Turn-oo Transients in Current-modulated Multi-transverse-mode Vertical-cavity Surface-emitting Lasers

Turn-oo transients in current-modulated weakly-index-guided vertical-cavity surface-emitting lasers (VCSELs) are analyzed by using a model that takes into account all the transverse modes supported by the waveguide. Turn-oo transients strength is maximum for the current at which the VCSEL enters the multi-transverse-mode regime. Their strength signiicatively decreases for the multi-mode regime and then operation in several modes is beneecial to avoiding turn-oo transients when modulating the VCSEL well above threshold in order to achieve a required modulation rate or a suucient optical output power. 1 Vertical-cavity surface-emitting lasers (VCSELs) are key components in the fast-growing market for short haul, multi-gigabit speed optical communication systems. In these applications the VCSEL is modulated by a high-frequency digital bit stream. Evaluation of eye diagrams for these systems indicates that several irregularities like mode jumps, relaxation oscillations, jitter and turn-oo transients can limit the use of the VCSEL to frequencies sig-niicantly lower than the 3dB point 1]. One of these irregularities, the turn-oo transients, consists in the generation of signiicant optical power during the turn-oo of a VCSEL. This power can appear as secondary pulsations, bumps or slow optical tails. Turn-oo transients were theoretically predicted in single transverse mode VCSELs 2] and subsequently observed in experiments 3,4]. Turn-oo transients are thought to be caused by the joint eeect of two spatial mechanisms: lateral carrier diiusion and Spatial Hole Burning (SHB) 2]. Since SHB is the mechanism leading to multi-transverse-mode operation of VCSELs 5,6] a natural question arises: what is the eeect of having several lasing transverse modes on turn-oo transients?. This is relevant in gigabit speed optical communication systems because high frequencies are reached by increasing the injection current, which is precisely the regime where multimode operation appears. This problem is the subject of the present work. In this paper we extend the analysis of turn-oo transients in single-mode index-guided VCSELs performed in ref. 2] to the multi-transverse-mode case. This is done by using a model in which the electric eld is expressed as a combination of all the transverse modes of the laser waveguide. Calculations take into account both the azimuthal and radial dependences of electric eld and charge carriers 7,8]. This model has been able to explain some experimental results concerning the dynamic behaviour of multi-transverse-mode VCSELs 9,10]. The model describes a cylindrical weakly-index guided VCSEL as illustrated in Fig. 1. of Ref. 7]. The refraction index is slightly greater in the …