Light scattering by horizontally oriented square pyramid in the Wentzel–Kramers–Brillouin approximation

Abstract

In this research, we studied the sensitivity of the form factor of a pyramidal ice crystal in the Wentzel–Kramers–Brillouin (WKB) approximation to its geometrical characteristics: the shape, spatial orientation, aspect ratio and size parameter. Using the WKB method, we derive an analytical formula of the form factor of horizontally oriented square pyramid. We will begin this work by applying the WKB approximation to the case of a particle which rotates about its main axis. Then, we will move to deal with the case of a particle which rotates about an axis perpendicular to its main axis in a future work. In addition, the coefficient of extinction is also given. To illustrate our analytical results, some numerical examples are analyzed.