物理
锥面
衍射
激发态
对称(几何)
操作员(生物学)
薛定谔方程
量子力学
光学
数学分析
数学
几何学
转录因子
基因
抑制因子
生物化学
化学
作者
Yiqi Zhang,Hua Zhong,Milivoj R. Belić,Yi Zhu,Wei‐Ping Zhong,Demetrios N. Christodoulides,Min Xiao
标识
DOI:10.1002/lpor.201600037
摘要
We investigate the fractional Schr\"odinger equation with a periodic $\mathcal{PT}$-symmetric potential. In the inverse space, the problem transfers into a first-order nonlocal frequency-delay partial differential equation. We show that at a critical point, the band structure becomes linear and symmetric in the one-dimensional case, which results in a nondiffracting propagation and conical diffraction of input beams. If only one channel in the periodic potential is excited, adjacent channels become uniformly excited along the propagation direction, which can be used to generate laser beams of high power and narrow width. In the two-dimensional case, there appears conical diffraction that depends on the competition between the fractional Laplacian operator and the $\mathcal{PT}$-symmetric potential. This investigation may find applications in novel on-chip optical devices.
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