volume | PIER Journals

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.

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

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 Google Scholar

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. Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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. Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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 Google Scholar

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 Google Scholar

Dr. Stefan Helfert