najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2023-14-1-74-85najo-191Research ArticlePHYSICSФИЗИКАElectric field effect on the light penetration depth and switching times in liquid crystal cells with nonuniform director orientationВлияние электрического поля на глубину проникновения света и времена переключения в жидкокристаллических ячейках с неоднородной ориентацией директораhttps://orcid.org/0000-0002-4324-1491АксеноваЕ. В.AksenovaE. V.

Санкт-Петербург.

Elena V. Aksenova,

7/9, Universitetskaya str., St. Petersburg, 199034.

e.aksenova@spbu.ruhttps://orcid.org/0000-0002-4267-8122КаретниковА. А.KaretnikovA. A.

Санкт-Петербург.

Aleksandr A. Karetnikov,

7/9, Universitetskaya str., St. Petersburg, 199034.

akaret@mail.ruhttps://orcid.org/0000-0002-3262-2790КаретниковН. А.KaretnikovN. A.

Санкт-Петербург.

Nikita A. Karetnikov,

49, bldg. A, Kronverksky Pr., St. Petersburg, 197101.

nkaret@mail.ruhttps://orcid.org/0000-0003-1326-2184КовшикА. П.KovshikA. P.

Санкт-Петербург.

Aleksandr P. Kovshik,

7/9, Universitetskaya str., St. Petersburg, 199034.

Sashakovshik@yandex.ruhttps://orcid.org/0000-0002-8278-3429СванидзеА. В.SvanidzeA. V.

Санкт-Петербург.

Anastasiya V. Svanidze,

7/9, Universitetskaya str., St. Petersburg, 199034;

281, W Lane Ave, Columbus, Ohio, 43210, USA.

avsvanidze@gmail.comhttps://orcid.org/0000-0002-6082-3733УльяновС. В.Ul’yanovS. V.

Санкт-Петербург.

Sergey V. Ul’yanov,

7/9, Universitetskaya str., St. Petersburg, 199034.

s.ulyanov@spbu.ruSaint Petersburg State UniversityRussian FederationITMO UniversityRussian FederationSaint Petersburg State University; Ohio State UniversityRussian Federation2023050620251417485Copyright © Aksenova E.V., Karetnikov A.A., Karetnikov N.A., Kovshik A.P., Svanidze A.V., Ul’yanov S.V., 20252025Аксенова Е.В., Каретников А.А., Каретников Н.А., Ковшик А.П., Сванидзе А.В., Ульянов С.В.Aksenova E.V., Karetnikov A.A., Karetnikov N.A., Kovshik A.P., Svanidze A.V., Ul’yanov S.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/191

The features of light refraction in liquid crystal cells with a continuously changing director distribution are studied. The theoretical description is constructed within the framework of the geometrical optics approximation. The neighborhoods of the turning points are considered, where due to the variable refractive index the ray smoothly changes the direction of propagation to the opposite one. It is shown that the applied electric field changes the nature of the extraordinary ray refraction. Electrically controlled refraction of light in cells with a planar and hybrid director orientation for incident angles exceeding the angle of total internal reflection is experimentally studied. The dependencies of the turn on and turn off times of the optical response on the applied voltage and the incident angles on the glass – liquid crystal boundary are obtained.

Исследованы особенности преломления света в жидкокристаллических ячейках с непрерывно меняющимся распределением директора. Теоретическое описание построено в рамках приближения геометрической оптики. Рассматриваются окрестности точек поворота, около которых луч плавно меняет направление распространения на противоположное из-за переменного показателя преломления. Показано, что приложенное электрическое поле меняет характер преломления необыкновенного луча. Экспериментально исследовано электроуправляемое преломление света в ячейках с планарной и гибридной ориентацией директора при углах падения, превышающих угол полного внутреннего отражения. Получены зависимости времен включения и выключения электрооптического отклика от приложенного напряжения и углов падения на границу стекло – жидкий кристалл.

