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Properties of Longitudinal Electromagnetic Oscillations in Metals and Their Excitation at Planar and Spherical Surfaces

机译:金属中纵向电磁振荡的性质及其在平面和球形表面上的激发

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摘要

The common definition of the spatially dispersive permittivity is revised. The response of the degenerate electron gas on an electric field satisfying the vector Helmholtz equation is found with a solution to the Boltzmann equation. The calculated longitudinal dielectric function coincides with that obtained by Klimontovich and Silin in 1952 and Lindhard in 1954. However, it depends on the square of the wavenumber, a parameter of the vector Helmholtz equation, but not the wave vector of a plane electromagnetic wave. This new concept simplifies simulation of the nonlocal effects, for example, with a generalized Lorents–Mie theory, since no Fourier transforms should be made. The Fresnel coefficients are generalized allowing for excitation of the longitudinal electromagnetic waves. To verify the theory, the extinction spectra for silver and gold nanometer-sized spheres are calculated. For these particles, the generalized Lorents–Mie theory gives the blue shift and broadening of the plasmon resonance which are in excellent agreement with experimental data. In addition, the nonlocal theory explains vanishing of the plasmon resonance observed for gold spheres with diameters less than or equal to 2 nm. The calculations using the Klimontovich-Silin-Lindhard and hydrodynamic dielectric functions for silver are found to give close results at photon energies from 3 to 4 eV. We show that the absolute values of the wavenumbers of the longitudinal waves in solids are much higher than those of the transverse waves.
机译:修改了空间色散介电常数的通用定义。通过对玻尔兹曼方程的解,可以找到简并电子气对满足矢量亥姆霍兹方程的电场的响应。所计算的纵向介电函数与1952年Klimontovich和Silin以及1954年Lindhard所获得的纵向介电函数重合。但是,它取决于波数的平方,矢量亥姆霍兹方程的参数,而不取决于平面电磁波的波矢量。这个新概念简化了非局部效应的仿真,例如,采用了广义的Lorents-Mie理论,因为不需要进行傅立叶变换。菲涅耳系数被概括为允许纵向电磁波的激发。为了验证该理论,计算了银和金纳米尺寸球体的消光光谱。对于这些粒子,广义的Lorents-Mie理论给出了蓝移和等离子体激元共振的展宽,与实验数据非常吻合。另外,非局部理论解释了对于直径小于或等于2 nm的金球观察到的等离子体共振消失。发现使用Klimontovich-Silin-Lindhard和银的流体动力学介电函数进行的计算在3至4 eV的光子能量下给出了接近的结果。我们表明,固体中纵波的波数绝对值比横波的绝对值高得多。

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