Anderson localization confines waves in space through disorder in a material's spatial structure. The wave bounces between random scatterers and interferes destructively in all directions except one, trapping itself. The temporal analogue would confine waves in time — concentrating energy at specific moments rather than specific locations.
Jiang, Hu, Long, and colleagues demonstrate broadband temporal localization in time photonic crystals. The mechanism combines two ingredients: temporal modulation of the material (creating a “crystal” in time rather than space) and material-induced non-Hermiticity (gain and loss that break time-reversal symmetry of the wave equation).
Temporal modulation alone creates bandgaps in frequency — forbidden bands where propagation is suppressed, analogous to spatial photonic crystals. But with the addition of bi-anisotropic electromagnetic responses, the temporal bulk states exhibit remarkable attenuation or amplification depending on the material parameters. Tuned correctly, the combination produces broadband temporal localization: energy that was spread across time becomes concentrated at specific moments.
The framework extends the generalized Brillouin zone — a tool from non-Hermitian spatial photonics — to the temporal domain. The Brillouin zone becomes complex-valued, and the imaginary parts of the temporal wavevectors determine whether states are temporally localized or delocalized.
The paper also discovers delocalized temporal edge states — temporal analogues of topological edge states that exist at the boundary between two temporal crystal phases and extend freely in time rather than being confined. Localized bulk, delocalized edge. The spatial analogy carried to its conclusion in time.