Exceptional Points of Degeneracy Induced by Linear Time-Periodic Variation
Exceptional Points of Degeneracy Induced by Linear Time-Periodic Variation
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DOI：
10.1103/physrevapplied.11.014007
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发表时间：
2019-01-04
影响因子：
4.6
通讯作者：
Capolino, Filippo
中科院分区：
文献类型：
--
作者：
Kazemi, Hamidreza;Nada, Mohamed Y.;Capolino, Filippo
本文提出了周期时变系统的例外退化点（EPD）理论。我们表明，即使是一个单一的谐振器的时间周期组件是能够开发EPD，相反的奇偶校验时间（PT）对称系统，需要两个耦合谐振器。EPD是系统参数空间中的一个特殊点，在该点处，两个或多个本征模在其本征值和本征向量中合并成单个简并本征模。我们证明了EPD存在的条件时，他们直接引起的时间周期变化的系统没有损失和增益元素。我们还表明，一个单一的谐振器系统与零时间平均损耗增益表现出EPD与纯粹的真实的谐振频率，但谐振器的能量增长代数的时间，因为能量注入系统的时变机制。虽然所介绍的概念和形式主义是一般的任何时间周期系统，在这里，我们专注于EPD的发生在一个单一的LC谐振器与时间周期调制。这些发现在各种电磁和光子系统中具有重要意义，并为传感器，放大器和调制器等许多应用铺平了道路。我们展示了这种随时间变化的EPD作为一种高灵敏度传感器的潜在应用。
We present a general theory of exceptional points of degeneracy (EPD) in periodically time-variant systems. We show that even a single resonator with a time-periodic component is able to develop EPDs, contrary to parity-time-(PT) symmetric systems that require two coupled resonators. An EPD is a special point in a system parameter space at which two or more eigenmodes coalesce in both their eigenvalues and eigenvectors into a single degenerate eigenmode. We demonstrate the conditions for EPDs to exist when they are directly induced by time-periodic variation of a system without loss and gain elements. We also show that a single resonator system with zero time-average loss-gain exhibits EPDs with purely real resonance frequencies, yet the resonator energy grows algebraically in time since energy is injected into the system from the time-variation mechanism. Although the introduced concept and formalism are general for any time-periodic system, here, we focus on the occurrence of EPDs in a single LC resonator with time-periodic modulation. These findings have significant importance in various electromagnetic and photonic systems and pave the way for many applications, such as sensors, amplifiers, and modulators. We show a potential application of this time-varying EPD as a highly sensitive sensor.