Hyperuniform disorder — randomness with suppressed long-wavelength density fluctuations — creates photonic materials that are disordered locally but uniform at large scales. In lossless systems, this structured randomness enables isotropic band gaps and engineered waveguides with predictable scattering properties governed by clean power laws. But real photonic crystal slabs radiate. They leak energy into the continuum. When radiative loss enters the picture as an intrinsically non-Hermitian effect — a complex effective mass in the photonic band — the scattering rules change fundamentally.
Instead of the power-law dependence on wavevector that characterizes Hermitian hyperuniform systems, the non-Hermitian case introduces a constant offset: scattering loss follows C_0 + C|k|^{beta} with beta less than or equal to 2. The constant floor means that even perfect hyperuniform correlations cannot suppress loss below a threshold set by the non-Hermitian band structure. Loss imposes a noise floor that disorder engineering alone cannot breach.
The deeper pattern: when a system is open to its environment — when energy can escape — the tools that control internal structure hit a wall. Radiative coupling to the outside world creates an irreducible baseline that no amount of structural optimization within the material can eliminate. Openness sets a lower bound that order cannot reach.
(arXiv:2603.04389)