Homogeneous surface

Finding the slowness curves for a SAW or a PSAW on either a free or a metallized surface is normally rather easy with SlownessBuddy. Only when the (P)SAW slowness is really far from a bulk wave slowness will it be difficult to start the search. This happens only with really strongly anisotropic crystals such as TeO2.

The algorithms used are based on the determinants of the surface boundary conditions (as explained in Laurent Boyer's thesis). These methods are fully equivalent to the classical effective permittivity method, except that SlownessBuddy can detect surface waves that are not piezoelectrically coupled.

One difference between a SAW and a PSAW is that no attenuation exists in the first case, so that the existence of a SAW is indicated by a real zero of some function. As a consequence, the numerical algorithm actually looks for a zero in that case, with a precise result. In the case of a PSAW, only a minimum can be searched for (at least in the method of Zhang, Desbois and Boyer), and the accuracy is somewhat worse although te program runs faster.

You should also be aware that a (P)SAW does not always exist for all angles.

With the PSAW method (method of Zhang, Desbois and Boyer), the coupling is estimated from the first derivative of the effective permittivity. This is only an approximate method, and the result should not be expected to be as reliable as the SAW result. For instance, you can use both the SAW and PSAW algorithm to search for a SAW (e.g. on LTO 112), and you should find that all values are equal (slowness, attenuation, beam-steering, and gamma) but for the coupling. This is because the Taylor expansion of the effective permittivity cannot always be approximated by its first term!

Forecasted improvement

Based on still unpublished results (VL), the Adler method is equivalent to the Zhang, Desbois and Boyer method. In the Adler method, the partial mode classification is unphysically modified (reflected bulk partial modes are replaced by their incident counterparts), by the PSAW is directly obtained by a search for a zero in the complex slowness plane for s1. Numerically this is faster and more precise, although the physical meaning is lost!