By Xin-Hua Wang
This e-book presents researchers on the leading edge of nonlinear optical applied sciences with powerful tactics and software program for the research of the elemental phenomena in nonlinear optical waveguide constructions. a whole vectorial electromagnetic formula is followed and the less than which simplification to a scalar formula is feasible are basically indicated. the necessity to version the dielectric saturation adequately is pointed out and better algorithms are offered for acquiring the total energy dispersion curve of buildings showing bistability. because the balance research of nonlinear modes is essential to the advancements of nonlinear version tools, an efficient technique to enquire the propagation of the scalar nonlinear waves in 3D is one other very important characteristic of the booklet. all the approaches defined in addition to an automated mesh generator for the finite point strategy are included right into a software program package deal that's incorporated with this ebook.
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Extra resources for Finite Element Methods for Nonlinear Optical Waveguides
Example text
With finite element simulations of field problems, it is efficient to arrange the mesh to be finer where the magnitudes of the field and/or its gradient are larger. Hence, adaptive FEM (AFEM) [119]-[122] may be preferred. Since the efficiency of AFEM is structure-dependent and not always superior as compared with the fixed-grid FEM (FGFEM), an alternative approach of using pre-graded grids (PGGFEM) is worth trying owing to the fact that in most cases the field patterns are known qualitatively a priori.
G. the components of a vector field) of a practical problem locally in terms of simple functions denned over small, but not infinitesimal, elements. Once this is done, an algebraic matrix equation is produced through a projection or variational procedure. With the conventional vector finite element methods (FEMs), each dependent variable for a vectorial problem is approximated independently [91]. Consequently, the resulting basis functions are not admissible to problems with inherent constraints between dependent variables, and those constrained problems have to be solved by Lagrange multiplier or by penalty FEMs [57, 60, 92, 93].
The method has been successfully employed by Cambrell [45, 65], Harrington [46], Friedman [59], Lanczos [64], Cambrell and Williams [66], and others. The extended operator procedure becomes particularly important in multidimensional problems as it is not always easy to find simple expansion functions in the domain of the original operator. With the operator extended, a wider class of basis functions can be used for solution by the method of moments [46]. 5 can be extended by extending its domain £>t(fi) to the domain DL,(£L) (consequently, Di°(£l) to £>£,«(П)).