преломлениежидкий кристаллвремя релаксациинеобыкновенная волнаглубина проникновенияrefractionliquid crystalrelaxation timeextraordinary wavepenetration depthA. V. Svanidze thanks for the support Saint Petersburg State University (Pure ID 28571656, IAS 11.41.1554.2017).ReferencesWu Shin-Tson, Yang Deng-Ke. Fundamentals of liquid crystal devices. John Wiley & Sons, Chichester., 2006, 394 p.Wu Shin-Tson, Yang Deng-Ke. Fundamentals of liquid crystal devices. John Wiley & Sons, Chichester., 2006, 394 p.Cai W., Shalaev V. Optical metamaterials. Springer, New York, 2010, 200 p.Cai W., Shalaev V. Optical metamaterials. Springer, New York, 2010, 200 p.Joannopoulos J., Meade R., Winn J., Johnson S. Photonic crystals. Princeton University Press, Princeton, 2008, 286 p.Joannopoulos J., Meade R., Winn J., Johnson S. Photonic crystals. Princeton University Press, Princeton, 2008, 286 p.Leslie F.M. Distortion of twisted orientation patterns in liquid crystals by magnetic fields. Mol. Cryst. Liq. Cryst, 1970, 12(1), P. 57–72.Leslie F.M. Distortion of twisted orientation patterns in liquid crystals by magnetic fields. Mol. Cryst. Liq. Cryst, 1970, 12(1), P. 57–72.Berreman D.W., Heffner W.R. New bistable liquid-crystal twist cell. J. Appl. Phys, 1981, 52, P. 3032–3039.Berreman D.W., Heffner W.R. New bistable liquid-crystal twist cell. J. Appl. Phys, 1981, 52, P. 3032–3039.Thurston R.N., Berreman D.W. Equilibrium and stability of liquid-crystal configurations in an electric field. J. Appl. Phys, 1981, 52(1), P. 508–509.Thurston R.N., Berreman D.W. Equilibrium and stability of liquid-crystal configurations in an electric field. J. Appl. Phys, 1981, 52(1), P. 508–509.Hiring R., Funk W., Trebin H.R., Shmidt M., Schmiedel H. Threshold behavior and electro-optical properties of twisted nematic layer with weak anchoring in the tilt and twist angle. J. Appl. Phys., 1991, 70(8), P. 4211–4216.Hiring R., Funk W., Trebin H.R., Shmidt M., Schmiedel H. Threshold behavior and electro-optical properties of twisted nematic layer with weak anchoring in the tilt and twist angle. J. Appl. Phys., 1991, 70(8), P. 4211–4216.Hong Qi, Wu T.X., Wu Shin-Tson. Optical wave propagation in a cholesteric liquid crystal using the finite element method. Liq. Cryst, 2003, 30(3), P. 367–375.Hong Qi, Wu T.X., Wu Shin-Tson. Optical wave propagation in a cholesteric liquid crystal using the finite element method. Liq. Cryst, 2003, 30(3), P. 367–375.Berreman D.W., Scheffer T.J. Order versus temperature in cholesteric liquid crystals from reflectance spectra. Phys.Rev. A, 1972, 5(3), P. 1397– 1403.Berreman D.W., Scheffer T.J. Order versus temperature in cholesteric liquid crystals from reflectance spectra. Phys.Rev. A, 1972, 5(3), P. 1397– 1403.Berreman D.W. Optics in stratified and anisotropic media: 4×4–matrix formulation. J. Opt. Soc. Am, 1972, 62, P. 502–510.Berreman D.W. Optics in stratified and anisotropic media: 4×4–matrix formulation. J. Opt. Soc. Am, 1972, 62, P. 502–510.Berreman D.W. Stratified media: optics in smoothly varying anisotropic planar structures: application to liquid-crystal twist cells. J. Opt. Soc. Am, 1973, 63, P. 1374–1380.Berreman D.W. Stratified media: optics in smoothly varying anisotropic planar structures: