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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 4 — Feb. 14, 2011
  • pp: 3363–3378

Solving the full anisotropic liquid crystal waveguides by using an iterative pseudospectral-based eigenvalue method

Chia-Chien Huang  »View Author Affiliations


Optics Express, Vol. 19, Issue 4, pp. 3363-3378 (2011)
http://dx.doi.org/10.1364/OE.19.003363


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Abstract

This study develops an efficient mode solver based on pseudospectral eigenvalue algorithm to analyze liquid crystal waveguides with full 3 × 3 anisotropic permittivity tensors. Present formulation yields a cubic eigenvalue matrix equation with an eigenvalue of the propagation constant, and they are solved using an iterative approach following the transformation of the matrix equation to a standard linear eigenvalue equation. The proposed scheme significantly reduces the memory storage and computational time by using only transverse magnetic field components. Although the proposed scheme requires an iterative procedure, the convergent eigenvalues are achieved after performing only four iterations. Therefore, for this scheme, computational efforts remain greatly lower than those for other reported schemes that used at least three field components. For solving the modes of nematic liquid crystal waveguides, the numerical results obtained by the proposed scheme are in good agreement with those calculated by using the finite-element and the finite-difference frequency-domain schemes, thus verifying the applicability of the proposed approach. Furthermore, the mode patterns of liquid crystal waveguides under arbitrary molecular orientations are also characterized in detail.

© 2011 OSA

OCIS Codes
(130.2790) Integrated optics : Guided waves
(230.3720) Optical devices : Liquid-crystal devices
(230.7380) Optical devices : Waveguides, channeled

ToC Category:
Integrated Optics

History
Original Manuscript: December 7, 2010
Revised Manuscript: January 25, 2011
Manuscript Accepted: January 28, 2011
Published: February 4, 2011

Citation
Chia-Chien Huang, "Solving the full anisotropic liquid crystal waveguides by using an iterative pseudospectral-based eigenvalue method," Opt. Express 19, 3363-3378 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-4-3363


