Dynamically Encircling Exceptional Points: Exact Evolution and Polarization State Conversion
Dynamically Encircling Exceptional Points: Exact Evolution and Polarization State Conversion
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DOI：
10.1103/physrevlett.118.093002
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发表时间：
2017-03-03
影响因子：
8.6
通讯作者：
Christodoulides, Demetrios N.
中科院分区：
文献类型：
--
作者：
Hassan, Absar U.;Zhen, Bo;Christodoulides, Demetrios N.
我们表明，一个两个层次的非厄米哈密顿常数非对角交换元素时，可以准确地分析潜在的例外点是完全包围在复平面。这个系统的状态演化是明确获得的一个随之而来的传输矩阵，即使是大encirclements，无论绝热条件。我们的结果清楚地解释了这个过程的方向依赖性，以及为什么在绝热极限下，它的结果是由一个特定的本征态主导的，而与初始条件无关。此外，数值模拟表明，这种机制仍然可以持续存在的非线性效应。我们进一步表明，这个强大的过程可以利用实现光学全偏振器：一种配置，无论输入偏振态如何，都会产生所需的偏振输出，而从相反的方向，它总是产生对应的本征态。
We show that a two-level non-Hermitian Hamiltonian with constant off-diagonal exchange elements can be analyzed exactly when the underlying exceptional point is perfectly encircled in the complex plane. The state evolution of this system is explicitly obtained in terms of an ensuing transfer matrix, even for large encirclements, regardless of adiabatic conditions. Our results clearly explain the direction-dependent nature of this process and why in the adiabatic limit its outcome is dominated by a specific eigenstate-irrespective of initial conditions. Moreover, numerical simulations suggest that this mechanism can still persist in the presence of nonlinear effects. We further show that this robust process can be harnessed to realize an optical omnipolarizer: a configuration that generates a desired polarization output regardless of the input polarization state, while from the opposite direction it always produces the counterpart eigenstate.