Vol. 61
Latest Volume
All Volumes
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]
2006-05-20
Applying Oblique Coordinates in the Method of Lines
By
, Vol. 61, 271-278, 2006
Abstract
Oblique coordinates are introduced into the method of lines. For the purpose of analysis, suitable equations are derived. The formulas are applied to compute the transmission in a waveguide device consisting of straight waveguides connected by a tilted one. Furthermore, the band structure of a hexagonal photonic bandgap structure was computed using these oblique coordinates.
Citation
Stefan Helfert , "Applying Oblique Coordinates in the Method of Lines," , Vol. 61, 271-278, 2006.
doi:10.2528/PIER06041204
http://www.jpier.org/PIER/pier.php?paper=0604124
References

1. Pregla, R. and W. Pascher, "The method of lines," Numerical Techniques for Microwave and Mil limeter Wave Passive Struc- tures, 381-446, 1989.

2. Conradi, O., S. Helfert, and R. Pregla, "Comprehensive modeling of vertical-cavity laser-diodes by the method of lines," IEEE J. Quantum Electron., Vol. 37, 928-935, 2001.
doi:10.1109/3.929594

3. Pascher, W. and R. Pregla, "Vectorial analysis of bends in optical strip waveguides by the method of lines," Radio Sci., Vol. 28, 1229-1233, 1993.

4. Pregla, R., "The method of lines for the analysis of dielectric waveguides bends," J. Lightwave Technol., Vol. 14, No. 4, 634-639, 1996.
doi:10.1109/50.491403

5. Helfert, S., "Analysis of curved bends in arbitrary optical devices using cylindrical coordinates," Opt. Quantum Electron., Vol. 30, 359-368, 1998.
doi:10.1023/A:1006937410789

6. Pregla, R., "Modeling of optical waveguide structures with general anisotropy in arbitrary orthogonal coordinate systems," IEEE J. of Sel. Topics in Quantum Electronics, Vol. 8, No. 12, 1217-1224, 2002.
doi:10.1109/JSTQE.2002.806681

7. Helfert, S. F. and R. Pregla, "Efficient analysis of periodic structures," J. Lightwave Technol., Vol. 16, No. 9, 1694-1702, 1998.
doi:10.1109/50.712255

8. Helfert, S. F., "Numerical stable determination of Floquet-modes and the application to the computation of band structures," Opt. Quantum Electron., Vol. 36, 87-107, 2004.
doi:10.1023/B:OQEL.0000015632.23175.40

9. Barcz, A., S. Helfert, and R. Pregla, "Modeling of 2D photonic crystals by using the method of lines," ICTON Conf., Vol. 4, 45-48, 2002.

10. Yamauchi, J., J. Shibayama, and H. Nakano, "Propagating beam analysis based on the implicit finite-difference method using the oblique coordinate system," OSA Integr. Photo. Resear. Tech. Dig., No. 2, 19-21, 1994.

11. Benson, T. M., P. Sewell, S. Sujecki, and P. C. Kendall, "Structure related beam propagation," Opt. Quantum Electron., Vol. 31, 689-703, 1999.
doi:10.1023/A:1006952528169

12. Sewell, P., T. M. Benson, S. Sujecki, and P. C. Kendall, "The dispersion characteristics of oblique coordinate beam propagation algorithms," J. Lightwave Technol., Vol. 17, No. 3, 514-518, 1999.
doi:10.1109/50.749394

13. Helfert, S. F. and R. Pregla Electromagnetics, "The method of lines: a versatile tool for the analysis of waveguide structures," Invited paper for the special issue on ``Optical Wave Propagation in Guiding Structures, Vol. 22, 615-637, 2002.

14. Villeneuve, P. R., S. Fan, S. G. Johnson, and J. D. Joannopoulos, "Three-dimensional photon confinement in photonic crystals of low-dimensional periodicity," IEE Proc.-Optoelectron., Vol. 145, No. 6, 384-390, 1998.
doi:10.1049/ip-opt:19982467

15. Helfert, S. F., "Determination of Floquet-modes in asymmetric periodic structures," Opt. Quantum Electron., Vol. 37, 185-197, 2005.
doi:10.1007/s11082-005-1137-0