Analysis of self-induced transparency modelocking of quantum cascade lasers
Creators: name: Talukder, Muhammad Anisuzzaman
Publisher: name: Maryland Shared Open Access Repository
Year: 2010
Subjects: Lasers
Mid-infrared
Modelocking
Quantum Cascade Lasers
Self-induced Transparency
Ultra-short pulse

description: The possibility of using the self-induced transparency (SIT) effect to modelock lasers has been discussed since the late 1960s, but has never been observed. It is proposed that quantum cascade lasers (QCLs) are the ideal tool to realize SIT modelocking due to their rapid gain recovery times and relatively long coherence times, and because it is possible to interleave gain and absorbing periods. Designs of QCLs are presented here that satisfy the requirements for SIT modelocking. The coupled Maxwell-Bloch equations that define the dynamics in QCLs that have both gain and absorbing periods have been solved both analytically and computationally. Analytical modelocked solutions have been found under the conditions that there is no frequency detuning, the absorbing periods have a dipole moment twice that of the gain periods, the input pulse is a pi pulse in the gain medium, and the gain recovery times in the gain and the absorbing periods are much longer than the coherence time T2 and are short compared to the round-trip time. It is shown that the modelocked pulse durations are on the order of T2, which is typically about 100 fs. The Maxwell-Bloch equations have been solved computationally to determine the robustness of the modelocked solutions when frequency detuning is present, the dipole moment of the absorbing periods differs from twice that of the gain periods, the gain recovery time T1 is on the order of 1-10 ps, as is typically the case in QCLs, and the initial pulse is not a pi pulse in the gain medium. We find that modelocked solutions exist over a broad parameter range. We have also investigated the evolution of pulses that are initially much broader than the final modelocked pulses. As long as the initial pulse duration is on the order of T1 or shorter and has enough energy to create a pi pulse in the medium, a modelocked pulse with a duration on the order of T2 will ultimately form. We have developed a carrier transport model that includes both incoherent scattering and coherent tunneling mechanisms. The decay of the coherence of the levels is also included in the model. We have implemented the carrier transport model for a QCL, and we have studied the effects of an external applied electric field, a finite temperature, and the doping density on the carrier distribution in different energy levels. We find that coherence of the energy levels plays a significant role in carrier transport. In particular, when temperature increases, coherent tunneling of the electrons between the injector and the active regions decreases because the coherence time of the levels is shorter. We have then used these models to calculate the ratio of the gain obtained from one gain period and absorption obtained from one absorbing period in the SIT-modelocked QCLs. Hence we have estimated the ratio of the gain and absorbing periods for stable modelocked operation. We have studied the effects of backward propagating waves and lumped mirror losses on SIT modelocking of QCLs. The qualitative features of the modelocking are unaffected when these effects are included in the model, but the parameter regime in which stable  modelocked pulses may be found is reduced. This reduction is due to incomplete gain recovery near the edges of the QCL when pulses pass through after reflecting from the mirrors, coincident with the loss of pulse energy at the mirrors. Spatial hole burning is observed in parameter regimes in which continuous waves can grow, but it does not affect the stability of the modelocking. We extend the model by including the effects of saturable nonlinearity and chromatic dispersion. Due to the strong intensity dependence of the refractive index of the QCL core, the loss or gain that the pulses experience may become saturated. We find that QCL modelocking is still obtained as long as either the saturable gain or the saturable loss is below a critical limit. The limit is larger in magnitude for saturable gain than it is for saturable loss by more than a factor of 10 in all cases that we examined. The critical limit also depends on the gain and absorption coefficients of the laser. There is also a critical limit for the magnitude of the chromatic dispersion. When saturable loss and chromatic dispersion act simultaneously, these two effects compensate each other and their respective stability limits increase. By contrast, when saturable gain and chromatic dispersion act simultaneously, their stability limits decrease.