A novel spectral method with variable transformation, the adaptive Hermite–Gauss decomposition method (A-HGDM), has been developed and applied to the analysis of three-dimensional (3D) dielectric structures. The proposed method includes an optimization strategy to automatically find the quasi-optimum numerical parameters of the variable transformation with low computational effort. The technique has been tested by analyzing two typical 3D dielectric structures: the rectangular step-index waveguide and the rib-waveguide directional coupler. In both cases, the A-HGDM increases the accuracy of the Hermite–Gauss decomposition method (HGDM), especially when the mode is near cutoff, and improves the computational efficiency of previously published optimization strategies (optimized HGDM).
© 2003 Optical Society of America
Original Manuscript: August 2, 2002
Revised Manuscript: October 7, 2002
Manuscript Accepted: October 9, 2002
Published: March 1, 2003
Alejandro Ortega-Moñux, J. Gonzalo Wangüemert-Pérez, and Iñigo Molina-Fernández, "Adaptive Hermite–Gauss decomposition method to analyze optical dielectric waveguides," J. Opt. Soc. Am. A 20, 557-568 (2003)