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.
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.
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.
5. Helfert, S., "Analysis of curved bends in arbitrary optical devices using cylindrical coordinates," Opt. Quantum Electron., Vol. 30, 359-368, 1998.
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.
7. Helfert, S. F. and R. Pregla, "Efficient analysis of periodic structures," J. Lightwave Technol., Vol. 16, No. 9, 1694-1702, 1998.
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.
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.
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.
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.
15. Helfert, S. F., "Determination of Floquet-modes in asymmetric periodic structures," Opt. Quantum Electron., Vol. 37, 185-197, 2005.