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Limits of applicability of the direct ray approximation in modeling optical properties of liquid-crystal diffraction gratings
D.D. Yakovlev 1, D.A. Yakovlev 1
1 Saratov State University, Saratov, Russia
PDF, 1008 kB
DOI: 10.18287/2412-6179-CO-562
Pages: 40-52.
Full text of article: Russian language.
Abstract:
Using computer modeling, we estimate limits of applicability of the direct ray approximation in modeling the optical properties of liquid-crystal diffraction gratings with continuous spatial modulation of the local optic axis orientation in a liquid crystal layer. The data presented concerning the influence of the spatial frequency and character of modulation of the local optic axis, as well as the magnitude of birefringence of the medium, on the accuracy of the results obtained in this approximation are also useful in considering birefringent layers with an aperiodic variation of the local optic axis.
Keywords:
diffraction and gratings, optical devices, physical optics, birefringent diffraction gratings, direct ray approximation, modal grating method.
Citation:
Yakovlev DD, Yakovlev DA. Limits of applicability of the direct ray approximation in modeling optical properties of liquid-crystal diffraction gratings. Computer Optics 2020; 44(1): 40-52. DOI: 10.18287/2412-6179-CO-562.
Acknowledgements:
This work was supported by the Ministry of Education and Science of the Russian Federation under Grant #3.1586.2017/4.6 and the Russian Foundation for Basic Research under Grant #18-52-16025/18.
References:
- Schadt M, Seiberie H, Schuster A. Optical patterning of multi-domain liquid-crystal displays with wide viewing angles. Nature 1996; 381(6579): 212-215. DOI: 10.1038/381212a0.
- Eakin JN, Xie Y, Pelcovits RA, Radcliffe MD, Crawford GP. Zero voltage Freedericksz transition in periodically aligned liquid crystals. Appl Phys Lett 2004; 85(10): 1671-1673. DOI: 10.1063/1.1789578.
- Escuti MJ, Jones WM. Polarization-independent switching with high contrast from a liquid crystal polarization grating. SID Symposium Digest of Technical Papers 2006; 37(1): 1443-1446. DOI: 10.1889/1.2433259.
- Provenzano C, Pagliusi P, Cipparrone G. Highly efficient liquid crystal based diffraction grating induced by polarization holograms at the aligning surfaces. Appl Phys Lett 2006; 89(12): 121105. DOI: 10.1063/1.2355456.
- Sarkissian H, Serak SV, Tabiryan NV, Glebov LB, Rotar V, Zeldovich BYa. Polarization-controlled switching between diffraction orders in transverse-periodically aligned nematic liquid crystals. Opt Lett 2006; 31(15): 2248-2250. DOI: 10.1364/OL.31.002248.
- Komanduri RK, Escuti MJ. Elastic continuum analysis of the liquid crystal polarization grating. Phys Rev E 2007; 76(2): 021701. DOI: 10.1103/PhysRevE.76.021701.
- Komanduri RK, Jones WM, Oh C, Escuti MJ. Polarization-independent modulation for projection displays using small-period LC polarization gratings. Journal of the Society for Information Display 2007; 15(8): 589-594. DOI: 10.1889/1.2770860.
- Nicolescu E, Escuti MJ. Polarization-independent tunable optical filters based on liquid crystal polarization gratings. Proc SPIE 2007; 6654: 665405. DOI: 10.1117/12.735305.
- Serak S, Tabiryan N, Zeldovich B. High-efficiency 1.5 mm thick optical axis grating and its use for laser beam combining. Opt Express 2007; 32(2): 169-171. DOI: 10.1364/OL.32.000169.
- Komanduri RK, Escuti MJ. High efficiency reflective liquid crystal polarization gratings. Appl Phys Lett 2009; 95(9): 091106. DOI: 10.1063/1.3197011.
- Nersisyan SR, Tabiryan NV, Steeves DM, Kimball BR. Characterization of optically imprinted polarization gratings. Appl Opt 2009; 48(21): 4062-4067. DOI: 10.1364/AO.48.004062.
- Nicolescu E, Escuti MJ. Polarization-independent tunable optical filters using bilayer polarization gratings. Appl Opt 2010; 49(20): 3900-3904. DOI: 10.1364/AO.49.003900.
- Kudenov MW, Escuti MJ, Dereniak EL, Oka K. White-light channeled imaging polarimeter using broadband polarization gratings. Appl Opt 2011; 50(15): 2283-2293. DOI: 10.1364/AO.50.002283.
- Crawford GP, Eakin JN, Radcliffe MD, Callan-Jones A, Pelcovits RA. Liquid-crystal diffraction gratings using polarization holography alignment techniques. J Appl Phys 2005; 98(12): 123102. DOI: 10.1063/1.2146075.
- Wu WY, Li MS, Lin HC, Fuh AY-G. Two-dimensional holographic polarization grating formed on azo-dye-doped polyvinyl alcohol films. J Appl Phys 2008; 103(8): 083119. DOI: 10.1063/1.2907959.
