, Friesem A A, Bomzon Z and Hasman E, 2000. The formation of laser beams with pure azimuthal or radial polarization. Appl. Phys. Lett. 77: 3322-3324. doi:10.1063/1.1327271
    28. Toussaint K C Jr, Park S, Jureller J E and Scherer N F, 2005. Generation of optical vector beams with a diffractive optical element interferometer. Opt. Lett. 30: 2846-2848. doi:10.1364/OL.30.002846
    29. Yao-Wei Huang, Rubin N A, Ambrosio A, Zhujun Shi, Devlin R C, Cheng-Wei Qiu and Capasso F, 2019. Versatile total angular momentum generation using cascaded J-plates. Opt. Express. 27: 7469-7484. doi:10.1364/OE.27.007469
    30. Rubano A, Cardano F, Piccirillo B and Marrucci L, 2019. Q-plate technology: a progress review [Invited]. J. Opt. Soc. Amer. B. 36: D70-D87. doi:10.1364/JOSAB.36.000D70
    31. Piccirillo B, D'Ambrosio V, Slussarenko S, Marrucci L and Santamato E, 2010. Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate. Appl. Phys. Lett. 97: 241104. doi:10.1063/1.3527083
    32. Slussarenko S, Piccirillo B, Chigrinov V, Marrucci L and Santamato E, 2013. Liquid crystal spatial-mode converters for the orbital angular momentum of light. J. Opt. 15: 025406. doi:10.1088/2040-8978/15/2/025406
    33. Nastishin Yu A, Dudok T, Savaryn V, Kostyrko M, Vasylkiv Yu, Hrabchak V, Ryzhov Ye and Vlokh R, 2021. Liquid crystal textures and optical characterization of a dye-doped nematic for generating vector beams. Ukr. J. Phys. Opt. 22: 151-164. doi:10.3116/16091833/22/3/151/2021
    34. Etienne Brasselet, Naoki Murazawa, Hiroaki Misawa and Saulius Juodkazis, 2009. Optical vortices from liquid crystal droplets. Phys. Rev. Lett. 103: 103903. doi:10.1103/PhysRevLett.103.103903
    35. Loussert C, Delabre U and Brasselet E, 2013. Manipulating the orbital angular momentum of light at the micron scale with nematic disclinations in a liquid crystal film. Phys. Rev. Lett. 111: 037802. doi:10.1103/PhysRevLett.111.037802
    36. Frank F C, 1958. I. Liquid crystals. On the theory of liquid crystals. Disc. Farad. Soc. 25: 19-28. doi:10.1039/df9582500019
    37. Moreno I, Sanchez-Lopez M M, Badham K, Davis J A and Cottrell D M, 2016. Generation of integer and fractional vector beams with q-plates encoded onto a spatial light modulator. Opt. Lett. 41:1305-1308. doi:10.1364/OL.41.001305
    38. Barboza R, Bortolozzo U, Assanto G, Vidal-Henriquez E, Clerc M G and Residori S, 2013. Harnessing optical vortex lattices in nematic liquid crystals. Phys. Rev. Lett. 111: 093902. doi:10.1103/PhysRevLett.111.093902
    39. Wei Ji, Chun-Hong Lee, Peng Chen, Wei Hu, Yang Ming, Lijian Zhang, Tsung-Hsien Lin, Vladimir Chigrinov and Yan-Qing Lu, 2016. Meta-q-plate for complex beam shaping. Sci. Rep. 6: 25528. doi:10.1038/srep25528
    40. Yao-Han Huang, Ming-Shian Li, Shih-Wei Ko and Andy Y-G Fuh, 2013. Helical wavefront and beam shape modulated by advanced liquid crystal q-plate fabricated via photoalignment and analysed by Michelson's interference. Appl. Opt. 52: 6557-6561. doi:10.1364/AO.52.006557
    41. Clark N L, 1985. Surface memory effects in liquid crystals: Influence of surface composition. Phys. Rev. Lett. 55: 292-295. doi:10.1103/PhysRevLett.55.292
    42. Marrucci L, Manzo C and Paparo D, 2006. Pancharatnam-Berry phase optical elements for wavefront shaping in the visible domain: switchable helical modes generation. Appl. Phys. Lett. 88: 221102. doi:10.1063/1.2207993
    43. Glushchenko A, Kresse H, Reshetnyak V, Reznikov Yu and Yaroshchuk O, 1997. Memory effect in filled nematic liquid crystals. Liq. Cryst. 23: 241- 246. doi:10.1080/026782997208505
    44. Nych A B, Reznikov D Yu, Boiko O P, Nazarenko V G, Pergamenshchik V M and Bos P, 2008. Alignment memory of a nematic liquid crystal and thermal isotropization of the surface adsorbed layer. Europhys. Lett. 81: 16001. doi:10.1209/0295-5075/81/16001
    45. Cladis P E and Kleman M, 1972. Non-singular disclinations of strength S = +1 in nematics. J. Physique. 33: 591-598. doi:10.1051/jphys:01972003305-6059100
