Turn-on delay of VCSEL and effect of carriers recombination

It is well known that when the laser is turned on by increasing the device current from its initial value J(0) to the above-threshold value J greater than J(th), stimulated recombination is delayed by t(d), the time during which the carrier population rises to its threshold value. On the besis of the rate equations for quantum well VCSEL, a closed expression describing the time evolution of the carrier density within the turn-on period of a VCSEL has been derived for the case that the Auger effect is considered with a term proportional to the cube of the carrier density. The theoretic results are simulated with Simulink of MATLAB software. As a result, an explicit analytical expression for the turn-on delay of the VCSEL has also been deduced. Since the turn-on delay is an important parameter of a semiconductor laser, intensified studies on this parameter have been carried out in the past years.