Comparison of a Vectorial and New Semivectorial Finite Difference Approach for Optical Waveguides (original) (raw)
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IEEE/OSA Journal of Lightwave Technology, 1993
Abstracf-An integrated finite difference approach is formulated for the full vector solution using transverse magnetic field components for dielectric waveguides, which is particularly suitable for nonuniform mesh and internal flux boundary conditions. This approach creates a sparse banded asymmetric matrix. Only few largest positive eigenvalues and the corresponding eigenvectors are calculated by the Arnoldi method @awl on the modified Gram-Schmidt) coupled with multiple detlation by computing a suitable small size matrix. The Arnddi process is followed by an inverse power method combined with an iterative solver. The nonphysical modes have been exeluded by applying the divergence relation V . H = 0. Three numerical examples are calculated for verifying the reliability and emciency of this technique, the first two of them are used for the cOmpIrjsOn with the results obtained by other methods, and last one is a quantum well single mode optical waveguide. Tbe technique in this paper could be used for any shape of dielectric waveguides with any profile of refractive index in the cmss section plane with proper Taylor expansion of the index.
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IEEE/OSA Journal of Lightwave Technology, 1996
A new method is presented for reconstructing smooth refractive index profiles of optical waveguides from measured effective indexes. It is based on the semivectorial finite difference method to solve the polarized wave equation for a given refractive index profile. An iterative simplex algorithm is used to find the best refractive index parameters that give, as a solution, effective indexes close to the measured ones. The method is applied successfully to Ag+-Na+ ion-exchanged glass slab waveguides and to diffused Mg/Ti:LiNbQ3 slab waveguides. Dopant concentration profiles are obtained by using secondary ion mass spectrometry. The relationship between the refractive index change and the dopant concentration is determined for both cases. The Iterative simplex algorithm-finite difference method (EA-FDM) is compared to other index profile reconstruction methods, and the advantages with respect to WKB-based methods are pointed out.
Journal of Lightwave Technology, 1993
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Analysis of anisotropic optical waveguides using a three-dimensional finite difference method
2011 International Workshop on Nonlinear Photonics, 2011
The model describing excitation and distribution of electromagnetic waves in an anisotropic optical waveguide in the three-dimensional case is presented in this paper. The finite difference method (FDM) has been employed for the Maxwell equation discretization for a random anisotropic medium. The resulting system of linear algebraic equations for the electric-field components in an inhomogeneous anisotropic medium is solved by the method of biconjugate gradient.