研究目的
Investigating the diffraction of a plane electromagnetic wave by a multilayer dielectric sphere and studying the resonance properties of metal-dielectric nanoparticles in the optical band.
研究成果
The study presents an analytical solution for the diffraction of a plane electromagnetic wave by a multilayer dielectric sphere, demonstrating high numerical efficiency and reliability. It shows that increasing the number of layers approximating the dielectric permittivity profile enhances the electric field at the focusing point, allowing determination of the minimal required number of layers for practical applications. The study also highlights the resonance properties of metal-dielectric nanoparticles, particularly when coated with dielectric sheaths having high refractive indices.
研究不足
The study primarily focuses on theoretical analysis and numerical simulations, with limited discussion on practical implementation challenges or experimental validation. The applicability of the quasistatic approximation for calculations of metal-dielectric nanostructures is limited to cases where the ratio of the particle sizes and the wavelength is no more than 0.05.
1：Experimental Design and Method Selection
The study uses the method of separation of variables to solve the problem of diffraction of a plane electromagnetic wave by a multilayer dielectric sphere. The solution involves representing the fields in the layers in terms of the Debye potentials, written as series with respect to associated Legendre functions and spherical Bessel functions.
2：Sample Selection and Data Sources
The study considers multilayer dielectric spheres with arbitrary numbers of dielectric layers having arbitrary radii and dielectric permittivity values. The analysis includes spherical lenses in the RF band and metal-dielectric nanoparticles in the optical range.
3：List of Experimental Equipment and Materials
The study does not specify particular experimental equipment or materials but focuses on theoretical analysis and numerical simulations.
4：Experimental Procedures and Operational Workflow
The solution involves obtaining new recurrence relationships for calculating the fields in the layers and deriving formulas for the fields in the near and far diffraction zones. The study also analyzes the distribution of the scattered field of a plane wave by spherical lenses and the resonance properties of metal-dielectric nanoparticles.
5：Data Analysis Methods
The study uses analytical representations for the components of the scattered field in the near and far diffraction zones. High accuracy and reliability of the solution are confirmed by the analysis of the inner solution convergence and comparison with numerical methods.
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