This paper shows that Sommerfeld's multiple-valued function image method for electrostatics and electromagnetic boundary value problems can be extended to both conducting and diel-ectric surfaces bounded by space curves of general shape. The latter are models of material flakes of essentially arbitrary shape.
Frederick E Alzofon,
"Radiation Scattering By Flakes Of Arbitrary Shape", Proc. SPIE 0927, Wave Propagation and Scattering in Varied Media, (14 July 1988); doi: 10.1117/12.945814; https://doi.org/10.1117/12.945814