We theoretically study the Goos-Hänchen (GH) shifts of Gaussian beams reflected in parity-time (PT) symmetric multilayered structure coating graphene structures. And there are the exceptional points (EPs) in this structure, whose position can be adjusted by the real part of the dielectric constant and the incident angle. Moreover, we find that the value and direction of the GH shifts change significantly under different EPs, so we could control the GH shifts by the position of the EPs. When the dielectric constant is fixed, the GH shifts can also be adjusted by the Fermi energy of graphene and the period number of the PT-symmetric structure. With the increase of the period number of the PT system, the system will produce the Bragg resonance, which refers to the phenomenon of total reflection caused by the interaction between the wave and the periodic structure with a specific frequency. And at the Bragg resonance, the special GH shifts independent of the incident direction can be obtained with large reflectivity. In addition, the incident direction of the beam can also affect the GH shifts in this asymmetric structure. Our results may find great applications in highly sensitive sensors, optoelectronic switches, and all-optical devices.

中文翻译：

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由涂有石墨烯的 PT 对称周期性多层结构中的特殊点控制的巨大 Goos-Hänchen 位移

我们从理论上研究了高斯光束在奇偶时间 (PT) 对称多层结构涂层石墨烯结构中反射的 Goos-Hänchen (GH) 位移。并且该结构中存在异常点（EPs），其位置可以通过介电常数的实部和入射角进行调整。此外，我们发现在不同的 EP 下，GH 位移的值和方向发生了显着变化，因此我们可以通过 EP 的位置来控制 GH 位移。当介电常数固定时，GH 位移也可以通过石墨烯的费米能量和 PT 对称结构的周期数进行调整。随着 PT 系统周期数的增加，系统会产生布拉格共振，是指波与具有特定频率的周期结构相互作用而引起的全反射现象。并且在布拉格共振下，可以通过大反射率获得与入射方向无关的特殊 GH 位移。此外，光束的入射方向也会影响这种非对称结构中的 GH 位移。我们的结果可能会在高灵敏度传感器、光电开关和全光器件中找到很好的应用。