    46. Meyer R, 1973. On the existence of even indexed disclinations in nematic liquid crystals. Phil. Mag. 27: 405-424. doi:10.1080/14786437308227417
    47. Melzer D and Nabarro F R N, 1977. Optical studies of a nematic liquid crystal with circumferential surface orientation in a capillary. Phil. Mag. 35: 901-906. doi:10.1080/14786437708232632
    48. Marrucci L, 2008. Generation of helical modes of light by spin-to-orbital angular momentum conversion in inhomogeneous liquid crystals. Mol. Cryst. Liq. Cryst. 488: 148-162. doi:10.1080/15421400802240524
    49. Nastishin Yu A and Dudok T H, 2013. Optically pumped mirrorless lasing. A review. Part I. Random lasing. Ukr. J. Phys. Opt. 14: 146-170. doi:10.3116/16091833/14/3/146/2013
    50. Dudok T H and Nastishin Yu, 2014. Optically pumped mirrorless lasing. A Review. Part II. Lasing in photonic crystals and microcavities. Ukr. J. Phys. Opt. 15: 47-67. doi:10.3116/16091833/15/2/47/2014
    51. Dudok T H, Krupych O M, Savaryn V I, Cherpak V V, Fechan A V, Gudeika D, Grazulevicius J V, Pansu B and Nastishin Yu A, 2014. Lasing in a cholesteric liquid crystal doped with derivative of triphenylamine and 1,8-naphthalimide, and optical characterization of the materials. Ukr. J. Phys. Opt. 15: 162-172. doi:10.3116/16091833/15/3/162/2014
    52. Dudok T H, Savaryn V I, Fechan AV, Cherpak V V, Pansu B and Nastishin Yu A, 2014. Dot lasers: isotropic droplets in a cholesteric matrix, and vice versa. Ukr. J. Phys. Opt. 15: 227-232. doi:10.3116/16091833/15/4/227/2014
    53. Dudok T H, Savaryn V I, Krupych O M, Fechan A V, Lychkovskyy E, Cherpak V V, Pansu B and Nastishin Yu A, 2015. Lasing in imperfectly aligned cholesterics. Appl. Opt. 54: 9644-9653. doi:10.1364/AO.54.009644
    54. Dudok T H, Savaryn V I, Meyer C, Cherpak V V, Fechan A V, Lychkovskyy E I, Pansu B and Nastishin Yu A, 2016. Lasing cholesteric capsules. Ukr. J. Phys. Opt. 17: 169-175. doi:10.3116/16091833/17/4/169/2016
    55. Chapran M, Angioni E, Findlay N J, Breig B, Cherpak V, Stakhira P, Tuttle T, Volyniuk D, Grazulevicius J V, Nastishin Yu A, Lavrentovich O D and Skabara P J, 2017. An ambipolar BODIPY derivative for a white exciplex OLED and cholesteric liquid crystal laser towards multi-functional devices. Appl. Mater. & Interfaces. 9: 4750−4757. doi:10.1021/acsami.6b13689
    56. Konstantinova A F, Grechushnikov B N, Bokut B V and Valyashko Ye G. Optical Properties of Crystals. Minsk: Navuka i Teknnika, 1995.
    57. Nastishin Yu A and Nastyshyn S Yu, 2011. Explicit representation of extended Jones matrix for oblique light propagation through a crystalline slab. Ukr. J. Phys. Opt. 12: 191-201. doi:10.3116/16091833/12/4/190/2011
    58. Nastishin Yu A and Nastyshyn S Yu, 2013. Differential and integral extended Jones matrices for oblique light propagation through a deformed crystal. Phys. Rev. A. 87: 033810. doi:10.1103/PhysRevA.87.033810
    59. Nastyshyn S Yu, Bolesta I M, Tsybulia S A, Lychkovskyy E, Yakovlev M Yu, Ryzhov Ye, Vankevych P I and Nastishin Yu A, 2018. Differential and integral Jones matrices for a cholesteric. Phys. Rev. A. 97: 053804. doi:10.1103/PhysRevA.97.053804
    60. Nastyshyn S Yu, Bolesta I M, Tsybulia S A, Lychkovskyy E, Fedorovych Z Ya, Khaustov D Ye, Ryzhov Ye, Vankevych P I and Nastishin Yu A, 2019. Optical spatial dispersion in terms of Jones calculus. Phys. Rev. A. 100: 013806. doi:10.1103/PhysRevA.100.013806
    61. Mauguin C, 1911. Sur les cristaux liquides de Lehman. Bull. Soc. Fr. Miner. Cristallogr. 34: 71-117. doi:10.3406/bulmi.1911.3472
    62. Guang-Hoon Kim, Hae June Lee, Jong-Uk Kim and Hyyong Suk, 2003. Propagation dynamics of optical vortices with anisotropic phase profiles. J. Opt. Soc. Amer. B. 20: 351-359. doi:10.1364/JOSAB.20.000351
    63. Kleman M. Points, lines and walls. In: Liquid crystals, magnetic systems and various ordered media. Chichester: Wiley, 1983.
