Quantum Mechanical Treatment of Optical Amplifiers Based on Population Inversion

Optical amplification in a population-inverted medium is quantum-mechanically described, using the Heisenberg picture. Unlike conventional approaches that use a photon rate equation or a phenomenological field equation, the time evolution of the field operator, the photon number operator, and their squares are directly derived from first principles. The results give a logical theoretical base for the traditional phenomenological expressions describing quantum-mechanical characteristics of optical amplifiers.