volume | PIER Journals

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.

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

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 Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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

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 Google Scholar

15. Bogaerts, W., R. Baets, P. Dumon, 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 Google Scholar

16. Chiang, P. J., C. L. Wu, 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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

Dr. Jianwei Mu

Dr. Haibo Liang

Dr. Xun Li

Dr. Bin Xu

Dr. Wei-Ping Huang