Nonreciprocal Wave Propagation

Nonreciprocal media break time-reversal or parity symmetry, enabling unidirectional wave transport. In active metamaterials and gyroscopic lattices, the effective wave equation gains an advection-like term: ∂²u/∂t² + γ·∂u/∂x·c = c²∂²u/∂x². When γ→1, waves traveling left are amplified while rightward waves decay — an acoustic/elastic analogue of the quantum Hall edge state. Used in isolators, circulators, and topological wave guides.