The problem of concentrating electromagnetic fields into a nanotube from an ambient source of light, is considered. An isogeometric analysis approach, in a boundary element method setting, is employed to evaluate the local electric field, which is represented with the exact same basis functions used in the geometric representation of the nanotube. Subsequently, shape optimization of the nanotubes is performed with the aim of maximizing the field concentration in their interior. The optimization framework comprises: (i) one global optimizer implemented as the combination of a derivative-free guided random search approach and a gradient-based algorithm for accurately determining the shape at the final stages, (ii) one parametric modeler generating valid non-self-intersecting nanotube shapes with a relatively small number of parameters, and (iii) one isogeometric-enabled boundary element method solver approximating the value of the electric field on the nanotube with high accuracy. The optimal shapes for a wide range of optical sizes are determined, resulting in a collected energy enhancement of more than two orders of magnitude, compared to the respective circular designs. Importantly, the frequency and angular responses of selected optimal shapes tend to maintain their superior performance over extensive wavelength and directional bands. Therefore, the presented results may assist substantially the photonic inverse design in nanotube-based setups with applications spanning from field localization and power accumulation to wave steering and energy harvesting.

中文翻译：

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用于场集中的最佳形状纳米管


考虑了将电磁场从环境光源集中到纳米管中的问题。在边界元方法设置中，采用等几何分析方法来评估局部电场，该电场用与纳米管的几何表示完全相同的基函数表示。随后，对纳米管进行形状优化，以最大限度地提高其内部的场集中度。优化框架包括：（i） 一个全局优化器，作为无导数引导随机搜索方法和基于梯度的算法的组合实现，用于在最后阶段准确确定形状，（ii） 一个参数建模器，以相对较少的参数生成有效的非自相交纳米管形状，以及 （iii） 一个启用等几何的边界元方法求解器，以高准确性。确定了各种光学尺寸的最佳形状，与相应的圆形设计相比，收集的能量提高了两个数量级以上。重要的是，所选最佳形状的频率和角度响应往往在广泛的波长和定向波段上保持其卓越的性能。因此，所提出的结果可能对基于纳米管的装置中的光子逆设计有很大帮助，其应用范围从场定位和功率积累到波转向和能量收集。