Backward wave excitation and generation o f oscillations in free-electron lasers in the absence of feedback - Beyond the high gain approximation

Quantum and free-electron lasers (FELs) are based on distributed interactions between electromagnetic radiation and gain media. In an amplifier configuration, a forward wave is amplified while propagating in a polarized medium. Formulating a coupled mode theory for excitation of both forward and backward waves, we identify conditions for phase matching, leading to efficient excitation of backward wave without any mechanism of feedback or resonator assembly. The excitations of incident and reflected waves are described by a set of coupled differential equations expressed in the frequency domain. The induced polarization is given in terms of an electronic susceptibility tensor. In quantum lasers the interaction is described by two first order differential equations. In free-electron lasers, the excitation of the forward and backward modes is described by two coupled third order differential equations. In our previous investigation analytical and numerical solutions of reflectance and transmittance for both quantum lasers and high-gain FELs were presented. In this work we extend the study to a general free-electron laser without restriction of the high-gain approximation. It is found that when the solutions become infinite, the device operates as an oscillator, producing radiation at the output with no field at its input, entirely without any localized or distributed feedback.