Abstract：
The near-field interaction between quantum emitters, governed by Förster resonance energy transfer (FRET), plays a pivotal role in nanoscale energy transfer mechanisms. However, FRET measurements in the optical regime are challenging as they require nanoscale control of the position and orientation of the emitters. To overcome these challenges, microwave measurements were proposed for enhanced spatial resolution and precise orientation control. However, unlike in optical systems for which the dipole can be taken to be infinitesimal in size, the finite size of microwave antennas can affect energy transfer measurements, especially at short distances. This highlights the necessity to consider the finite antenna length to obtain accurate results. In this study, we advance the understanding of dipole-dipole energy transfer in the microwave regime by developing an analytical model that explicitly considers finite antennas. Unlike previous works, our model calculates the mutual impedance of finite-length thin-wire dipole antennas without assuming a uniform current distribution. We validate our analytical model through experiments investigating energy transfer between antennas placed adjacent to a perfect electric conductor mirror. This allows us to provide clear guidelines for designing microwave experiments, distinguishing conditions where finite-size effects can be neglected and where they must be taken into account. Our study not only contributes to the fundamental physics of energy transfer but also opens avenues for microwave antenna impedance-based measurements to complement optical FRET experiments and quantitatively explore dipole-dipole energy transfer in a wider range of conditions.
摘要：
量子发射器之间的近场相互作用，受福斯特共振能量转移(FRET)支配，在纳米尺度的能量传递机制中起着举足轻重的作用。然而,光学区域中的FRET测量具有挑战性，因为它们需要对发射器的位置和方向进行纳米级控制。为了克服这些挑战，微波测量提出了增强的空间分辨率和精确的方向控制。然而,与光学系统中偶极子可以被认为是无穷小的不同，微波天线的有限尺寸会影响能量转移测量，尤其是在短距离。这突出了考虑有限天线长度以获得准确结果的必要性。在这项研究中,通过建立明确考虑有限天线的分析模型，我们可以提高对微波条件下偶极-偶极能量转移的理解。与以前的作品不同，我们的模型计算有限长度的细线偶极天线的互阻抗没有假设一个均匀的电流分布。我们通过研究与完美电导体镜相邻的天线之间的能量转移的实验来验证我们的分析模型。这使我们能够为设计微波实验提供明确的指导,区分有限尺寸效应可以忽略和必须考虑的条件。我们的研究不仅有助于能量转移的基本物理学，而且还为基于微波天线阻抗的测量开辟了途径，以补充光学FRET实验，并在更广泛的条件下定量探索偶极-偶极能量转移。
