HAMILTONIAN APPROACH TO EXCITON–POLARITON LUMINESCENCE SPECTRUM CALCULATION (International Conference on Modern Science and Scientific Studies, 2025)
The Hamiltonian approach provides a comprehensive theoretical framework for calculating exciton-polariton luminescence spectra in semiconductor microcavities. This study presents the fundamental theoretical foundations and methodological advances in applying Hamiltonian formulations to describe the optical emission properties of strongly coupled exciton-photon systems. We derive the key mathematical expressions for polariton eigenstates, analyze the spectral characteristics through master equation techniques, and demonstrate how the Hamiltonian approach enables accurate prediction of luminescence line shapes, intensities, and polarization dependencies. The theoretical framework encompasses both equilibrium and non-equilibrium polariton dynamics, providing essential tools for understanding cavity-mediated light-matter interactions in modern photonic devices. Our analysis reveals that proper treatment of the interaction Hamiltonian is crucial for capturing the rich physics of polariton emission, including coherence properties, nonlinear effects, and quantum statistical behavior.