Full-Wave Green's-Function Modeling of Collective Single-Photon Emission in Non-Markovian Open-System QED with Finite-Bandwidth Compensation of Dispersive Interactions

This work presents a full-wave Green's function framework for modeling collective and coherent single-photon emission from multiple quantum emitters embedded in complex electromagnetic structures.

Starting from a transverse modal completeness relation of modified Langevin noise formalism, we derive a closed set of coupled equations for population dynamics and frequency-resolved field amplitudes in the single-excitation regime.

Since the electromagnetic reservoir is not traced out at the level of the dynamical amplitudes, the emitted single-photon dynamics can be modeled within the same closed set of equations without Markovian approximation in open and dissipative environments.

We demonstrate that finite-bandwidth truncation of the spectral density leads to systematic deviations in coherent dispersive interactions, even when dissipative rates appear converged.

To restore causal consistency, we introduce a counter-term compensation scheme that restores the missing dispersive contributions without modifying the retained non-Markovian memory kernel.

To validate the scheme and demonstrate the practicality of the proposed framework, we present numerical examples ranging from benchmark configurations to a three-dimensional dispersive ring-resonator structure via finite element method.

These capabilities provide a practical route for rigorously incorporating full-wave electromagnetic simulations into non-Markovian multi-emitter quantum electrodynamics, enabling predictive modeling of collective emission, coherent energy exchange, and single-photon radiation in realistic open structures.