Scattering and Absorption of Electromagnetic Waves in the Case of Excitation of Dipole Modes of a Spherical Particle

We compare the solution to the problem of scattering and absorption of a plane electromagnetic wave by a small spherical particle in the quasistatic dipole approximation with the general solution obtained by Gustav Mie for this problem. It is shown that in certain cases, the condition of smallness of the particle radius compared with the wavelength in the outer medium is insufficient for justification of the use of the quasistatic dipole approximation, and the quasistatic formulas for induced dipole moments, the absorbed power, and the scattered power become incorrect. Refined inequalities are found, which describe applicability of the quasistatic dipole approximation for a spherical particle both in free space and a homogeneous medium, and applicability of this approximation is tested in various cases. The results of solution of the problem are presented, which yield the absorbed and scattered powers at dipole resonances of various types for various parameters of the scattering object and the surrounding medium. Expressions for the parameters of the Lorentzian line near the magnetic dipole resonance of a small dielectric particle with a high refractive index and low losses are presented.