The Electromagnetic Field and Laser Dynamics in a Cavity Bounded by Moving Mirrors

摘要

The propagation of light in a one-dimensional cavity bounded by moving mirrors is studied in the context of the theory of gas lasers. A canonical quantization of the free field is carried out by utilizing the symplectic structure of the space of solutions of the wave equation. It is shown that no Hamiltonian and no Schrodinger picture exists and that the photon number operator is in general not conserved. Changes in the number operator are, however, ordinarily too small to be observed experimentally. Automorphic coordinate transformations are used to develop adiabatic expansions for the mode functions of cavities with one fixed and one moving mirror. The coupling of the field to two-level atoms is done both quantum-mechanically and semi-classically. For the interacting quantum field an interaction Hamiltonian does exist, even though there is no total Hamiltonian. The semi-classical equations treat the atomic density matrix as a distribution in phase space. They possess traveling wave solutions which are expected to be important in understanding the behavior of mode-locked lasers. (Author)