Vol. 27

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2012-11-15

Vector Mode Analysis of Optical Waveguides by Quadratic Spline Collocation Method

By Jianwei Mu, Haibo Liang, Xun Li, Bin Xu, and Wei-Ping Huang
Progress In Electromagnetics Research M, Vol. 27, 97-107, 2012
doi:10.2528/PIERM12101216

Abstract

We present an accurate, efficient numerical analysis for vector modes of dielectric optical waveguide structures with an arbitrary refractive index profile using a quadratic spline collocation method (QSCM). The unknown weights of the polynomials are determined by forcing the errors at the collocation points to be zero. Consequently, the original second order differential equation is converted to a set of algebraic equations which can be solved by matrix techniques. The proposed QSCM method demonstrates better performance than the standard finite-difference method of the same convergence rate in terms of grid size with the same degree of computational complexity.

Citation


Jianwei Mu, Haibo Liang, Xun Li, Bin Xu, and Wei-Ping Huang, "Vector Mode Analysis of Optical Waveguides by Quadratic Spline Collocation Method," Progress In Electromagnetics Research M, Vol. 27, 97-107, 2012.
doi:10.2528/PIERM12101216
http://www.jpier.org/PIERM/pier.php?paper=12101216

References


    1. Huang, W. ed., Methods for Modeling and Simulation of Guided-wave Optoelectronic Devices: Part I. Modes and Couplings, EMW Publishing, Cambridge, MA, 1995.

    2. Rahman, B. M. A. and J. B. Davies, "Finite-element analysis of optical and microwave waveguide problems," IEEE Trans. Microwave Theory Tech., Vol. 32, No. 1, 20-28, 1984.
    doi:10.1109/TMTT.1984.1132606

    3. Koshiba, M. and K. Inoue, "Simple and efficient finite-element analysis of microwave and optical waveguides," IEEE Trans. Microwave Theory Tech., Vol. 40, No. 2, 371-377, 1992.
    doi:10.1109/22.120111

    4. Stern, M. S., "Semivectorial polarized finite difference method for optical waveguides with arbitrary index profiles," IEE Proc. J., Vol. 135, No. 2, 56-63, 1988.
    doi:10.1049/ip-j.1988.0013

    5. Xu, C. L., W. P. Huang, M. S. Stern, and S. K. Chaudhuri, "Full-vectorial mode calculations by finite difference method," IEE Proc. Optoelectron, Vol. 142, No. 5, 281-286, 1994.
    doi:10.1049/ip-opt:19941419

    6. Vassallo, C., "Improvement of finite difference method for step-index optical waveguides," Inst. Elect. Eng. Proc.--- J., Vol. 139, No. 2, 137-142, 1992.

    7. Yamauchi, J., M. Sekiguchi, O. Uchiyama, J. Shibayama, and H. Nakano, "Modified finite-difference formula for the analysis of semivectorial modes in step-index optical waveguides," IEEE Photon. Technol. Lett., Vol. 9, 961-963, 1997.
    doi:10.1109/68.593366

    8. Vassallo, C., "Interest of improved three-point formulas for finite-difference modeling of optical devices," J. Opt. Soc. Amer., Vol. 14, 3273-3284, 1997.
    doi:10.1364/JOSAA.14.003273

    9. Chiou, Y.-P., Y. C. Chiang, and H. C. Chang, "Improved three point formulas considering the interface conditions in the finite-di®erence analysis of step-index optical devices," J. Lightwave Technology, Vol. 18, No. 2, 243-251, 2000.
    doi:10.1109/50.822799

    10. Chiou, Y.-P. and C.-H. Du, "Arbitrary-order full-vectorial interface conditions and higher-order finite-difference analysis of optical waveguides," J. Lightwave Technology, Vol. 29, No. 22, 3445-3452, Nov. 2011.
    doi:10.1109/JLT.2011.2168600

    11. Chiou, Y.-P. and C.-H. Du, "Arbitrary-order interface conditions for slab structures and their applications in waveguide analysis," OSA Optics Express, Vol. 18, No. 5, 4088-4102, Mar. 2010.
    doi:10.1364/OE.18.004088

    12. Rogge, U. and R. Pregla, "Method of lines for the analysis of dielectric waveguides," J. Lightwave Technology, Vol. 11, 2015-2020, Dec. 1993.
    doi:10.1109/50.257964

    13. Vassallo, C., "1993-1995 optical mode solvers," Opt. Quantum Electron., Vol. 29, 95-114, 1997.
    doi:10.1023/A:1018537602159

    14. Celler, G. K. and S. Cristoloveanu, "Frontiers of silicon-on-insulator," Applied Phys. Reviews, Vol. 93, No. 9, 4955-4978, 2003.
    doi:10.1063/1.1558223

    15. Bogaerts, W., et al., "Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology," J. Lightwave Technology, Vol. 23, No. 1, 2005.
    doi:10.1109/JLT.2004.834471

    16. Chiang, P. J., et al., "Full-vectorial optical waveguide mode solvers using multidomain pseudospectral frequency-domain (PSFD) formulations," IEEE J. Quantum Electronics, Vol. 44, No. 1, 56-66, 2008.
    doi:10.1109/JQE.2007.910454

    17. Christara, C. C., "Quadratic spline collocation methods for elliptic partial differential equations," BIT, Vol. 34, No. 1, 33-61, 1994.
    doi:10.1007/BF01935015

    18. Sharma, A. and S. Banerjee, "Method for propagation of total fields or beams through optical waveguides," Opt. Lett., Vol. 14, No. 1, 96-98, 1989.
    doi:10.1364/OL.14.000096

    19. Xiao, J. B. and X. H. Sun, "Full-vectorial mode solver for anisotropic optical waveguides using multidomain spectral collocation method," Opt. Comm., Vol. 28, No. 14, 2835-2840, 2010.
    doi:10.1016/j.optcom.2010.03.057

    20. Huang, C. X., C. C. Huang, and J. Y. Yang, "A full-vectorialpseudospectral modal analysis of dielectric optical waveguides with stepped refractive index profiles," IEEE J. Sel. Top. Quantum Electron., Vol. 11, No. 2, 457-465, 2005.
    doi:10.1109/JSTQE.2005.846540

    21. Huang, C. C. and C. C. Huang, "An efficient and accurate semivectorial spectral collocation method for analyzing polarized modes of rib waveguides," J. Lightwave Technology, Vol. 23, No. 7, 2309-2317, 2005.
    doi:10.1109/JLT.2005.850041

    22. Chen, J. and Q. H. Liu, "A non-spurious vector spectral element method for Maxwell's equations," Progress In Electromagnetics Research, Vol. 96, 205-215, 2009.
    doi:10.2528/PIER09082705