Vol. 27
Latest Volume
All Volumes
PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2012-11-15
Vector Mode Analysis of Optical Waveguides by Quadratic Spline Collocation Method
By
Progress In Electromagnetics Research M, Vol. 27, 97-107, 2012
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 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