Skip to main content
Log in

Modeling light propagation in liquid crystal devices with a 3-D full-vector finite-element beam propagation method

  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

A full-vector finite-element beam propagation method in 3-D is introduced for the simulation of light propagation in liquid crystal (LC) devices. The three electric field components are expressed in terms of mixed finite elements, providing the correct enforcement of boundary conditions. Moreover, the optical dielectric tensor of the medium can have all its nine elements nonzero, thus allowing the LC director to have an arbitrary orientation. A photonic crystal fiber with a LC infiltrated core and a homeotropic to multi-domain cell are analyzed. Comparison with other existing simulation techniques is provided, in order to validate the accuracy of the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Amarasinghe N., Gartland E. Jr, Kelly J.: Modeling optical properties of liquid-crystal devices by numerical solution of time-harmonic Maxwell equations. J. Opt. Soc. Am. A 21, 1344–1361 (2004)

    Article  ADS  Google Scholar 

  • Berreman D.: Optics in stratified and anisotropic media: 4 × 4 matrix formulation. J. Opt. Soc. Am. 62, 505–510 (1972)

    Article  ADS  Google Scholar 

  • Chen J., Jungling S.: Computation of higher-order waveguide modes by imaginary-distance beam propagation method. Opt. Quant. Electron. 26, 199–205 (1994)

    Article  Google Scholar 

  • Davidson A., Elston S.: Three-dimensional beam propagation method for the optical path of light through a nematic liquid crystal. J. Mod. Opt. 53, 979–989 (2006)

    Article  MATH  ADS  Google Scholar 

  • Gundu K., Brio M., Moloney J.: A mixed high-order vector finite element method for waveguides: convergence and spurious mode studies. Int. J. Numer. Model. 18, 351–364 (2005)

    Article  MATH  Google Scholar 

  • Jin J.: The Finite Element Method in Electromagnetics. Wiley, New York (2002)

    MATH  Google Scholar 

  • Johnson S., Joannopoulos J.: Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis. Opt. Express 8, 173–190 (2001)

    Article  ADS  Google Scholar 

  • Kawano K., Kitoh T.: Introduction to Optical Waveguide Analysis: Solving Maxwell’s Equations and the Schrodinger Equation. Wiley, New York (2001)

    Google Scholar 

  • Kriezis E., Elston S.: Light wave propagation in periodic tilted liquid crystal structures: a periodic beam propagation method. Liq. Cryst. 26, 1663–1669 (1999)

    Article  Google Scholar 

  • Kriezis E., Elston S.: Light wave propagation in liquid crystal displays by the 2-D finite-difference time-domain method. Opt. Commun. 177, 69–77 (2000a)

    Article  ADS  Google Scholar 

  • Kriezis E., Elston S.: Wide-angle beam propagation method for liquid-crystal device calculations. Appl. Opt. 39, 5707–5714 (2000b)

    Article  ADS  Google Scholar 

  • Kriezis E., Papagiannakis A.: A three-dimensional full vectorial beam propagation method for z-dependent structures. IEEE J. Quantum Electron. 33, 883–890 (1997)

    Article  ADS  Google Scholar 

  • Kriezis E., Newton C., Spiller T., Elston S.: Three-dimensional simulations of light propagation in periodic liquid-crystal microstructures. Appl. Opt. 41, 5346–5356 (2002)

    Article  ADS  Google Scholar 

  • Li D., Van Brug H., Frankena H.: Application of a fully vectorial beam propagation method. Opt. Quant. Electron. 29, 313–322 (1997)

    Article  Google Scholar 

  • Lien A.: A detailed derivation of extended Jones matrix representation for twisted nematic liquid crystal displays. Liq. Cryst. 22, 171–175 (1997)

    Article  Google Scholar 

  • Obayya S., Rahman B., El-Mikati H.: New full-vectorial numerically efficient propagation algorithm based on the finite element method. J. Lightwave Technol. 18, 409–415 (2000)

