论文标题
ENZ材料中对介电介电常数的复杂分析依赖性：光子掺杂示例
Complex Analytic Dependence on the Dielectric Permittivity in ENZ Materials: The Photonic Doping Example
论文作者
论文摘要
由由“ epsilon-near-Zero”（ENZ）矩阵制成的散射器“光子掺杂”的物理文献所激发的，我们考虑如何通过圆柱形区域$ω\ times \ times \ times \ nationbb {r} $ subs of a $ dopecter of Anceant of Anclant of Anclant of Anclant of Anclant of Anclant of Anclant of Ancant'dopopecter's cylindrical enz enz enz enz enz区域$介电常数不接近零。从数学上讲，这简化为分析2D Helmholtz方程$ \ MATHRM {div} \，（A（x）\ nabla u） + k^2 U = f $，带有分段恒定的，复杂的值的$ a $几乎是无限的（例如$ a = $ a = \ freac $ a $ a = $ a $） \ bar {d}。$我们显示（在适当的假设下），解决方案$ u $在分析上取决于$δ$接近$ 0 $，我们在其泰勒扩展中对术语进行了简单的PDE表征。对于光子掺杂的应用，最有趣的是$δ$中的前阶校正：它们解释了为什么光子掺杂仅受损失的存在轻度影响，以及为什么在介电介电常数仅小的频率上也可以看到它。同样重要的是：我们的结果包括对ENZ区域中领先电场的PDE表征为$δ\ 0 $，而现有的光子掺杂文献仅提供了前阶磁场。
Motivated by the physics literature on "photonic doping" of scatterers made from "epsilon-near-zero" (ENZ) matrials, we consider how the scattering of time-harmonic TM electromagnetic waves by a cylindrical ENZ region $Ω\times \mathbb{R}$ is affected by the presence of a "dopant" $D \subset Ω$ in which the dielectric permittivity is not near zero. Mathematically, this reduces to analysis of a 2D Helmholtz equation $\mathrm{div}\, (a(x)\nabla u) + k^2 u = f$ with a piecewise-constant, complex valued coefficient $a$ that is nearly infinite (say $a = \frac{1}δ$ with $δ\approx 0$) in $Ω\setminus \bar{D}.$ We show (under suitable hypotheses) that the solution $u$ depends analytically on $δ$ near $0$, and we give a simple PDE characterization of the terms in its Taylor expansion. For the application to photonic doping, it is the leading-order corrections in $δ$ that are most interesting: they explain why photonic doping is only mildly affected by the presence of losses, and why it is seen even at frequencies where dielectric permittivity is merely small. Equally important: our results include a PDE characterization of the leading-order electric field in the ENZ region as $δ\to 0$, whereas the existing literature on photonic doping provides only the leading-order magnetic field.