- Hu W, Srivastava AK, Lin X-W, Liang X, Wu Z-J, Sun J-T, Zhu G, Chigrinov V, Lu Y-Q. Polarization independent liquid crystal gratings based on orthogonal photoalignments. Appl Phys Lett 2012; 100(11): 111116. DOI: 10.1063/1.3694921.
- Honma M, Nose T. Twisted nematic liquid crystal polarization grating with the handedness conservation of a circularly polarized state. Opt Express 2012; 20(16): 18449-18458. DOI: 10.1364/OE.20.018449.
- Kawai K, Sasaki T, Noda K, Kawatsuki N, Ono H. Simple fabrication of liquid crystal-line grating cells with homogeneous and twisted nematic structures and effects of orientational relaxation on diffraction properties. Appl Opt 2014; 53(17): 3679-3686. DOI: 10.1364/AO.53.003679.
- Kawai K, Sasaki T, Sakamoto M, Noda K, Kawatsuki N, Ono H. Diffraction properties of a vector grating liquid crystal cell fabricated using a one-step expo-sure of a nonorthogonal elliptically polarized interference beam. J Opt Soc Am B 2015; 32(12): 2435-2440. DOI: 10.1364/JOSAB.32.002435.
- Kawai K, Sasaki T, Noda K, Sakamoto M, Kawatsuki N, Ono H. Holographic binary grating liquid crystal cells fabricated by one-step exposure of photocrosslinkable polymer liquid crystalline alignment substrates to a polarization interference ultraviolet beam. Appl Opt 2015; 54(19): 6010-6018. DOI: 10.1364/AO.54.006010.
- Provenzano C, Pagliusi P, Cipparrone G. Electrically tunable two-dimensional liquid crystals gratings induced by polarization holography. Opt Express 2007; 15(9): 5872-5878. DOI: 10.1364/OE.15.005872.
- Ringsdorf H, Urban C, Knoll W, Sawodny M. Photoreactive chiral liquid-crystalline side-group copolymers containing azobenzene mesogens. Die Makromolekulare Chemie 1992; 193(5): 1235-1247. DOI: 10.1002/macp.1992.021930520.
- Bobrovsky A, Ryabchun A, Cigl M, Hamplová V, Kašpar M, Hampl F, Shibaev V. New azobenzene-based chiral-photochromic substances with thermally stable Z-isomers and their use for the induction of a cholesteric mesophase with a phototunable helix pitch. J Mater Chem C 2014; 2(40): 8622-8629. DOI: 10.1039/C4TC01167H.
- Ryabchun A, Bobrovsky A, Stumpe J, Shibaev V. Rotatable diffraction gratings based on cholesteric liquid crystals with phototunable helix pitch. Adv Opt Mater 2015; 3(9): 1273-1279. DOI: 10.1002/adom.201500159.
- Ryabchun A, Yakovlev D, Bobrovsky A, Katsonis N. Dynamic diffractive patterns in helix-inverting cholesteric liquid crystals. ACS Appl Mater Interfaces 2019; 11(11): 10895-10904. DOI: 10.1021/acsami.8b22465.
- Li WS, Shen Y, Chen ZJ, Cui Q, Li SS, Chen LJ Demonstration of patterned polymer-stabilized cholesteric liquid crystal textures for anti-counterfeiting two-dimensional barcodes. Appl Opt 2017; 56(3): 601-606. DOI: 10.1364/AO.56.000601.
- Yakovlev DA, Tsoy VI, Chigrinov VG. 5.4: Advanced tools for modeling of 2D-optics of LCDs. SID Symposium Digest of Technical Papers 2005; 36(1): 58-61. DOI: 10.1889/1.2036508.
- Carroll TO. Liquid-crystal diffraction grating. J Appl Phys 1972; 43(3): 767-770. DOI: 10.1063/1.1661277.
- Desimpel C, Neyts K, Olivero D, Oldano C, de Boer DKG, Cortie R. Optical transmission model for thin two-dimensional layers. Molecular Crystals and Liquid Crystals 2004; 422(1): 185-195. DOI: 10.1080/15421400490502526.
- Yakovlev DA. Chigrinov VG, Kwok H-S. Modeling and optimization of LCD optical performance. Chichester: Wiley; 2015.
- Rokushima K, Yamakita J. Analysis of anisotropic dielectric gratings. J Opt Soc Am A 1983; 73(7): 901-908. DOI: 10.1364/JOSA.73.000901.
- Matsumoto K, Rokushima K, Yamakita J. Three-dimensional rigorous analysis of dielectric grating waveguides for general cases of oblique propagation. J Opt Soc Am A 1993; 10(2): 269-276. DOI: 10.1364/JOSAA.10.000269.
- Galatola P, Oldano C, Sunil Kumar PB. Symmetry properties of anisotropic dielectric gratings. J Opt Soc Am A 1994; 11(4): 1332-1341. DOI: 10.1364/JOSAA.11.001332.
- Li L. Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings. J Opt Soc Am A 1996; 13(5): 1024-1035. DOI: 10.1364/JOSAA.13.001024.