    Article  ADS  Google Scholar 

  • Obayya S., Rahman B., Grattan K., El-Mikati H.: Full vectorial finite-element-based imaginary distance beam propagation solution of complex modes in optical waveguides. J. Lightwave Technol. 20, 1054–1060 (2002)

    Article  ADS  Google Scholar 

  • Panasyuk G., Allender D.: Model for the director and electric field in liquid crystal cells having twist wall or disclination lines. J. Appl. Phys. 91, 9603–9612 (2002)

    Article  ADS  Google Scholar 

  • Panasyuk G., Kelly J., Gartland E., Allender D.: Geometrical optics approach in liquid crystal films with three-dimensional director variations. Phys. Rev. E 67, 041702 (2003)

    Article  ADS  Google Scholar 

  • Panasyuk G., Kelly J., Bos P., Gartland E. Jr, Allender D.: The geometrical optics approach for multidimensional liquid crystal cells. Liq. Cryst. 31, 1503–1515 (2004)

    Article  Google Scholar 

  • Saitoh K., Koshiba M.: Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides. J. Lightwave Technol. 19, 405–413 (2001)

    Article  ADS  Google Scholar 

  • Schulz D., Gingener C., Bludsuweit M., Voges E.: Mixed finite element beam propagation method. J. Lightwave Technol. 16, 1336–1341 (1998)

    Article  ADS  Google Scholar 

  • Selleri S., Vincetti L., Cucinotta A.: Finite element method resolution of non-linear Helmholtz equation. Opt. Quant. Electron. 30, 457–465 (1998)

    Article  Google Scholar 

  • Selleri S., Vincetti L., Zoboli M.: Full-vector finite-element beam propagation method for anisotropic optical device analysis. IEEE J. Quantum Electron. 36, 1392–1401 (2000)

    Article  ADS  Google Scholar 

  • Tang S., Kelly J.: An alternative description of multi-dimensional optics in liquid crystals and uniaxial media solved by operators and sparse linear systems. Mol. Cryst. Liq. Cryst. 478, 175–199 (2007)

    Article  Google Scholar 

  • Teixeira F., Chew W.: General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media. IEEE Microw. Guided Wave Lett. 8, 223–225 (1998)

    Article  Google Scholar 

  • Tsuji Y., Koshiba M., Shiraishi T.: Finite element beam propagation method for three-dimensional optical waveguide structures. J. Lightwave Technol. 15, 1728–1734 (1997)

    Article  ADS  Google Scholar 

  • Volakis J., Chatterjee A., Kempel L.: Finite Element Method for Electromagnetics. IEEE Press, New York (1998)

    MATH  Google Scholar 

  • Wang X., Wang B., Bos P., Anderson J., Pouch J., Miranda F.: Finite-difference time-domain simulation of a liquid-crystal optical phased array. J. Opt. Soc. Am. A 22, 346–354 (2005)

    Article  MATH  ADS  Google Scholar 

  • Wang Q., Farell G., Semenova Y.: Modeling liquid-crystal devices with the tree-dimensional full-vector beam propagation method. J. Opt. Soc. Am. A 23, 2014–2019 (2006)

    Article  ADS  Google Scholar 

  • Xu C., Huang W., Chrostowski J., Chaudhuri C.: A full-vectorial beam propagation method for anisotropic waveguides. J. Lightwave Techol. 12, 1926–1931 (1994)

    Article  ADS  Google Scholar 

  • Zografopoulos D., Kriezis E., Tsiboukis T.: Photonic crystal-liquid crystal fibers for single-polarization or high-birefringence guidance. Opt. Express 14, 914–925 (2006)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Emmanouil E. Kriezis.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ziogos, G.D., Kriezis, E.E. Modeling light propagation in liquid crystal devices with a 3-D full-vector finite-element beam propagation method. Opt Quant Electron 40, 733–748 (2008). https://doi.org/10.1007/s11082-008-9261-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11082-008-9261-2

Keywords

Navigation