Stabilization of an unstable steady state in intracavity frequency-doubled lasers

We predict theoretically that it is possible to stabilize the steady state in multimode, intracavity doubled, diode pumped Nd:YAG (neodymium-doped yttrium aluminum garnet) lasers using two output signals, namely, the sum intensities of the infrared laser modes polarized in two different orthogonal directions (X and Y) and one feedback input parameter, the pump rate. The stabilization is possible for arbitrarily large numbers of modes polarized in the X and Y direction. Different strategies of stabilization based on proportional feedback, derivative control, and their combination are discussed. The analytical and numerical results of the linear control theory are illustrated with numerical simulations of the underlying nonlinear differential equations. We show that one can maintain the stable steady state of the laser output for an arbitrarily large pump rate by taking advantage of a tracking procedure.