[論文レビュー] Hyperuniform Disorder in Photonic Crystal Slabs with Intrinsic non-Hermiticity

Zeyu Zhang, Koorosh Sadri+2 more|arXiv (Cornell University)|Mar 4, 2026

Quantum Mechanics and Non-Hermitian Physics被引用数 0

ひとこと要約

The paper develops a theoretical framework for hyperuniform disorder in non-Hermitian photonic crystal slabs with radiative loss, showing that Hermitian cases yield Im(Σk) ~ k^α while non-Hermitian cases produce a leading constant plus a subleading k^β2 term, verified by TB and FDTD simulations.

ABSTRACT

Hyperuniform disorder is a type of correlated disorder characterized by vanishing spectral density at small wavevectors, making the configuration effectively homogeneous on long length scales. In photonics, hyperuniform disorder is promising for generating isotropic photonic pseudogaps and engineering photonic crystal waveguides. However, these studies are largely restricted to idealized lossless settings, although all photonic systems necessarily have loss. In this work, light propagation in photonic crystal slabs with imposed hyperuniform disorder is investigated theoretically and numerically. The system is intrinsically non-Hermitian due to radiative loss, with non-Hermiticity appearing as a complex effective mass of a quadratic photonic band. A theoretical framework for disorder scattering is analytically derived in Hermitian and non-Hermitian quadratic bands with real and complex effective mass, respectively. In contrast to the power law behavior $|\mathbf{k}|^α$ observed in the Hermitian case (where $α$ is the hyperuniformity exponent), the scattering loss in the non-Hermitian band is given by $C_0+C_{β_2}\cdot|\mathbf{k}|^{β_2}$, where $C_0$ is a finite constant and the exponent $β_2\leq 2$. Our theoretical predictions are verified with tight-binding and Finite-Difference Time-Domain simulations with realistic photonic crystal parameters, based on recent experiments.

研究の動機と目的

• Motivate and model hyperuniform disorder in photonic crystal slabs with intrinsic radiative loss (non-Hermiticity).
• Derive a disorder-scattering framework for Hermitian and non-Hermitian quadratic bands with real and complex effective mass.
• predict how the scattering loss scales with momentum k for different hyperuniformity exponents α.
• Validate theoretical predictions using tight-binding and finite-difference time-domain simulations with realistic parameters.

提案手法

• Represent disorder as a spatial potential V'i,j calibrated from local band tip energy shifts.
• Impose hyperuniform disorder via Fourier filtering to achieve spectral density ρ̃(q) ∝ qα for small q.
• Use perturbative (Born) self-energy Σk to compute Im(Σk) and its dependence on α and k.
• Extend to non-Hermitian bands with complex m, giving Im(Σk) leading with a finite C0 and a next term Cβ2·kβ2.
• Introduce self-consistent Born approximation (SCBA) to account for multiple scattering when α is small.
• Verify predictions with tight-binding simulations and FDTD simulations using realistic photonic-crystal parameters.

Figure 1: The non-Hermitian nature of photonic crystal slabs. (a) An illustration of the photonic crystal slab. The in-plane geometry contains circular air holes in a square lattice. (b) The simulated reflection spectrum of the structure in (a) along $k_{y}=0$ . (c) The resonance frequency of the ba

実験結果

リサーチクエスチョン

• RQ1 How does hyperuniform disorder modify scattering loss in Hermitian quadratic bands?
• RQ2 What is the scaling of scattering loss with momentum k in non-Hermitian quadratic bands with complex effective mass?
• RQ3 How does the hyperuniformity exponent α influence leading and subleading terms in Im(Σk) in both Hermitian and non-Hermitian cases?
• RQ4 To what extent do multiple scattering effects (SCBA) impact the theoretical predictions compared to TB and FDTD results?

主な発見

• In Hermitian quadratic bands, Im(Σk) ∝ k^α, capturing the hyperuniform disorder signature.
• In non-Hermitian quadratic bands, Im(Σk) has a finite leading constant C0 ∝ Im(m) and a subleading term ∝ k^β2 with β2 ≤ 2.
• The leading scattering loss in the non-Hermitian case scales as (α+2)/(α) times w^2 a^2 divided by 6π α, times Im(m).
• For α > 2, the second-leading exponent β2 equals 2; β2 exhibits a jump near α = (2/π) arctan(Re(m)/Im(m)) + 1 due to coefficient vanishing in the k^α term.
• SCBA calculations align well with TB and FDTD results, especially at larger α, while deviations at small α are attributed to higher-order multiple scattering effects.
• The work provides a benchmark for hyperuniform disorder in non-Hermitian systems and guides device design under realistic loss.

Figure 2: Hyperuniform disorder in photonic crystal slabs. (a) Local potential configuration with uncorrelated disorder. The color and the size of the holes represent the local potential change at each site with respect to the periodic (without disorder) case. Only an area of $30\times 30$ unit cell