Establishing parity-time (PT) symmetry in non-spatial space is a promising way to simplify the PT-symmetry system structure. In this paper, an implementation of PT symmetry in optical polarization space is reported. By utilizing the polarization multiplexing technology, PT symmetry is formed in overlapping spatial parameter space. The degeneracy of eigenmodes with two distinct PT phases in polarization space is demonstrated. In the PT-symmetric phase, the eigenmodes have real eigenfrequencies that respect PT symmetry, exhibiting broken degeneracy (mode splitting); in the PT-broken phase, the eigenmodes are degenerate with a pair of complex conjugate eigenfrequencies. The sharp-pointed peak filter response in the PT-broken phase due to the strong field localization is characterized, which explains the mode-selection mechanism of PT-symmetry breaking. The polarization-space PT symmetry is applied in a 7-km single-loop optoelectronic oscillator, and a stable single-mode oscillation signal is generated with a phase noise of −138 dBc/Hz at 10 kHz and side-mode suppression ratio of 49 dB. The approach expands the parameter spaces to carry out PT symmetry and could promote the integration of the PT-symmetry photon system.

中文翻译：

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极化参数空间中的奇偶时间对称性

在非空间空间中建立奇偶时间 (PT) 对称性是一种简化 PT 对称性系统结构的有前途的方法。在本文中，报道了光偏振空间中 PT 对称性的实现。利用偏振复用技术，在重叠的空间参数空间中形成PT对称。证明了偏振空间中具有两个不同 PT 相位的本征模式的简并性。在 PT 对称阶段，本征模式具有尊重 PT 对称性的真实本征频率，表现出破坏简并（模式分裂）；在 PT 断裂阶段，本征模式退化为一对复共轭本征频率。由于强场定位，在 PT 断开阶段的尖峰滤波器响应的特征在于，这解释了 PT 对称性破坏的模式选择机制。偏振空间PT对称性应用于7km单环光电振荡器，产生稳定的单模振荡信号，10 kHz相位噪声为-138 dBc/Hz，边模抑制比为49 D b。该方法扩展了参数空间以进行 PT 对称，并可以促进 PT 对称光子系统的集成。