Vol. 97
Latest Volume
All Volumes
PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2009-10-13
Field Analysis of Dielectric Waveguide Devices Based on Coupled Transverse-Mode Integral Equation-Numerical Investigation
By
Progress In Electromagnetics Research, Vol. 97, 159-176, 2009
Abstract
This is a numerical investigation of a recently proposed formulation, called coupled transverse-mode integral equation (CTMIE), for analyzing EM field properties in general 2-D dielectric waveguide devices. The device is first approximated by stack of piece-wise 1-D horizontally layered structures. Transverse field components on the interface between waveguide slices are unknown functions, which are governed by a coupled integral equation. When unknowns are expanded as a linear combination of given functions, CTMIE is converted to a coupled block matrix equation. We study three waveguide devices, in detail, to understand the relation between modeling parameters and accuracy and convergent rate of the solutions. Examples include a step waveguide junction, a multi-mode interferometer power cross coupler and a linearly tapered waveguide. All results are verified with independent calculations using other proven methods.
Citation
Hung-Wen Chang, Yan-Huei Wu, Shih-Min Lu, Wei-Chi Cheng, and Meng-Huei Sheng, "Field Analysis of Dielectric Waveguide Devices Based on Coupled Transverse-Mode Integral Equation-Numerical Investigation," Progress In Electromagnetics Research, Vol. 97, 159-176, 2009.
doi:10.2528/PIER09091402
References

1. Saleh, B. E. A. and M. C. Teich, Fundamental of Photonics, John Wiley & Son, New York, 1991.
doi:10.1002/0471213748

2. Lin, C. F., Optical Components for Communications, Kluwer Academic Publishing, Boston, 2004.

3. Chew, W.-C., Waves and Fields in Inhomogeneous Media, Van Norstrand Reinhold, New York, 1990.

4. Ishimaru, A., "Electromagnetic Propagation, Radiation, and Scattering," Prentice Hall, Englewood Cliffs, N.J., 1991.

5. Taflove, A. and S. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, Artech House, Norwood, MA, 2000.

6. Chiang, Y. C., Y. Chiou, and H. C. Chang, "Improved full-vectorial finite-difference mode solver for optical waveguides with step-index profiles," J. of Lightwave Technology, Vol. 2, No. 8, 1609-1618, Aug. 2002.
doi:10.1109/JLT.2002.800292

7. Chang, H.-W. and W.-C. Cheng, "Analysis of dielectric waveguide termination with tilted facets by analytic continuity method," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 12, 1653-1662, 2007.

8. Chang, H.-W., W.-C. Cheng, and S.-M. Lu, "Layer-mode transparent boundary condition for the hybrid FD-FD method," Progress In Electromagnetics Research, Vol. 94, 175-195, 2009.
doi:10.2528/PIER09061606

9. Jin, J., The Finite Element Method in Electromagnetics, John Wiley & Son, New York, 2002.

10. Feit, M. D., J. A. Fleck, and Jr., "Light propagation in graded-index optical fibers," Applied Optics, Vol. 17, No. 24, 3990-3998, 1978.
doi:10.1364/AO.17.003990

11. Koch, T. B., J. Davies, and D. Wickramasinghe, "Finite element finite-difference propagation algorithm for integrated optical devices," Electronics Letters, Vol. 25, No. 8, 514-516, 1989.
doi:10.1049/el:19890352

12. Chang, H.-W. and M.-H. Sheng, "Field analysis of dielectric waveguide devices based on coupled transverse-mode integral equation --- Mathematical and numerical formulations," Progress In Electromagnetics Research, Vol. 78, 329-347, 2008.
doi:10.2528/PIER07091002

13. Mittra, R., Y. L. Hou, and V. Jannejad, "Analysis of open dielectric waveguides using mode-matching technique and variational methods," IEEE Trans. Microwave Theory Tech., Vol. 28, 36-43, 1980.
doi:10.1109/TMTT.1980.1130003

14. Sudbo, A. S., "Film mode matching: A versatile numerical method for vector mode field calculations in dielectric waveguides," Pure Appl. Opt., Vol. 2, 211-233, 1993.
doi:10.1088/0963-9659/2/3/007

15. Chang, H.-W., T.-L. Wu, and M.-H. Sheng, "Vectorial modal analysis of dielectric waveguides based on coupled transverse-mode integral equation: I | Mathematical formulations," J. Opt. Soc. Amer. A, Vol. 23, 1468-1477, Jun. 2006.
doi:10.1364/JOSAA.23.001468

16. Chang, H.-W. and T.-L. Wu, "Vectorial modal analysis of dielectric waveguides based on coupled transverse-mode integral equation: II --- Numerical analysis," J. Opt. Soc. Amer. A, Vol. 23, 1478-1487, Jun. 2006.
doi:10.1364/JOSAA.23.001478

17. Cheng, Q. and T. J. Cui, "Guided modes and continuous modes in parallel-plate waveguides excited by a line source," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 12, 1577-1587, 2007.

18. Chang, H.-W. and M.-H. Sheng, "Errata for the paper entitled `Dielectric waveguide devices based on coupled transverse-mode integral equation --- Mathematical and numerical formulations' ," Progress In Electromagnetics Research C, Vol. 8, 195-197, 2009.
doi:10.2528/PIERC09041001

19. Rostami, A. and H. Motavali, "Asymptotic iteration method: A powerful approach for analysis of inhomogeneous dielectric slab waveguides," Progress In Electromagnetics Research B, Vol. 4, 171-182, 2008.
doi:10.2528/PIERB08011701

20. Motavali, H. and A. Rostami, "Exactly modal analysis of inhomogeneous slab waveguide using nikiforov-uvarov method," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 5-6, 681-692, 2008.
doi:10.1163/156939308784159507

21. Wu, T.-L. and H.-W. Chang, "Guiding mode expansion of a TE and TM transverse-mode integral equation for dielectric slab waveguides with an abrupt termination," J. Opt. Soc. Amer. A, Vol. 18, 2823-2832, Nov. 2003.

22. Soldano, L. B. and E. Pennings, "Optical multi-mode interference devices based on self-imaging: Principles and applications," J. of Lightwave Technology, Vol. 13, 615-627, 1995.
doi:10.1109/50.372474

23. Bachmann, M., P. Besse, and H. Melchior, "Overlapping-image multimode interference couplers with a reduced number of self-images for uniform and nonuniform power splitting," Applied Optics, Vol. 34, 6898-6910, Oct. 1995.

24. Feng, J.-Y., P. Chang, T. Lay, and T. Chang, "Novel stepped-width design concept for compact multimode-interference couplers with low cross-coupling ratio," IEEE Photonics Tech. Letters, Vol. 19, No. 4, 224-226, Feb. 2007.
doi:10.1109/LPT.2006.890762

25. Lilonga-Boyenga, D., C. N. Mabika, and G. OkoumouMoko, "Rigorous analysis of uniaxial discontinuities microwave components using a new multimodal variational formulation," Progress In Electromagnetics Research B, Vol. 2, 61-71, 2008.
doi:10.2528/PIERB07102403

26. Liao, S., "Miter bend mirror design for corrugated waveguides," Progress In Electromagnetics Research Letters, Vol. 10, 157-162, 2009.
doi:10.2528/PIERL09062103