Abstract
The most widely used finite element formulation for the vector analysis of dielectric/optical guides uses the three vector H fields [1] or the three vector E fields. The major problem with these formulations is that the divergence condition for these fields is not satisfied, with resultant spurious modes. Rahman and Dȧvis [1] have used the penalty method of separating the spurious modes from the genuine modes, by adding the divergence condition matrix to the wave equation matrix with a penalty factor. The method requires that each case is run several times with different values of the penalty factor, and the spurious modes are identified as their values change with the penalty parameter. Thus, a single wavelength solution may require as many as three or four runs to resolve the genuine modes. The alternative adopted by several groups [2], [3], [4] uses edge elements for the transverse fields, which specifies the direction of the field between any two nodes, but retains the shape functions for the z-directed axial field, the magnitudes to be determined by the solution of the problem.
© 1994 Optical Society of America
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