    64. Nabarro F R N, 1972. Singular lines and singular points of ferromagnetic spin systems and of nematic liquid crystals. J. Physique. 33: 1089-1098. doi:10.1051/jphys:019720033011-120108900
    65. Nastishin Yu A, Polak R D, Shiyanovskii S V, Bodnar V H and Lavrentovich O D, 1999. Nematic polar anchoring strength measured by electric field techniques. J. Appl. Phys. 86: 4199-4213. doi:10.1063/1.371347
    66. Nastishin Yu A, Polak R D, Shiyanovskii S V and Lavrentovich O D, 1999. Determination of nematic polar anchoring from retardation versus voltage measurements. Appl. Phys. Lett. 75: 202-204. doi:10.1063/1.124319
    67. Shenoy D, Gruenberg K, Naciri J, Shashidhar R, Nastishin Yu, Polak R and Lavrentovich O D, 1999. Device properties and polar anchoring of nematic molecules at photodimerized surfaces. Proc. SPIE. 3635: 24-30. doi:10.1117/12.343869
    68. Nantomah K, 2018. On some properties and inequalities of the sigmoid function. RGMIA Res. Rep. Coll. 21: 89. doi:10.2139/ssrn.3903038
    69. Khaustov D Ye, Nastishin Yu A and Khaustov Ya Ye, 2021. Probability of the visual search task execution as a sigmoid function. Weap. Milit. Equip. 3: 80-94.
    70. Lavrentovich O D and Nastishin Yu A, 1987. Defects with nontrivial topological charges in hybrid-aligned films of nematic liquid crystal. Sov. Phys. Cryst. 34: 914-917
    71. Lavrentovich O D and Nastishin Yu A, 1990. Defects in degenerate hybrid aligned nematic liquid crystals. Europhys. Lett. 13: 135-141. doi:10.1209/0295-5075/12/2/008
    72. Kleman M and Laverntovich O D. Soft Matter Physics: an Introduction. New York: Springer-Verlag, 2003.
    73. Kleman M, Lavrentovich O D and Nastishin Yu A. Dislocation and disclination in mesomorphic phases. Vol. 12, pp. 147-271. In: Dislocations in Solids. Ed by Nabarro F R N and Hirth J P, Elsevier, 2004. doi:10.1016/S1572-4859(05)80005-1
    74. Slussarenko S, Murauski A, Chigrinov V, Tao Du, Marrucci L and Santamato E, 2011. Tunable liquid crystal q-plates with arbitrary topological charge. Opt. Express. 19: 4085-4090. doi:10.1364/OE.19.004085
    75. Susser A L, Harkai S, Kralj S and Rosenblatt C, 2020. Transition from escaped to decomposed nematic defects, and vice versa. Soft Matter. 16: 4814-4822. doi:10.1039/D0SM00218F
    76. White A G, Smith C P, Heckenberg N R, Rubinsztein-Dunlop H, McDuff R, Weiss C O and Tamm C, 1991. Interferometric measurements of phase singularities in the output of a visible laser. J. Mod. Opt. 38: 2531-2541. doi:10.1080/09500349114552651

    Анотація. Серед різноманіття оптичних елементів, які використовують для генерування векторних і вихрових світлових пучків, на окрему увагу заслуговують рідкокристалічні комірки, що містять топологічні дефекти. На сьогодні вони є однією з найпопулярніших методик через простоту їхнього приготування. У цій роботі досліджено оптичні сингулярності для лазерних променів, які проходять крізь комірку з круглим планарним розташуванням директора на обох підкладках (т.зв. CC-комірку). Інший об’єкт наших досліджень – це т.зв. CH-комірка з циркулярним планарним упорядкуванням на одній підкладці та гомеотропним (тобто перпендикулярним до площини підкладки) упорядкуванням на протилежній підкладці. Виконано оптичну характеризацію CC- і CH-комірок за допомогою поляризаційної оптичної мікроскопії та поляриметрії формування зображень. Оптичні особливості об’єктних пучків, що проходять крізь згадані комірки, візуалізовано за допомогою їхньої інтерференції з квазісферичними та квазіплоскохвильовими опорними ґаусовими пучками. Для CC-комірок очікується утворення на поверхнях дефектів із топологічною силою q=+1. Сингулярний розподіл директора не поширюється крізь об’єм комірки через ефект втечі в третій вимір. Аналізуючи літературу про застосування рідкокристалічних дисклінацій для генерування сингулярних пучків, ми виявили, що втечу директора в третій вимір зазвичай ігнорують для дисклінацій цілочисельної сили. Крім того, ми докладно проаналізували, як втеча в третій вимір виявляється при поширенні світла крізь CC-комірки. Для CH-комірок виявлено, що оптичні картини, одержані за допомогою поляризаційної оптичної мікроскопії, поляриметрії зображення та методів інтерференції, вказують на те, що кругова симетрія структури зразка істотно порушена.

    Ключові слова: рідкі кристали, оптичні вихори, топологічні дефекти, оптична індикатриса, оптична різниця фаз

© Ukrainian Journal of Physical Optics ©