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References

  1. 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(1-3), 95–106 (2005). [CrossRef]
  2. A. D’Alessandro, B. D. Donisi, R. Beccherelli, and R. Asquini, “Nematic liquid crystal optical channel waveguides on silicon,” IEEE J. Quantum Electron. 42(10), 1084–1090 (2006). [CrossRef]
  3. G. D. Ziogos and E. E. Kriezis, “Modeling light propagation in liquid crystal devices with a 3-D full-vector finite-element beam propagation method,” Opt. Quantum Electron. 40(10), 733–748 (2008). [CrossRef]
  4. E. E. Kriezis and S. J. Elston, “Wide-angle beam propagation method for liquid-crystal device calculations,” Appl. Opt. 39(31), 5707–5714 (2000). [CrossRef]
  5. B. Bellini and R. Beccherelli, “Modeling, design and analysis of liquid crystal waveguides in preferentially etched silicon grooves,” J. Phys. D Appl. Phys. 42(4), 045111 (2009). [CrossRef]
  6. J. Beeckman, R. James, F. A. Í. Fernandez, W. De Cort, P. J. M. Vanbrabant, and K. Neyts, “Calculation of fully anisotropic liquid crystal waveguide modes,” J. Lightwave Technol. 27(17), 3812–3819 (2009). [CrossRef]
  7. P. J. M. Vanbrabant, J. Beeckman, K. Neyts, R. James, and F. A. Fernandez, “A finite element beam propagation method for simulation of liquid crystal devices,” Opt. Express 17(13), 10895–10909 (2009). [CrossRef] [PubMed]
  8. M. F. O. Hameed, S. S. A. Obayya, K. Al-Begain, M. I. Abo el Maaty, and A. M. Nasr, “Modal properties of an index guiding nematic liquid crystal based photonic crystal fiber,” J. Lightwave Technol. 27(21), 4754–4762 (2009). [CrossRef]
  9. P. J. M. Vanbrabant, J. Beeckman, K. Neyts, R. James, and F. A. Fernandez, “A finite element beam propagation method for simulation of liquid crystal devices,” Opt. Express 17(13), 10895–10909 (2009). [CrossRef] [PubMed]
  10. M. Y. Chen, S. M. Hsu, and H. C. Chang, “A finite-difference frequency-domain method for full-vectorial mode solutions of anisotropic optical waveguides with arbitrary permittivity tensor,” Opt. Express 17(8), 5965–5979 (2009). [CrossRef] [PubMed]
  11. D. Donisi, B. Bellini, R. Beccherelli, R. Asquini, G. Gilardi, M. Trotta, and A. Dálessandro, “A switchable liquid-crystal optical channel waveguide on silicon,” IEEE J. Quantum Electron. 46(5), 762–768 (2010). [CrossRef]
  12. M. Kawachi, N. Shibata, and T. Edahiro, “Possibility of use of liquid crystals as optical waveguide material for 1.3μm and 1.55μm bands,” Jpn. J. Appl. Phys. 21(Part 2, No. 3), L162–L164 (1982). [CrossRef]
  13. M. Koshiba, K. Hayata, and M. Suzuki, “Finite element solution of anisotropic waveguides with arbitrary tensor permittivity,” J. Lightwave Technol. 4(2), 121–126 (1986). [CrossRef]
  14. G. Tartarini and H. Renner, “Efficient finite-element analysis of tilted open anisotropic optical channel waveguides,”, ” IEEE Microw. Guid. Wave Lett. 9(10), 389–391 (1999). [CrossRef]
  15. S. M. Hsu and H. C. Chang, “Full-vectorial finite element method based eigenvalue algorithm for the analysis of 2D photonic crystals with arbitrary 3D anisotropy,” Opt. Express 15(24), 15797–15811 (2007). [CrossRef] [PubMed]
  16. S. Selleri, L. Vincetti, and M. Zoboli, “Full-vector finite-element beam propagation method for anisotropic optical device analysis,” IEEE J. Quantum Electron. 36(12), 1392–1401 (2000). [CrossRef]
  17. K. Saitoh and M. Koshiba, “Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,” J. Lightwave Technol. 19(3), 405–413 (2001). [CrossRef]
  18. J. C. Chen and S. Jüngling, “Computation of high-order waveguide modes by imaginary-distance beam propagation method,” Opt. Quantum Electron. 26, 199–205 (1994). [CrossRef]
  19. T. Ando, H. Nakayama, S. Numata, J. Yamauchi, and H. Nakano, “Eigenmode analysis of optical waveguides by a Yee-mesh-based imaginary-distance propagation method for an arbitrary dielectric interface,” J. Lightwave Technol. 20(8), 1627–1634 (2002). [CrossRef]
  20. J. P. Boyd, Chebyshev and Fourier Spectral Methods (Springer–Verlag, 2nd edition, 2001).
  21. C. C. Huang, C. C. Huang, and J. Y. Yang, “A full-vectorial pseudospectral modal analysis of dielectric optical waveguides with stepped refractive index profiles,” IEEE J. Sel. Top. Quantum Electron. 11(2), 457–465 (2005). [CrossRef]
  22. P. J. Chiang, C. P. Yu, and H. C. Chang, “Analysis of two-dimensional photonic crystals using a multidomain pseudospectral method,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2 Pt 2), 026703 (2007). [CrossRef] [PubMed]
  23. P.-J. Chiang, C.-L. Wu, C.-H. Teng, C.-S. Yang, and H.- Chang, “Full-vectorial optical waveguide mode solvers using multidomain pseudospectral frequency-domain (PSFD) formulations,” IEEE J. Quantum Electron. 44(1), 56–66 (2008). [CrossRef]
  24. C. C. Huang, “Simulation of optical waveguides by novel full-vectorial pseudospectral-based imaginary-distance beam propagation method,” Opt. Express 16(22), 17915–17934 (2008). [CrossRef] [PubMed]
  25. C. C. Huang, “Improved pseudospectral mode solver by prolate spheroidal wave functions for optical waveguides with step-index,” J. Lightwave Technol. 27(5), 597–605 (2009). [CrossRef]
  26. J. B. Xiao and X. H. Sun, “Full-vectorial mode solver for anisotropic optical waveguides using multidomain spectral collocation method,” Opt. Commun. 283(14), 2835–2840 (2010). [CrossRef]
  27. C. C. Huang, “Modeling mode characteristics of transverse anisotropic waveguides using a vector pseudospectral approach,” Opt. Express 18(25), 26583–26599 (2010). [CrossRef] [PubMed]
  28. T. Scharf, Polarized Light in Liquid Crystals and Polymers (John Wiley and Sons. Inc., NJ, 2007, Chap 4).
  29. W. J. Gordon and C. A. Hall, “Transfinite element methods: blending function interpolation over arbitrary curved element domains,” Numer. Math. 21(2), 109–129 (1973). [CrossRef]
  30. D. A. Kopriva, Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers (Springer–Verlag, 2009).
  31. T. Tang, “The Hermite spectral method for Gauss-type functions,” SIAM J. Sci. Comput. 14(3), 594–605 (1993). [CrossRef]
  32. T. Tamir, Guides-Wave Optoelectronics (Springer-Verlag, 1988).
  33. R. B. Lehoucq and D. C. Sorensen, “Deflation techniques for an implicitly re-started Arnoldi iteration,” SIAM J. Matrix Anal. Appl. 17(4), 789–821 (1996). [CrossRef]
  34. P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley and Sons. Inc., New York, 1999).

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