Criterion of applicable models for planar type Cherenkov laser based on quantum mechanical treatments

A generalized theoretical analysis for amplification mechanism in the planar-type Cherenkov laser is given. An electron is represented to be a material wave having temporal and spatial varying phases with finite spreading length. Interaction between the electrons and the electromagnetic (EM) wave is analyzed by counting the quantum statistical properties. The interaction mechanism is classified into the Velocity and Density Modulation (VDM) model and the Energy Level Transition (ELT) model basing on the relation between the wavelength of the EM wave and the electron spreading length. The VDM model is applicable when the wavelength of the EM wave is longer than the electron spreading length as in the microwave region. The dynamic equation of the electron, which is popularly used in the classical Newtonian mechanics, has been derived from the quantum mechanical Schrodinger equation. The amplification of the EM wave can be explained basing on the bunching effect of the electron density in the electron beam. The amplification gain and whose dispersion relation with respect to the electron velocity is given in this paper. On the other hand, the ELT model is applicable for the case that the wavelength of the EM wave is shorter than the electron spreading length as in the optical region. The dynamics of the electron is explained to be caused by the electron transition between different energy levels. The amplification gain and whose dispersion relation with respect to the electron acceleration voltage was derived on the basis of the quantum mechanical density matrix. (c) 2013 Elsevier B.V. All rights reserved.