Liu Zhenzhen, Zhang Qiang, Liu Xiangli, Yao Y, Xiao Jun-Jun
College of Electronic and Information Engineering, Shenzhen Graduate School, Harbin Institute of Technology, Xili, Shenzhen 518055, China.
Department of Materials Science and Engineering, Shenzhen Graduate School, Harbin Institute of Technology, Xili, Shenzhen 518055, China.
Sci Rep. 2016 Mar 7;6:22711. doi: 10.1038/srep22711.
The concept of parity-time (PT) symmetry in the field of optics has been intensively explored. This study shows the absence of exceptional points in a three-dimensional system composed of a square waveguide array with diagonally-balanced gain/loss distribution. More specifically, we show that an array of four coupled waveguides supports eight fundamental propagation supermodes, four of which are singlet, and the other two pairs are double degenerated. It is found that the singlet states follow the routine PT phase transition; however, the double-degenerated modes never coalesce as the gain/loss-to-coupling strength level varies, showing no actual PT symmetry-derived behavior. This is evident in the phase rigidity which does not approach zero. The absence of exceptional points is ascribed to the coupling of non-symmetric supermodes formed in the diagonal waveguide pairs. Our results suggest comprehensive interplay between the mode pattern symmetry, the lattice symmetry, and the PT-symmetry, which should be carefully considered in PT-phenomena design in waveguide arrays.
光学领域中的宇称 - 时间（PT）对称性概念已得到深入研究。本研究表明，在由具有对角平衡增益/损耗分布的方形波导阵列组成的三维系统中不存在例外点。更具体地说，我们表明四个耦合波导的阵列支持八个基本传播超模，其中四个是单态，另外两对是双重简并的。研究发现，单态遵循常规的PT相变；然而，随着增益/损耗与耦合强度水平的变化，双重简并模式从未合并，未表现出实际的PT对称性衍生行为。这在相位刚性不趋近于零的情况下很明显。例外点的不存在归因于对角波导对中形成的非对称超模的耦合。我们的结果表明模式图案对称性、晶格对称性和PT对称性之间存在综合相互作用，这在波导阵列的PT现象设计中应予以仔细考虑。
