This work was supported in part by the National Science Foundation and by Tektronix, Inc. The author also expresses his appreciation to members of the Department of Physics at the University of Otago for valuable discussions and hospitality during his sabbatical visit.
Physical Review A
Lasers, Free electron lasers, Differential equations, Perturbation (Quantum dynamics)
In a related study the equations governing a high-gain laser amplifier have been solved numerically without making the usual slowly-varying-amplitude derivative approximation in Maxwell’s equations, and thus the field amplitudes are not restricted to vary negligibly in a distance of one wavelength. The results reveal an instability that involves reflections and oscillatory growth of perturbations away from steady state. In the present study steady-state solutions of the field equations are obtained analytically, and transformations are described for converting the equations to alternative intensity-equation sets. These intensity equations are linearized and solved for the growth rate and oscillation period of the perturbations.
Casperson, L. W. (1991). Field-equation approximations and amplification in high-gain lasers: Analytical results. 44 (5), 3305-3316.