OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 13 — Jun. 22, 2009
  • pp: 10895–10909

A finite element beam propagation method for simulation of liquid crystal devices

Pieter J. M. Vanbrabant, Jeroen Beeckman, Kristiaan Neyts, Richard James, and F. Anibal Fernandez  »View Author Affiliations

Optics Express, Vol. 17, Issue 13, pp. 10895-10909 (2009)

View Full Text Article

Enhanced HTML    Acrobat PDF (2928 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



An efficient full-vectorial finite element beam propagation method is presented that uses higher order vector elements to calculate the wide angle propagation of an optical field through inhomogeneous, anisotropic optical materials such as liquid crystals. The full dielectric permittivity tensor is considered in solving Maxwell’s equations. The wide applicability of the method is illustrated with different examples: the propagation of a laser beam in a uniaxial medium, the tunability of a directional coupler based on liquid crystals and the near-field diffraction of a plane wave in a structure containing micrometer scale variations in the transverse refractive index, similar to the pixels of a spatial light modulator.

© 2009 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(130.2790) Integrated optics : Guided waves
(350.5500) Other areas of optics : Propagation

ToC Category:
Optical Devices

Original Manuscript: February 10, 2009
Revised Manuscript: April 30, 2009
Manuscript Accepted: May 8, 2009
Published: June 16, 2009

Pieter J. M. Vanbrabant, Jeroen Beeckman, Kristiaan Neyts, Richard James, and F. Anibal Fernandez, "A finite element beam propagation method for simulation of liquid crystal devices," Opt. Express 17, 10895-10909 (2009)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. M. Lopez-Dona, J. G. Wanguemert-Perez, and I. Molina-Fernandez, "Fast-fourier-based three-dimensional full-vectorial beam propagation method," IEEE Photonics Technol. Lett. 17, 2319-2321 (2005). [CrossRef]
  2. C. Ma and E. Van Keuren, "A three-dimensional wide-angle BPM for optical waveguide structures," Opt. Express 15, 402-407 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?uri= OE-15-2-402. [CrossRef] [PubMed]
  3. A. J. Davidson and S. J. Elston, "Three-dimensional beam propagation model for the optical path of light through a nematic liquid crystal," J. Mod. Opt. 53, 979-989 (2006). [CrossRef]
  4. Q. Wang, G. Farrell, and Y. Semenova, "Modeling liquid-crystal devices with the three-dimensional full-vector beam propagation method," J. Opt. Soc. Am. 23, 2014-2019 (2006). [CrossRef]
  5. K. Saitoh and M. Koshiba, "Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides," J. Lightwave Technol. 19, 405-413 (2001). [CrossRef]
  6. D. Schulz, C. Glingener, M. Bludszuweit, and E. Voges, "Mixed finite element beam propagation method," J. Lightwave Technol. 16, 1336-1342 (1998). [CrossRef]
  7. M. Koshiba and Y. Tsuji, "Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems," J. Lightwave Technol. 18, 737-743 (2000). [CrossRef]
  8. F. L. Teixeira and W. C. Chew, "General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media," IEEE Microw. Guid. Wave Lett. 8, 223-225 (1998). [CrossRef]
  9. J. Jin, The finite element method in electromagnetics, 2nd edition (Wiley, New York US, 2002).
  10. J. Beeckman, R. James, F. A. Fernandez, W. De Cort, P. J. M. Vanbrabant, and K. Neyts, "Calculation of fully anisotropic liquid crystal waveguide modes," accepted for publication in J. Lightwave Technol. (2009). [CrossRef]
  11. M. Koshiba and K. Inoue, "Simple and efficient finite-element analysis of microwave and optical waveguides," IEEE Trans. Microwave Theory Tech. 40, 371-377 (1992). [CrossRef]
  12. G. R. Hadley, "Multistep method for wide-angle beam propagation," Opt. Lett. 17, 1743-1745 (1992). [CrossRef] [PubMed]
  13. GiD, the personal pre and post processor, http://gid.cimne.upc.es/.
  14. R. James, E. Willman, F. A. Fernandez, and S. E. Day, "Finite-Element Modeling of Liquid-Crystal Hydrodynamics With a Variable Degree of Order," IEEE Trans. Electron Devices 53, 1575-1582 (2006). [CrossRef]
  15. J. Beeckman, K. Neyts, X. Hutsebaut, C. Cambournac, and M. Haelterman, "Simulation of 2-D lateral light propagation in nematic-liquid-crystal cells with tilted molecules and nonlinear reorientational effect," Opt. Quantum Electron. 37, 95-106 (2005). [CrossRef]
  16. J. C. Campbell, F. A. Blum, D. W. Shaw, and K. L. Lawlay, "GaAs Electro-optic directional coupler switch," Appl. Phys. Lett. 27, 202-205 (1975). [CrossRef]
  17. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd edition (Clarendon, Oxford UK, 1993).
  18. N. Amarasinghe, E. Gartland, and J. Kelly, "Modeling optical properties of liquid-crystal devices by numerical solution of time-harmonic Maxwell equations," J. Opt. Soc. Am. 21, 1344-1361 (2004). [CrossRef]
  19. E. Buckley, "Holographic Laser Projection Technology," SID Int. Symp. Digest Tech. Papers 39, 1074-1079 (2008). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited