AI 中文总结
该研究探究局域耦合环形谐振器的宇称-时间相变，通过解析与数值方法分析线性区模式特性，利用绝热传播获得非线性克尔波形，揭示耦合空间轮廓可调控多模宇称-时间相变与非线性波形。
AI 中文摘要
我们研究了在由超高斯轮廓描述的有限角区域上耦合的两个宇称-时间对称环形谐振器。在线性区域，我们在均匀耦合和固定振幅窄接触极限下获得了解析光谱，而有限宽度问题则通过数值处理。局域耦合引入了非零空间傅里叶分量，这些分量混合了角谐波并解除了反向传播模式的简并性，将每个激发的二重态分解为与宇称相关的分支。这些分支之间的碰撞产生了多个例外点边界和不连通的破缺宇称-时间域。当改变增益-损耗强度、耦合宽度或峰值耦合振幅时，所得的相图表现出折返的未破缺-破缺-未破缺转变。数值光谱可连续恢复两种解析极限。在非线性区域，我们选择选定的基态和激发线性模式作为种子，用于绝热传播到有限振幅的克尔波形，这些波形在模拟观测区间内，对于有限范围的非线性强度保持动态持久性。这些结果表明，谐振器间耦合的空间轮廓提供了一种几何手段，可用于控制耦合环形系统中的多模宇称-时间相变，并选择动态可访问的非线性波形。
英文摘要
We investigate two parity-time-symmetric ring resonators coupled over a finite angular region described by a super-Gaussian profile. In the linear regime, analytical spectra are obtained in the homogeneous-coupling and fixed-amplitude narrow-contact limits, while the finite-width problem is treated numerically. Local coupling introduces nonzero spatial Fourier components that mix angular harmonics and lift the degeneracy of counterpropagating modes, resolving each excited doublet into parity-dependent branches. Collisions among these branches generate multiple exceptional-point boundaries and disconnected broken-PT domains. The resulting phase diagrams exhibit re-entrant unbroken-broken-unbroken transitions when the gain-loss strength, coupling width, or peak coupling amplitude is varied. The numerical spectra continuously recover both analytical limits. In the nonlinear regime, selected ground and excited linear modes are used as seeds for adiabatic propagation into finite-amplitude Kerr waveforms that remain dynamically persistent over the simulated observation interval for finite ranges of nonlinear strength. These results show that the spatial profile of inter-resonator coupling provides a geometric means of controlling multimode PT transitions and selecting dynamically accessible nonlinear waveforms in coupled-ring systems.
Comments10 pages, 9 figures, submitted for publication
