Rate equations and transient phenomena in semiconductor lasers

Abstract

This contribution attempts to review certain resonance effects which occur in the dynamic behaviour of semiconductor lasers. To study these effects theoretically, a rate equation approach is used for single-mode operation in the region of lasing threshold.The tWo basic rate equations are given and their transient solutions discussed. The existence of two time constants in these equations, viz. the electron lifetime % and the photon lifetime rp., gives rise to a characteristic resonance frequency in the GHz region. This resonance manifests itself in transient 'spiking' effects, in quantum noise phenomena, and in high-frequency modulation experiments. In a modified form the resonance frequency may also be studied in lasers with external cavities and in double-diode configurations (or, equivalently, conventional devices with non-uniform excitation along the cavity length).In the latter two examples mentioned above, the resonance is excited by optical feedback of the laser radiation into the active medium via a 'lossy' or insufficiently inverted region. In the 'spiking' oscillations commonly observed at the commencement of laser operation, the initial 'population overshoot' isthe cause of the resonance. For the case of quantum noise it is the requirement that the photon and electron populations have integer values which supplies the driving force-a true quantum effect. High-frequency modulation experiments directly reveal the same resonance frequency where a strong maximum in modulation intensity occurs.

Optical Gain in Commercial Laser Diodes

“…From the knowledge of RS one gets the direct plot (Figure 6) of the internal voltage VJ, by means of Equation (19), that indeed clamps as theoretically expected. The small decrease of the dV/dI curve after the threshold is due to geometric effects (progressive widening, after threshold, of the area of the inverted region), analyzed and explained in ref.…”

“…Equation (19) assumes that the voltage drops V J (junction voltage) at the ideal diode and the external bias only differ by a series ohmic contribution (Figure 4). If such simple representation holds, one expects that, as soon as the device reaches its threshold for laser emission and the quasi-Fermi levels clamp, the junction voltage V accordingly freezes at a constant value Vth.…”

Rate equation approach for diode lasers

“…Various models have been used to describe transient phenomena in semiconductor lasers [2,5] and to evaluate in steady state conditions the photon number in diode laser cavities [6] and in compound systems, such as a diode within an external resonator [7,8], double diodes [8][9][10][11] and optical coupled diodes [12]. Various models have been used to describe transient phenomena in semiconductor lasers [2,5] and to evaluate in steady state conditions the photon number in diode laser cavities [6] and in compound systems, such as a diode within an external resonator [7,8], double diodes [8][9][10][11] and optical coupled diodes [12].…”

Rate equation approach for diode lasers

“…Experiments on Q-switching [1,2] and self modulation [3,4] as well as on mode selection [5,6] and on mode synchronization [7][8][9] have confirmed these properties. This is especially the case for the power law dependence between optical gain g and electron density n (g oc n t) [13], which makes it feasible to find steady state analytical approximation formulae for the photon number within the active region of the diode. Several models have been reported on these subjects in the literature [2,.…”