Finite–element method analysis of microwave and optical waveguides—trends in countermeasures to spurious solutions

This paper presents a review of finite‐element methods for the analysis of microwave and optical waveguides, particularly focusing on the recent results for suppressing or eliminating techniques of the spurious solutions that have become a subject of discussion to date. The finite‐element method analysis of electromagnetic waveguides can be divided into four classes: (1) scalar wave analysis by the one‐dimensional finite‐element method; (2) vectorial wave analysis by the one‐dimensional finite‐element method; (3) scalar wave analysis by the two‐dimensional finite‐element method; and (4) vectorial wave analysis by the two‐dimensional finite‐element method. Spurious solutions appear in (4), and, depending on the variational expression used, they also appear in (2). Placing emphasis on (2) and (4), particularly on (4), various finite‐element formulations are presented such as axial fields of E and H, full vector H field, full vector E field, transverse fields of E and H, and transverse fields of E or H formulations, and various approaches capable of suppressing or eliminating the spurious solutions are reviewed in detail.