PDF

Abstract:
Using methods of classical electrodynamics, we consider the oblique incidence of a plane electromagnetic wave on a twisted planar anisotropic inhomogeneous layer, in which the optical axis changes direction with respect to the plane of incidence. We consider the general case when all components of the permittivity tensor of the medium are nonzero functions of the transverse coordinate in the layer. Using the Wentzel-Kramers-Brillouin method, we obtain in  the initial approximation a 4×4-matrix solution for the projections of the fields of an electromagnetic wave in an inhomogeneous anisotropic medium. The matrix reflection coefficients are calculated and shown to depend on the torsion angle of the medium.

Keywords:
thin films, optical properties, light polarization, anisotropic optical materials, birefringence, inhomogeneous media, WKB method, 4×4 method, reflection matrix.

Citation:
Moiseeva NM, Moiseev AV. The matrix solution of the 4×4 problem by the Wentzel-Kramers-Brillouin method for a planar inhomogeneous anisotropic layer. Computer Optics 2018; 42(3): 354-361. DOI: 10.18287/2412-6179-2018-42-3-354-361.

References:

1. Tabib-Azar M, Beheim G. Modern trends in microstructures and integrated optics for communication, sensing, and actuation. Optical Engineering 1997; 36(5): 1307-1318. DOI: 10.1117/1.601331.
2. Hussell CP, Ramaswamy RV, Srivastava R, Jackel JL. Adiabatic invariance in GRIN channel waveguides and its use in 3-dB cross couplers. Appl Opt 1990; 29(25): 4105-4110. DOI: 10.1364/AO.29.004105.
3. Razskazovskaya O, Ossiander M, Siegrist F, Pervak V, Schultze M. Carrier frequency tuning of few-cycle light pulses by a broadband attenuating mirror. Appl Opt 2017; 56(32): 8978-8982. DOI: 10.1364/AO.56.008978.
4. Kuroda C, Ohki Y, Fujimaki M. Optimization of a waveguide-mode sensing chip for an ultraviolet near-field illumination biosensor. Opt Express 2017; 25(21): 26011-26019. DOI: 10.1364/OE.25.026011.
5. Fennig EA, Schmidt G, Moore DT. Design of multilayer planar light guide concentrators. Light, Energy and the Environment, OSA Technical Digest (online) 2017: RW3B.4. DOI: 10.1364/OSE.2017.RW3B.4.
6. Guo D, Chu T. Silicon mode (de)multiplexers with parameters optimized using shortcuts to adiabaticity. Opt Express 2017; 25(8): 9160-9170. DOI: 10.1364/OE.25.009160.
7. Wang B, Dong F, Yang D, Song Z, Xu L, Chu W, Gong Q, Li Y. Polarization-controlled color-tunable holograms with dielectric metasurfaces. Optica 2017; 4(11): 1368-1371. DOI: 10.1364/OPTICA.4.001368.
8. Born M, Wolf E. Principles of optics. 3rd ed. New York: Pergamon Press, 1965.
9. Teitler S, Henvis BW. Refraction in stratified, anisotropic media. JOSA 1970; 60(6): 830-834. DOI: 10.1364/JOSA.60.000830.
10. Berreman DW. Optics in stratified and anisotropic media: 4×4-matrix formulation. JOSA 1972; 62(4): 502-510. DOI: 10.1364/JOSA.62.000502.
11. Allia P, Oldano C, Trossi L. 4 × 4 matrix approach to chyral liquid-crystal optics. JOSA B 1986; 3(3): 424-429. DOI: 10.1364/JOSAB.3.000424.
12. Yakovlev DA, Chigrinov VG, Kwok HS. Modeling and optimization of LCD optical performance. New Delhi: John Wiley & Sons Ltd; 2015. ISBN: 978-0-47068914-1.
13. Yeh P, Gu C. Optics of liquid crystal displays. 2nd ed. John Wiley & Sons Inc; 2009. ISBN: 978-0-470-18176-8.
14. Gvatua ShSh, Topuridze NS, Blagidze YM, Sharashidze LK, Pavlenishvili IY, Dzhaparidze KG, Nadareishvili LI. Polarization properties of polymer films with a birefringence gradient. J Opt Technol 2005; 72(10): 743-748. DOI: 10.1364/JOT.72.000743.
15. Chabanov AA. Strongly resonant transmission in periodic anisotropic layered media. Frontiers in Optics 2007: FThI4. DOI: 10.1364/FIO.2007.FThI4.
16. Landau LD, Lifshitz EM. Quantum mechanics (non-relativistic theory). Course of Theoretical Physics, Vol 3. 3rd ed. Burlington, MA: Butterworth-Heinemann Publishers; 2004. ISBN: 978-0-7506-3539-4.
17. Chung M-S, Kim C-M. General eigenvalue equations for optical planar waveguides with arbitrarily graded-index profiles. J Lightw Technol 2000; 18(6): 878-885. DOI: 10.1109/50.848401.
18. Moiseeva NM. Calculation of the dynamics of ellipsometric parameters of the reflected electromagnetic radiation of an inhomogeneous gaseous reacting medium [In Russian]. Informatics. Education. Ecology and human health. Proceedings of the 5th International Conference "Nonlinear World" 2001: 163-169.
19. Moiseeva NM, Yatshishen VV. Calculation of dispersion characteristics of surface plasmons on the boundary a non-homogeus anisotropic medium [In Russian]. Physics of Wave Propagation and Radio Systems 2005; 8(10): 77-81.
20. Moiseeva NM, Rudenok IP, Moiseev AV. Chang envelope of the optical signal at reflection in cell inhomogeneous nematic liquid crystals [In Russian]. Izvestiya vysshih uchebnyh zavedenij: Fizika 2016; 59(12-3): 157-160.
21. Moiseeva NM. Application of WKB for calculation eigenwaves an anisotropic inhomogeneous planar waveguide [In Russian]. Izvestiya vysshih uchebnyh zavedenij: Fizika 2013; 56(8-2): 282-284.
22. Ivanov OV, Sementsov DI. Propagation of light in nonuniform bianisotropic plane-layer structures. Optics and spectroscopy 1999; 87(3): P. 446-451.
23. Ivanov OV. The propagation of electromagnetic waves in anisotropic and bianisotropic layered structures [In Russian]. Ulyanovsk: “UlSTU” Publisher; 2010. ISBN: 978-5-9795-0684-5.
24. Wasow W. Asymptotic expansion for ordinary differential equations. Mineola, New York: Dover Publication Inc; 1987. ISBN: 0-486-49518-3.

---

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: journal@computeroptics.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20