High-accuracy calculation of singular electromagnetic fields in regions with re-entrant peripheries

Accurate analysis of the electromagnetic fields inside waveguides and cavities with re-entrant boundaries is crucial for many multi-scale device applications. In earlier approaches, the singularities that exist in electromagnetic field gradients inside such waveguides and cavities significantly reduce the accuracy of the calculations. In our scheme, these singular behaviors are treated using Hermite finite elements combined with analytical regularization of the action integral. We show that this approach provides considerably higher accuracy as compared with other methods employed in the literature. Specific calculations are presented for three typical regions: (a) an L-shaped waveguide, (b) an L-cavity, and (c) a cubic cavity with an octant removed to form a triple-junction corner. The method can be adapted to evaluate very high electromagnetic fields in any complex structures displaying "hot points."