AI 中文总结
研究有限耗散Hatano-Nelson光子晶格的线性光学响应，利用双正交格林函数分解响应，分析损耗、周期性边界光谱缠绕、 onsite无序对模式分布的影响，确定有限尺寸交叉点，适用于多种线性光子平台。
AI 中文摘要
我们研究有限耗散Hatano-Nelson光子晶格的线性光学响应。利用双正交格林函数，将选定输入与输出端口间的响应分解为相位相干强度和非相干模式权重贡献；二者的对比可分离非厄米模式残差间的干涉，而响应权重熵及相关的有效模式数Neff可量化测量信号在复模式上的分布广度。数值结果表明：损耗会拓宽模式分布，周期性边界的光谱缠绕会增加模式参与度， onsite无序则会降低模式参与度。时域量子行走动力学独立显示了开放边界下非互易跃迁产生的漂移和右边缘积累。在(g,W)平面上的参数图（辅以无序系综平均）确定了有限尺寸交叉点，其中Neff对无序的响应早于响应加权中心从皮肤边界位移。该分析适用于耦合波导、微环阵列、驱动腔晶格及其他含损耗、增益或非互易耦合的线性光子平台。
英文摘要
We study the linear optical response of a finite dissipative Hatano--Nelson photonic lattice. The response between selected input and output ports is resolved into a phase-coherent intensity and an incoherent modal-weight contribution using the biorthogonal Green function. Their comparison isolates interference among non-Hermitian modal residues, while a response-weight entropy and the associated participation number $\Neff$ quantify how broadly the measured signal is distributed over the complex modes. The numerical results show that loss broadens the modal distribution, periodic-boundary spectral winding increases modal participation, and onsite disorder reduces it. Time-domain quantum-walk dynamics independently display the drift and right-edge accumulation produced by non-reciprocal hopping under open boundaries. A parameter map in the $(g,W)$ plane, supplemented by disorder-ensemble averages, identifies a finite-size crossover in which $\Neff$ responds to disorder before the response-weighted center is displaced from the skin boundary. The analysis applies to coupled waveguides, microring arrays, driven cavity lattices, and other linear photonic platforms with loss, gain, or non-reciprocal coupling.
