A Note on the Semiconductor Laser Equivalent Circuit

The small-signal rate equations for a semiconductor laser can be represented as a network of electrical components, as shown by Tucker and Kaminow for the case of finite gain compression epsilon>0. However, a calculation of small-signal response curves deltaS/deltaI versus I derived from this equivalent circuit exhibit a linear decrease ('droop') above threshold that is inconsistent with the DC solutions of the original rate equations. This problem flags a subtle flaw in the formulation of the circuit model. We observe, moreover, that the expression for the resonance damping parameter used throughout the laser literature follows exactly from this same RLC circuit model. The derivation of the circuit model from the rate equations is revisted. Consistency between the DC and AC solutions is achieved when the differential of the net gain delta{G/(1+epsilonS)} is appropriately represented as a shunt element with zero admittance. The corrected circuit model resolves the 'droop' problem in the small-signal deltaS/deltaI versus I relation. As expected, the new circuit model leads to a modified expression for the damping parameter.