Higher-order singularities of the effective permittivity function

A method is given of calculating second-order singularities which are related to inflection points of slowness curves. An approximated formula is derived for the effective permittivity function in the neighbourhood of its singular points. A numerical analysis is presented of several piezoelectrics, and crystal cuts are calculated for the singular points. The analysis shows that inflection points may appear for almost every crystal cut, as is the case of lithium niobate and langasite.