QUANTUM-THEORY FOR EXCITON POLARITONS IN A REAL-SPACE REPRESENTATION

We develop a real-space method for exciton polaritons in a bounded med ium with a tight-binding approximation. The creation and annihilation operators for photons are approximately constructed in a real-space re presentation. The quantum-mechanical derivation gives all necessary bo undary conditions and complete solutions to the problem of reflection and transmission near the resonance of excitons. The present theory wi thout the long-wavelength approximation covers the whole range of syst em size. In addition we calculate transient responses for short-pulse excitation. The results deeply reflect the spatial dispersion of excit on polaritons.