Bridging the quasi-static and the physical optics approximations: an elliptic disk case

A reformulated integral equation is solved inside an elliptic disk particle for an electromagnetic field formulation bridging the quasi-static and the physical optics approximations. The scattering amplitude tensor elements associated with such a field formulation are derived and then used to formulate the extinction cross sections. It is shown that the extinction cross sections have a frequency dependence and an incidence angle dependence similar to those associated with the physical optics approximation, and they have a particle shape dependence similar to that associated with the quasi-static approximation. Furthermore, at the high-frequency limits, it is shown that those cross sections could reach the value known in the literature by the extinction paradox, namely, twice the particle geometric shadow area.