Geodesic
Zero approximation of vector model for smoothly-irregular optical waveguide
Matematičeskoe modelirovanie, Tome 22 (2010) no. 8, pp. 42-54

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On the base of adiabatic representation for eigenmodes of integrated-optical multilayer waveguide are presented differential equations and boarder conditions to vertical distribution of electromagnetic field in the waveguide. To smoothly-irregular waveguides an asymptotic method is applied and zero approximation parts of differential equations and boarder conditions are determined. Exact expressions are considered for vertical distribution of electromagnetic field in a waveguide and for boarder conditions. Finally the problem is reduced to the solution of homogeneous system of linear algebraic equations depending on a spectral parameter and to the search of the parameter values. The method and algorithms of calculating vertical dispersion of adiabatic modes are considered in conclusion.
Keywords: integrated optics, waveguide modes, smooth three-dimensional irregularities, asymptotic method, differential equations, parametrically dependent algebraic equations. 
@article{MM_2010_22_8_a3,
     author = {A. A. Egorov and A. L. Sevastyanov and E. A. Ayrjan and K. P. Lovetskiy and L. A. Sevastianov},
     title = {Zero approximation of vector model for smoothly-irregular optical waveguide},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {42--54},
     publisher = {mathdoc},
     volume = {22},
     number = {8},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2010_22_8_a3/}
}
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A. A. Egorov; A. L. Sevastyanov; E. A. Ayrjan; K. P. Lovetskiy; L. A. Sevastianov. Zero approximation of vector model for smoothly-irregular optical waveguide. Matematičeskoe modelirovanie, Tome 22 (2010) no. 8, pp. 42-54. http://geodesic.mathdoc.fr/item/MM_2010_22_8_a3/