Lasing conditions for polarized medium and a free electron lasing using Maxwell’s equations

Abstract

Maxwell's equations with complex wave number, conductivity and electric Permittivity for electrons moving in a resistive medium under the effect of internal magnetic field and external oscillating electric field has been used to study lasing conditions. When the wave number and the conductivity are considered the medium acts as a resistor and inductor. The amplification factor is directly proportional to number of free electrons beside the internal magnetic field. Amplification takes place when the number of free electrons is very large ad when the applied magnetic field force is larger than the resistive force. This amplification condition is suitable to describe free electron lasing conditions. The proportionality of the amplification factor to the magnetic flux density resembles that obtained by some researchers. When the electric permittivity is also considered as a complex quantity,the amplification factor consists of an additional term depending on the number density of polarized excited atoms. This means that lasing can take place in a polarized medium. In this case lasing conditions require existence of large number of polarized excited atoms. This is equivalent to the population inversion condition.