结合广义米氏理论的伴随优化实现功能光子贴片的逆向设计
Inverse design of functional photonic patches by adjoint optimization coupled to the generalized Mie theory
AI总结：
本研究提出将伴随优化与二维广义米氏理论结合的严谨方法，实现功能光子贴片的逆向设计，可完成辐射塑形等多种功能，且非周期沃格尔螺旋结构在消色差聚焦上优势显著，计算量远低于标准数值优化方法。
摘要：
我们提出了一种用于功能光子结构逆向设计的严谨方法，该方法将伴随优化方法与二维广义米氏理论（2D-GMT，two-dimensional generalized Mie theory）相结合，用于解决经优化可展现预期功能的有限尺寸介质纳米圆柱阵列的多重散射问题。我们将这类功能散射结构称为“光子贴片（photonic patches）”。本文简要介绍了2D-GMT的理论形式，以及将伴随优化算法应用于具备设计辐射特性的光子贴片所需的关键步骤。我们特别展示了多个周期与非周期光子贴片的示例，这些贴片通过优化纳米圆柱的半径与排列，可实现辐射塑形、菲涅耳区的波前聚焦，以及在微米级区域内多波长下的局域态密度（LDOS，local density of states）增强。此外，我们系统比较了不同尺寸的周期与非周期贴片的性能，发现优化后的非周期沃格尔螺旋（Vogel spiral）结构在消色差聚焦方面，相较于周期结构具备显著优势。我们的结果表明，伴随优化与2D-GMT相结合的方法，是对工作在多重散射 regime、具备最优预期功能的紧凑型光子器件进行逆向设计的可靠方法。该方法无需空间网格划分，与标准数值优化技术相比，能以大幅降低的计算量提供高效解决方案，并可为片上光子学与超材料技术提供紧凑型器件结构方案。
英文摘要：
We propose a rigorous approach for the inverse design of functional photonic structures by coupling the adjoint optimization method and the two-dimensional generalized Mie theory (2D-GMT) for the multiple scattering problem of finite-size arrays of dielectric nanocylinders optimized to display desired functions. We refer to these functional scattering structures as "photonic patches". We briefly introduce the formalism of 2D-GMT and the critical steps necessary to implement the adjoint optimization algorithm to photonic patches with designed radiation properties. In particular, we showcase several examples of periodic and aperiodic photonic patches with optimal nanocylinder radii and arrangements for radiation shaping, wavefront focusing in the Fresnel zone, and for the enhancement of the local density of states (LDOS) at multiple wavelengths over micron-size areas. Moreover, we systematically compare the performances of periodic and aperiodic patches with different sizes and find that optimized aperiodic Vogel spiral geometries feature significant advantages in achromatic focusing compared to their periodic counterparts. Our results show that adjoint optimization coupled to 2D-GMT is a robust methodology for the inverse design of compact photonic devices that operate in the multiple scattering regime with optimal desired functionalities. Without the need of spatial meshing, our approach provides efficient solutions at strongly reduced computational burden compared to standard numerical optimization techniques and suggests compact device geometries for on-chip photonics and metamaterials technologies.
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