Dynamical Hysteresis and Thermal Effects in Vertical-Cavity Surface-Emitting Lasers

Abstract

Abstract-We study numerically the polarization-resolved light-output characteristic of vertical-cavity surface-emitting lasers (VCSELs) using the spin-flip model for VCSELs extended to take into account thermal effects via a dynamical equation for the active region temperature, including heat dissipation, heating due to nonradiative carrier recombination, and Joule effect. The temperature dynamics is coupled to the carrier and optical field dynamics via a frequency and temperaturedependent gain coefficient. We show that the interplay of thermal effects and injection current variation can result in turn-on and turn-off hysteresis cycles that can be, depending on various model parameters, positive or negative. In the first case, the turn-on occurs at a higher value of the bias current than the turn-off; in a negative hysteresis cycle, the laser turns-on at a lower value of the bias current than the turn-off. These results are interpreted in terms of the interplay of the two time-scales determined by the injection current swept rate and the thermal relaxation rate.

Thermal effects and dynamical hysteresis in the turn-on and turn-off of vertical-cavity surface-emitting lasers

“…The aim of this Letter is to study experimentally and theoretically the influence of the current modulation frequency and the substrate temperature on the VCSEL threshold current and gain a better understanding of thermal effects in VCSELs. The experimental results show that the hysteresis of turn-on and turn-off can be positive or negative, depending on the current modulation frequency and substrate temperature, in good agreement with the numerical results [4]. Numerical simulations that are in good qualitative agreement with the experiments are also presented and allow for a better understanding of the interplay of the time scales of current modulation and thermal dissipation.…”

“…A recent numerical study [4] has shown thermally induced hysteresis on the laser switch-on and switch-off points, which depends on the relationship between two time scales: that of the current modulation, which results in dynamical hysteresis [5,6], and that of thermal dissipation, which is an additional source of hysteresis that can give either positive or negative [7,8] hysteresis cycles. In positive cycles, the laser turns on at a higher current value than it turns off; in negative cycles, the turn-on occurs at a lower current value than the turn-off.…”

“…The rate equations for a semiconductor laser, incorporating the dynamic variation of the temperature of the active region are [4,10]…”

“…E=EÞ is the slowly varying optical frequency, g 0 ¼ T 0 =T is the gain peak, and Δω 2 g ¼ Δω 2 g;0 ðT=T 0 Þ is the gain bandwidth, with T 0 being the reference room temperature [4,10].…”

“…The model equations were integrated with typical parameters appropriate for a 1550 nm VCSEL: the room temperature gain-cavity offset, δ 0 ¼ −10 nm, γ N ¼ 1 ns −1 , γ T ¼ 1 μs −1 , Z ¼ 8:5 × 10 −3 , P ¼ 9:2 × 10 −5 , and all other parameters as in [4,10]. The size of the hysteresis cycle versus the modulation frequency at three values of the substrate temperature is displayed in Fig.…”