Light propagation in systems with anti-Hermitian coupling, described by a spinor-like wave equation, provides a general route for the observation of antiparity-time ($\mathcal{PT}$) symmetry in optics. Remarkably, under a different definition of parity operator, a $\mathcal{PT}$ symmetry can be found as well in such systems. Such symmetries are ubiquitous in nonlinear optical interactions and are exemplified by considering modulation instability in optical fibers and optical parametric amplification.

中文翻译：

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$\mathcal{PT}$ -Hermitian波耦合和非线性光学相互作用的对称性和反对称性

用类旋子的波动方程描述的具有反赫尔米特耦合的系统中的光传播为观察奇偶时间提供了一条通用的路径（$\mathcal{PT}$）光学中的对称性。值得注意的是，在奇偶运算符的不同定义下，$\mathcal{PT}$在这样的系统中也可以找到对称性。这种对称性在非线性光学相互作用中普遍存在，并通过考虑光纤中的调制不稳定性和光学参量放大来举例说明。