光子 Urbach 尾部的普遍性与各向异性
Universality and anisotropy of the Photonic Urbach Tail
AI总结：
研究揭示了光子晶体波导中各向异性无序导致的 Urbach 法律普遍性，以及 Urbach 能量的各向异性特性。
摘要：
光子晶体和波导中的无序会在光子带隙内产生状态。这些状态通常被描述为 Lifshitz 尾部，尽管其能量分布与 Lifshitz 统计在带边缘附近不一致。在这里，我们表明在故意设计的各向异性无序光子晶体波导中，可实验访问的带边缘尾部遵循普遍的 Urbach 法律，其累积统计为 F(Δ)=exp[-(Δ/α)^β]，其中 Δ 是谱偏移量，β≈1，与无序强度和方向无关。与 Lifshitz 行为不同，态密度在带边缘最大，并向间隙衰减。关键的是，我们发现 Urbach 能量 α 是各向异性的，具有明显的方向分裂，并且对于与波导轴平行或垂直的无序，其标度特性不同。这些结论得到了 GaAs 光子晶体波导的光学测量与全向模拟的定量一致的支持。各向异性 Urbach 能量作为无序-模式耦合的敏感探测器，并成为表征光子器件中结构无序的实用指标。
英文摘要：
Disorder in photonic crystals and waveguides creates states inside the photonic band gap. These states are often described as Lifshitz tails despite exhibiting energy distributions inconsistent with Lifshitz statistics near the band edge. Here we show that in photonic-crystal waveguides with intentionally engineered anisotropic disorder, the band-edge tail accessible experimentally follows an Urbach law universally, with cumulative statistics $F(Δ)=\exp[-(Δ/α)^β]$, where $Δ$ is the spectral detuning from the band edge, and an exponent $β\approx 1$ independent of disorder strength and orientation. In contrast to Lifshitz behavior, the density of states is maximal at the band edge and decays into the gap. Crucially, we find that the Urbach energy $α$ is anisotropic, with a pronounced directional splitting and qualitatively different scaling for disorder parallel and perpendicular to the waveguide axis. These conclusions are supported by quantitative agreement between optical measurements of GaAs photonic-crystal waveguides and full-vector simulations. The anisotropic Urbach energy emerges as a sensitive probe of disorder-mode coupling and a practical metric to characterize structural disorder in photonic devices.
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