紧密间隔的高折射率纳米粒子之间的非奇异热点
Non-singular hotspots between closely spaced high-index nanoparticles
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中文总结 AI 辅助
研究三维空间中两个近接触高折射率介质谐振器间场的集中，通过弱耦合机制解释场梯度在间隙先增长后饱和的现象，经数值实验证实从放大到饱和的转变，加强谱微扰估计实现从平均到逐点控制。
中文摘要 AI 辅助
我们研究了三维空间中两个几乎接触的高折射率介质谐振器之间场的集中情况。该模型是共振状态下的标量亥姆霍兹传输问题，其中谐振器内的波长与其典型直径同阶。材料对比度仅进入方程的低阶项而非主项。因此，场的梯度与粒子间距无关保持有界，不会发散。然而，模拟和实验表明梯度仍集中在间隙中：随着粒子靠近，在中间距离范围内它像粒子间距的倒数一样增长，一旦它们非常接近就会饱和。我们通过弱耦合机制解释这种预渐近效应，其中一对的共振模式是每个孤立粒子模式的微扰。当这样的模式在两个相对边界之间保持非零对比度时，间隙上的均值论证解释了梯度的增长；这需要将标准谱微扰估计从平均控制加强到逐点控制。一旦粒子间相互作用不再微弱且微扰理论失效，增长就会停止。数值实验证实了从放大到饱和的转变。
英文摘要
We study the concentration of the field between two nearly touching high-index dielectric resonators in three dimensions. The model is a scalar Helmholtz transmission problem in the resonant regime, wherein the wavelength inside the resonators of the same order as their typical diameter. The material contrast enters only a lower-order term of the equation and not its principal part. As a consequence, the gradient of the field stays bounded independently of the distance separating the particles, and does not blow up. Nevertheless, simulations and experiments show that the gradient still concentrates in the gap: as the particles approach, it grows like the inverse of their separation over an intermediate range of distances and then saturates once they are very close. We explain this pre-asymptotic effect through a weak-coupling regime, in which the resonant modes of the pair are perturbations of the modes of each isolated particle. When such a mode keeps a nonzero contrast between the two facing boundaries, a mean value argument across the gap accounts for the growth of the gradient; this requires strengthening the standard spectral perturbation estimates from an average to a pointwise control. The growth stops once the interaction between the particles is no longer weak and the perturbation theory fails. Numerical experiments confirm the transition from amplification to saturation.
