Diffraction of a plane electromagnetic wave by a VO$_2$ microsphere in the phase transition region

The paper presents the results of diffraction studies and the distribution of the electromagnetic (EM) field in a spherical particle of vanadium dioxide (VO$_2$) before and after the metal-semiconductor phase transition (MSPT). As a result of calculations, it was shown that after the phase transition point in VO$_2$ $(T > T_c)$, the EM wave radiation practically does not pass into the microsphere, but is almost completely reflected from it and scatters, which is associated with a sharp increase in the imaginary part of the dielectric constant of the microsphere and the transition of VO$_2$ into the metal state, and the commensurability of the EM wavelength with the radius of the ball. It was also revealed that the radiation intensity at a distance of 2$R$ from the surface of the spherical particle decreases sharply, which is associated with the interference of waves behind the particle (shadow region). From the modeling of diffraction and distribution of the EM field in the microsphere, we can propose a new method for studying of phase transitions of the MSPT type.