The dispersive resonant-state expansion, developed for an accurate calculation of the resonant states in open optical systems with frequency dispersion, is applied here to realistic materials, such as metallic nanoparticles and semiconductor microspheres. The material permittivity is determined by fitting the measured indices of refraction and absorption with a generalized Drude-Lorentz model containing a number of poles in the complex frequency plane. Each Drude or Lorentz pole generates an infinite series of resonant states. Furthermore, for small nanoparticles, each of these poles produces a distinct surface plasmon polariton mode. The evolution of these multiple surface modes with increasing radius traces the transition from the electrostatic limit to significant retardation and radiation. Treating the optical phonon range in a semiconductor microsphere, a reststrahlen band separating the resonant states is found. Considering a small energy range around the semiconductor band gap, the transition from absorption to gain is described by inverting the Lorentz pole weight, which results in the formation of lasing resonant states. Interestingly, the series of resonant states converging towards the absorption pole from the lower frequency side reshapes for a gain pole into a clockwise loop approaching the pole from the higher frequency side, being separated from a series spanning from low to high frequencies and containing the lasing modes.

中文翻译：

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将共振态扩展应用于具有频率色散的实际材料

为精确计算具有频率色散的开放光学系统中的共振态而开发的色散共振态扩展在此应用于实际材料，例如金属纳米粒子和半导体微球。材料的介电常数是通过将测得的折射率和吸收系数与广义Drude-Lorentz模型拟合而确定的，该模型在复频率平面中包含多个极点。每个Drude或Lorentz磁极都会产生一系列无限的共振状态。此外，对于小的纳米粒子，这些极中的每一个都会产生不同的表面等离激元极化模式。随着半径的增加，这些多个表面模式的演变追踪了从静电极限到明显的延迟和辐射的过渡。处理半导体微球中的光声子范围，发现将共振状态分开的reststrahlen带。考虑到半导体带隙周围较小的能量范围，通过反转洛伦兹极权重来描述从吸收到增益的跃迁，这导致形成激光谐振态。有趣的是，从低频侧向吸收极收敛的一系列共振态将增益极整形为从高频侧接近极点的顺时针环路，与从低频到高频的一系列分离，并包含激光。模式。从吸收到增益的转变通过反转洛伦兹极权重来描述，这导致了激光谐振态的形成。有趣的是，从低频侧向吸收极收敛的一系列共振态将增益极整形为从高频侧接近极点的顺时针环路，与从低频到高频的一系列分离，并包含激光。模式。从吸收到增益的转变通过反转洛伦兹极权重来描述，这导致了激光谐振态的形成。有趣的是，从低频侧向吸收极收敛的一系列共振态将增益极整形为从高频侧接近极点的顺时针环路，与从低频到高频的一系列分离，并包含激光。模式。