Vector analysis of dielectric waveguides using magnetic field finite elements with Helmholtz equation

Many authors have implemented numerical techniques to analyze the propagation of optical signals in dielectric waveguides, with purpose of eliminating the spurious modes. The finite element method has been used with excellent results for the propagation constant. The finite difference technique for rectangular dielectric structures added substantial contributions for these problems. Both of them, analyzed the case of loss inside the guide region. Most of these analyses assume the piecewise continuity of the dielectric constant. In this paper, that condition is applied to the curl-curl equation to derive an H-field finite element method to obtain the propagation constant. Numerical results agree with the other methods. The advantage of this formulation is that it does not require the use of the perturbation technique to solve for loss or gain in the waveguide and includes the continuity of the H_z and E_z components at the dielectric boundary interface