application to liquid-crystal twist cells. J. Opt. Soc. Am, 1973, 63, P. 1374–1380.Palto S.P. An algorithm for solving the optical problem for stratified anisotropic media. JETP, 2001, 92, P. 552–560.Palto S.P. An algorithm for solving the optical problem for stratified anisotropic media. JETP, 2001, 92, P. 552–560.Gevorgyan A.H. Photonic band gaps from a stack of right- and left-hand chiral photonic crystal layers. Phys. Rev. E, 2012, 85, P. 021704.Gevorgyan A.H. Photonic band gaps from a stack of right- and left-hand chiral photonic crystal layers. Phys. Rev. E, 2012, 85, P. 021704.Belyakov V.A., Dmitrienko V.E. Theory of the optical properties of cholesteric liquid crystals. Sov. Phys. Solid State, 1974, 15(9), P. 1811–1815.Belyakov V.A., Dmitrienko V.E. Theory of the optical properties of cholesteric liquid crystals. Sov. Phys. Solid State, 1974, 15(9), P. 1811–1815.Dmitrienko V.E., Belyakov V.A. Higher orders of the selective reflection of light by cholesteric liquid crystals. Sov. Phys. Solid State, 1974, 15(12), P. 2213–2216.Dmitrienko V.E., Belyakov V.A. Higher orders of the selective reflection of light by cholesteric liquid crystals. Sov. Phys. Solid State, 1974, 15(12), P. 2213–2216.Lakhtakia A., Weiglhofer W.S. Simple and exact analytic solution for oblique propagation in a cholesteric liquid crystal. Microwave Opt. Technol., 1996, 12, P. 245–248.Lakhtakia A., Weiglhofer W.S. Simple and exact analytic solution for oblique propagation in a cholesteric liquid crystal. Microwave Opt. Technol., 1996, 12, P. 245–248.Val’kov A.Yu., Aksenova E.V., Romanov V.P. First-order and continuous Freedericksz transitions in cholesteric liquid crystals.´ Phys. Rev. E, 2013, 87, P. 022508.Val’kov A.Yu., Aksenova E.V., Romanov V.P. First-order and continuous Freedericksz transitions in cholesteric liquid crystals.´ Phys. Rev. E, 2013, 87, P. 022508.Rokushima K., Yamakita J. Analysis of anisotropic dielectric gratings. J. Opt. Soc. Am., 1983, 73(7), P. 901–908.Rokushima K., Yamakita J. Analysis of anisotropic dielectric gratings. J. Opt. Soc. Am., 1983, 73(7), P. 901–908.Wang F., Lakhtakia A. Response of slanted chiral sculptured thin films to dipolar sources. Opt. Commun, 2004, 235, P. 133–151.Wang F., Lakhtakia A. Response of slanted chiral sculptured thin films to dipolar sources. Opt. Commun, 2004, 235, P. 133–151.Avendano-Alejo M. Analysis of the refraction of the extraordinary ray in a plane-parallel uniaxial plate with an arbitrary orientation of the optical axis. Optics Express, 2005, 13, P. 2549–2555.Avendano-Alejo M. Analysis of the refraction of the extraordinary ray in a plane-parallel uniaxial plate with an arbitrary orientation of the optical axis. Optics Express, 2005, 13, P. 2549–2555.Panasyuk G., Kelly J., Gartland E.C., Allender D.W. Geometrical optics approach in liquid crystal films with three-dimensional director variations. Phys.Rev. E, 2003, 67, P. 041702.Panasyuk G., Kelly J., Gartland E.C., Allender D.W. Geometrical optics approach in liquid crystal films with three-dimensional director variations. Phys.Rev. E, 2003, 67, P. 041702.Aksenova E.V., Karetnikov A.A., Kovshik A.P., Romanov V.P., Val’kov A.Yu. Return back of the extraordinary beam for oblique