Optimization of near-field amplification at resonant light scattering by nanoparticles

In the present work, expressions for the system parameters that realize the maximum of the scattered field in the Mie problem separately for metals and for dielectrics were obtained. For metals, the answer was obtained in the form of formulas, for dielectrics an algorithm that allows finding the coordinates of the maximum is presented. The behavior of the solution, applied to real substances (Al, Au, GaP), is considered. In the case of the metals under relatively low dissipation at the resonant frequency, it accurately points to the maximum, and as the dissipation increases, it points to the neighborhood of the maximum. For considered dielectrics it was shown that theoretically predicted maximums are unattainable due to the limited value of the refractive index of the substance, the reasons why the maximums exist despite the mentioned limitation. In particular, it was found that the wavelength of the incident radiation and the radius of the particle at the maxima for GaP coincide with the resonance value for the internal coefficients. It was the starting point of the present study. Obtained results show that it really provides a guideline for searching for the maximum of the field scattered by other dielectrics spherical particles with a relatively low refractive index.