Higher order intensity of light introduces third order nonlinear susceptibility in metallic nanostructures. Circuit theory is often used to represent complex phenomena and adequately models the frequency dependent linear resonance in metallic nanostructures with great accuracy. In this article, we use the linear circuit approach and propose a compact impedance model to represent resonance in metallic nanoparticle with cubic nonlinearity. The model uses full-wave dipole equation by employing all time-dependent fields and introduces the concept of nonlinear radiation impedances. Analytical expressions for the nonlinear radiation (internal and external) impedances are derived and used for the first time to get the close-form expression of nonlinear (NL) scattering cross-sectional area using voltages, currents and circuit elements. The effects of nanoparticle parameters i.e. radius, intensity and dielectric function of surrounding medium on cubic nonlinearity are analyzed using impedance model. The validated close-form impedance model preserves the macroscopic properties to give intuitive understanding of NL behavior necessary in facilitating next-generation nanophotonics applications.

中文翻译：

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具有三次非线性的金属纳米粒子的闭式共振解

光的高阶强度在金属纳米结构中引入了三阶非线性磁化率。电路理论通常用于表示复杂的现象，并以高精度充分模拟金属纳米结构中的频率相关线性共振。在本文中，我们使用线性电路方法并提出了一个紧凑的阻抗模型来表示具有三次非线性的金属纳米粒子的共振。该模型通过采用所有与时间相关的场来使用全波偶极子方程，并引入了非线性辐射阻抗的概念。非线性辐射（内部和外部）阻抗的解析表达式被推导出并首次用于使用电压、电流和电路元件获得非线性 (NL) 散射截面面积的近似表达式。使用阻抗模型分析了纳米粒子参数，即周围介质的半径、强度和介电函数对立方非线性的影响。经过验证的紧密形式阻抗模型保留了宏观特性，以直观地了解促进下一代纳米光子学应用所需的 NL 行为。