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24 May 1999 Solution of Helmholtz's equation in multilayered dielectric waveguide with periodic surface corrugation
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Dielectric waveguide with periodic surface corrugation are used in distributed feedback lasers and DBR lasers. In this paper the boundary element method (BEM) has been used to analyze 2D dielectric periodic corrugated waveguides. It is a very efficient method for analysis of this type of structure. The computational method relies on the numerical solution of the integral wave equation inside the grating region. This formalism has distinct advantages over the more traditional ones, especially when the boundary conditions are imposed through a collocation (point-matching) technique. The unknown field quantities together with all the boundary conditions of the problem are explicitly incorporated in the defining equation. For the problem at hand, the boundary conditions on the longitudinal interfaces of the grating layer are functionally known because of the Floquet expansion of the fields in the uniform layers above and below it. On the other hand, the boundary conditions for the interface between the periodic unit cells are naturally provided by Floquet's theorem and continuity requirements. Thus the method can be applied in a rather straightforward way towards a rigorous solution of the periodic problem, without any a priori assumptions, within a user specified accuracy. The BEM is a natural choice for this problem because we seek the field solution only on the grating layer interfaces in order to set up a transverse resonant-type characteristic equation for propagating mode. In this paper electromagnetic field and coupling coefficient for multi- layer dielectric waveguide is calculated.
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Hossein Mossallaei, Habibollah Abiri, Mohammad H. Rahnavard, and Mehrdad Zomorrodi "Solution of Helmholtz's equation in multilayered dielectric waveguide with periodic surface corrugation", Proc. SPIE 3611, Laser Resonators II, (24 May 1999);

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