- Li L. New formulation of the Fourier modal method for crossed surface-relief gratings. J Opt Soc Am A 1997, 14(10): 2758-2767. DOI: 10.1364/JOSAA.14.002758.
- Peverini OA, Olivero D, Oldano C, de Boer DKG, Cortie R, Orta R, Tascone R. Reduced-order model technique for the analysis of anisotropic inhomogeneous media: application to liquid-crystal displays. J Opt Soc Am A 2002; 19(9): 1901-1909. DOI: 10.1364/JOSAA.19.001901.
- Olivero D, Oldano C. Numerical methods for light propagation in large LC cells: a new approach. Liquid Crystals 2003; 30(3): 345-353. DOI: 10.1080/0267829031000080996.
- Moharam MG, Pommet DA, Grann EB, Gaylord TK. Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach. J Opt Soc Am A 1995; 12(5): 1077-1086. DOI: 10.1364/JOSAA.12.001077.
- Oh C, Escuti MJ. Time-domain analysis of periodic anisotropic media at oblique incidence: an efficient FDTD implementation. Opt Express 2006; 14(24): 11870-11884. DOI: 10.1364/OE.14.011870.
- Xiang X, Escuti MJ. Numerical Modeling of Polarization Gratings by Rigorous Coupled Wave Analysis. Proc SPIE 2016; 9769: 976918. DOI: 10.1117/12.2218276.
- Xiang X, Kim J, Escuti MJ. Bragg polarization gratings for wide angular bandwidth and high efficiency at steep deflection angles. Sci Rep 2018; 8(7202): 1-6. DOI: 10.1038/s41598-018-25535-0.
- Soifer VA, ed. Diffractive nanophotonics. Boca Raton: CRC Press; 2014. ISBN: 978-1-4665-9069-4.
- Sherman MM, Yakovlev DA. Features of light transmission through monolayer of structurally identical anisotropic domains with random azimuthal orientation. Optics and Spectroscopy 2010; 109(2): 178-187. DOI: 10.1134/S0030400X10080059
- Yakovlev DD, Yakovlev DA. Scattering patterns of orthogonally polarized light components for statistically rotationally invariant mosaic birefringent layers. Optics and Spectroscopy 2019; 126(3): 245-256.
- Kosmopoulos JA, Zenginoglou HM. Geometrical optics approach to the nematic liquid crystal grating: numerical results. Appl Opt 1987; 26(9): 1714-1721. DOI: 10.1364/AO.26.001714.
- Helfrich W. Deformation of cholesteric liquid crystals with low threshold voltage. Appl Phys Lett 1970; 17(12): 531-532. DOI: 10.1063/1.1653297.
- Helfrich W. Electrohydrodynamic and dielectric instabilities of cholesteric liquid crystals. J Chem Phys 1971; 55(2): 839-842. DOI: 10.1063/1.1676151.
- Hurault JP. Static distortions of a cholesteric planar structure induced by magnetic or ac electric fields. J Chem Phys 1973; 59(4): 2068-2075. DOI: 10.1063/1.1680293.
- Chigrinov VG, Belyaev VV, Belyaev SV, Grebenkin MF. Instability of cholesteric liquid crystals in an electric field. Soviet Journal of Experimental and Theoretical Physics 1979, 50: 994-999.
- Lavrentovich OD, Shiyanovskii SV, Voloschenko D. Fast beam steering cholesteric diffractive devices. Proc SPIE 1999; 3787: 149-155. DOI: 10.1117/12.351639.
- Senyuk B, Smalyukh I, Lavrentovich O. Electrically-controlled two-dimensional gratings based on layers undulations in cholesteric liquid crystals. Proc SPIE 2005; 5936: 59360W. DOI: 10.1117/12.615976.
- Scheffer TJ. Electric and magnetic field investigations of the periodic gridlike deformation of a cholesteric liquid crystal. Phys Rev Lett 1972; 28(10): 593-596. DOI: 10.1103/PhysRevLett.28.593.
- Tervo J, Turunen J. Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings. Opt Lett2000; 25(11): 785-786. DOI: 10.1364/OL.25.000785.
- Yakovlev DA. Calculation of transmission characteristics of smoothly inhomogeneous anisotropic media in the approximation of negligible smallness of the bulk reflection: II. Numerical methods. Optics and Spectroscopy 2003; 94(4): 600-606. DOI: 10.1134/1.1570488.
- Yakovlev DA. Calculation of transmission characteristics of smoothly inhomogeneous anisotropic media in the approximation of negligible smallness of the bulk reflection: I. Basic equation. Optics and Spectroscopy 1999; 87(6): 903-908. DOI: 10.1134/1.1635481.
- Yakovlev DA. Calculation of transmission characteristics of smoothly inhomogeneous anisotropic media in the approximation of negligible smallness of the bulk reflection: III. Analytical solutions. Optics and Spectroscopy 2003; 95(6): 944-951. DOI: 10.1134/1.1635481.
- Yakovlev DA. Simple formulas for the amplitude transmission and reflection coefficients at the interface of anisotropic media. Optics and Spectroscopy 1998, 84(5): 748-752.
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