Stability analysis of the simple laser model incorporating the statz - de mars rate equations

• Main Authors: Yap, C. L., Poh, B. S.
• Format: Article
• Language: English
• Published: Malaysian Institute of Physics 1984
• Online Access: http://psasir.upm.edu.my/id/eprint/34066/1/6.%2034066%20stability%20analysis.pdf; http://psasir.upm.edu.my/id/eprint/34066/

A stability analysis is performed on the simple laser model which incorporates the Statz-de Mars rate equations. This is done by linearising the rate equations, operating the Laplace transform, and finally applying the Hurwitz Criterion of Stability. By this simple procedure, it is-conclusively shown that the laser model is always stable regardless of whether a linear gain or a logarithmic gain is used. even when lateral carrier diffusion is taken into account. An expression for the resonance fre- quency of the laser model using logarithmic gain, and excluding carrier diffusion, is derived. It is shown t~t when the gain coefficient constant, 13, equals the value .l/Tp, where Tp is the photon life- time, the resonance frequency reduces to that of the model where a linear gain is used. It has been found also that lateral carrier diffusion increases the damping of the relaxation oscillations of the laser.