Vectorial modal analysis of dielectric waveguides based on a coupled transverse-mode integral equation. I. Mathematical formulation
JOSA A, Vol. 23, Issue 6, pp. 1468-1477 (2006)
http://dx.doi.org/10.1364/JOSAA.23.001468
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Abstract
We propose a rigorous full-vector integral-equation formulation for analyzing modal characteristics of the complex, two-dimensional, rectangular-like dielectric waveguide that is divisible into vertical slices of one-dimensional layered structures. The entire electromagnetic mode field is completely determined by the y-component electric and magnetic field functions on the interfaces between slices. These interfacial functions are governed by a system of vector-coupled transverse-mode integral equations (VCTMIE) whose kernels are made of orthonormal sets of both TE-to-y and TM-to-y modes from each slice. To solve for the unknown functions, we construct sets of suitable expansion functions and turn VCTMIE into a nonlinear matrix equation via orthogonal projection. The eigenvectors of the matrix provide the mode field solutions of the complex dielectric waveguide.
© 2006 Optical Society of America
OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.4430) General : Numerical approximation and analysis
(130.0130) Integrated optics : Integrated optics
(230.4170) Optical devices : Multilayers
(230.7370) Optical devices : Waveguides
ToC Category:
Optical Devices
History
Original Manuscript: August 26, 2005
Revised Manuscript: December 4, 2005
Manuscript Accepted: December 8, 2005
Citation
Hung-Wen Chang, Tso-Lun Wu, and Meng-Huei Sheng, "Vectorial modal analysis of dielectric waveguides based on a coupled transverse-mode integral equation. I. Mathematical formulation," J. Opt. Soc. Am. A 23, 1468-1477 (2006)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-6-1468
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