Non-Exponential Decay in Finite Photonic Waveguide Arrays

Open quantum-system dynamics can follow exponential decay, non-exponential relaxation, or oscillatory dynamics, depending on the system-environment coupling. We study a lattice with a boundary defect that transitions between these regimes, controlled by a single parameter. Extending the exact solution to the oscillatory case, we establish a unified theory confirmed by experiments in integrated waveguide arrays. We characterize finite-size effects by comparing analytics, numerics, and data. This provides a benchmark for emulating infinite systems and studying open systems in photonic lattices.