incidence in helical liquid crystals with large pitch. Europhys. Lett., 2005, 69(1), P. 68–74.Aksenova E.V., Karetnikov A.A., Kovshik A.P., Romanov V.P., Val’kov A.Yu. Return back of the extraordinary beam for oblique incidence in helical liquid crystals with large pitch. Europhys. Lett., 2005, 69(1), P. 68–74.Tenishchev S.S., Kiselev A.D., Ivanov A.V., Uzdin V.M. Multiple minimum-energy paths and scenarios of unwinding transitions in chiral nematic liquid crystals. Phys. Rev. E, 2019, 100, P. 062704.Tenishchev S.S., Kiselev A.D., Ivanov A.V., Uzdin V.M. Multiple minimum-energy paths and scenarios of unwinding transitions in chiral nematic liquid crystals. Phys. Rev. E, 2019, 100, P. 062704.Tenishchev S.S., Tambovtcev I.M., Kiselev A.D., Uzdin V.M. Hysteresis and Freedericksz thresholds for twisted states in chiral nematic liquid´ crystals: Minimum-energy path approach. Journal of Molecular Liquids, 2021, 325, P. 115242.Tenishchev S.S., Tambovtcev I.M., Kiselev A.D., Uzdin V.M. Hysteresis and Freedericksz thresholds for twisted states in chiral nematic liquid´ crystals: Minimum-energy path approach. Journal of Molecular Liquids, 2021, 325, P. 115242.de Gennes P.-G., Prost J. The Physics of liquid crystals, University Press, Oxford, 1993, 616 p.de Gennes P.-G., Prost J. The Physics of liquid crystals, University Press, Oxford, 1993, 616 p.Stewart I.W. The static and dynamic continuum theory of liquid crystals: a mathematical introduction, Liquid crystals book series. Taylor & Francis, London, 2004, 360 p.Stewart I.W. The static and dynamic continuum theory of liquid crystals: a mathematical introduction, Liquid crystals book series. Taylor & Francis, London, 2004, 360 p.Aksenova E.V., Karetnikov A.A., Kovshik A.P., Kryukov E.V., Romanov V.P. Propagation of light through a forbidden zone in chiral media. J. Opt. Soc. Amer. A, 2008, 25(3), P. 600–608.Aksenova E.V., Karetnikov A.A., Kovshik A.P., Kryukov E.V., Romanov V.P. Propagation of light through a forbidden zone in chiral media. J. Opt. Soc. Amer. A, 2008, 25(3), P. 600–608.Karetnikov A.A., Karetnikov N.A., Kovshik A.P., Ryumtsev E.I., Aksenova E.V., Kryukov E.V., Romanov V.P. Local dynamics of director reorientation under electric field in helical LC structure. Mol. Cryst. Liq. Cryst., 2012, 561(1), P. 97–106.Karetnikov A.A., Karetnikov N.A., Kovshik A.P., Ryumtsev E.I., Aksenova E.V., Kryukov E.V., Romanov V.P. Local dynamics of director reorientation under electric field in helical LC structure. Mol. Cryst. Liq. Cryst., 2012, 561(1), P. 97–106.Blinov L.M. Structure and properties of liquid crystals. Springer, Dordrecht, 2011, 439 p.Blinov L.M. Structure and properties of liquid crystals. Springer, Dordrecht, 2011, 439 p.Karetnikov N.A., Kovshik A.P., Karetnikov A.A., Ryumtsev E.I., Aksenova E.V., Svanidze A.V. Fast electro-optical response of a cell with a homeoplanar layer of a nematic liquid crystal. JETP Lett., 2017, 106(5), P. 313–316.Karetnikov N.A., Kovshik A.P., Karetnikov A.A., Ryumtsev E.I., Aksenova E.V., Svanidze A.V. Fast electro-optical response of a cell with a homeoplanar layer of a nematic liquid crystal. JETP Lett., 2017, 106(5), P. 313–316.

The authors declare that there are no conflicts of interest present.