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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">phmath</journal-id><journal-title-group><journal-title xml:lang="ru">Вестник Государственного университета просвещения. Серия: Физика-Математика</journal-title><trans-title-group xml:lang="en"><trans-title>Bulletin of Federal State University of Education. Series: Physics and Mathematics</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2949-5083</issn><issn pub-type="epub">2949-5067</issn><publisher><publisher-name>Federal State University of Education</publisher-name></publisher></journal-meta><article-meta><article-id custom-type="elpub" pub-id-type="custom">phmath-310</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ФИЗИКА</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>PHYSICS</subject></subj-group></article-categories><title-group><article-title>ОПТИЧЕСКИЕ СВОЙСТВА ЖК ЯЧЕЕК С ПРОИЗВОЛЬНЫМ КРАЕВЫМ УГЛОМ НАКЛОНА ДИРЕКТОРА</article-title><trans-title-group xml:lang="en"><trans-title>OPTICAL PROPERTIES OF THE LIQUID CRYSTAL IN CELLS WITH ARBITRARY LC DIRECTOR PRETILT ANGLE</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Беляев</surname><given-names>Виктор Васильевич</given-names></name><name name-style="western" xml:lang="en"><surname>Belyaev</surname><given-names>V. .</given-names></name></name-alternatives><email xlink:type="simple">vv.belyaev@mgou.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Соломатин</surname><given-names>Алексей Сергеевич</given-names></name><name name-style="western" xml:lang="en"><surname>Solomatin</surname><given-names>A. .</given-names></name></name-alternatives><email xlink:type="simple">assolomatin@hotmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Чаусов</surname><given-names>Денис Николаевич</given-names></name><name name-style="western" xml:lang="en"><surname>Chausov</surname><given-names>D. .</given-names></name></name-alternatives><email xlink:type="simple">dn.chausov@mgou.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Московский государственный областной университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Moscow Region State University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2013</year></pub-date><pub-date pub-type="epub"><day>08</day><month>01</month><year>2023</year></pub-date><volume>0</volume><issue>1</issue><fpage>32</fpage><lpage>40</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Беляев В.В., Соломатин А.С., Чаусов Д.Н., 2023</copyright-statement><copyright-year>2023</copyright-year><copyright-holder xml:lang="ru">Беляев В.В., Соломатин А.С., Чаусов Д.Н.</copyright-holder><copyright-holder xml:lang="en">Belyaev V..., Solomatin A..., Chausov D...</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.physmathmgou.ru/jour/article/view/310">https://www.physmathmgou.ru/jour/article/view/310</self-uri><abstract><p>Выполнена теоретическая и компьютерная модель зависимости разности фазовой задержки ∆Ф от угла преднаклона θ0 директора ЖК в ячейках как с однородным, так и с неоднородным распределением θ(z) директора по толщине ячейки. Рассмотрены конфигурации как с одинаковыми углами на противолежащих подложках ячейки, так и с разными углами. Предложен метод расчета зависимости нормированной разности фазовых задержек в зависимости от закона распределения угла наклона директора по толщине ячейки или, при известном законе распределения, от краевых углов (одинаковых или разных на противоположных сторонах). Метод применим для различных типов ячеек ЖК, с положительной или отрицательной диэлектрической анизотропией, однородно или неоднородно распределенных. В частности, он может применяться для расчета оптических компенсаторов.</p></abstract><trans-abstract xml:lang="en"><p>New optical and electro-optical methods of liquid crystal (LC) director pretilt angle measurement are described for LC cells with homogeneous and inhomogeneous LC director distribution. The LC pretilt on both LC substrates can have the same or opposite direction. Phase retardation difference of both extraordinary and ordinary polarized rays passing through a LC cell with homogeneous and inhomogeneous LC director distribution has been calculated vs. the LC pretilt angle θ0 on the cell’s substrates in the range 0≤θ0≤90°. Experimental procedure of phase retardation difference determination by measurement the LC cell transmission between crossed polarizers for the cells with the LC tilted alignment is described. The method developed can be used also in optical compensator design. A new method has been developed to measure the LC pretilt angle in the cells with sophisticated director configuration. It provides accurate data without LC cell mechanical rotation. A method of calculation of increments of the phase retardation difference for the cells with different boundary conditions and LC polarity is developed. The approach developed allows also a selection of the LC director configuration to change the LC cell phase retardation difference that can be used in optical compensator design. The method can be used for different LC cells with an arbitrary given LC director distribution and symmetric or asymmetric boundary conditions. Influence of Franck elastic coefficients on optical properties of such cells should be investigated. Main restriction of the method described is necessity of knowledge of the director distribution in the LC cell. In the case of unknown geometry of the cell application of other method (e.g., total internal reflection at the LC-orienting layer interface or reflection from an LC cell vs. applied voltage) is to use. Besides of the liquid crystal any other birefingent material can be used to develop optical elements of different application.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>ЖК ячейка</kwd><kwd>директор ЖК</kwd><kwd>краевой угол</kwd><kwd>гибридная ячейка</kwd><kwd>liquid crystal</kwd><kwd>LC director pretilt angle</kwd><kwd>LC director distribution</kwd><kwd>phase retardation difference</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Hanaoka K, Nakanishi Y, Inoue Y, Tanuma S, Koike Y. SID’04 Digest. 2004. pp.1200-1203.</mixed-citation><mixed-citation xml:lang="en">Hanaoka K, Nakanishi Y, Inoue Y, Tanuma S, Koike Y. 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