Nonlinear gain models in a quantum cascade laser.

Density matrix analysis of a three-state model of quantum cascade laser (QCL) reveals that in this device, the optical gain is composed of the linear part (proportional to population inversion Δn) and the remaining nonlinear part. The nonlinear component non-negligibly contributes even to the small-signal response of the medium. In many attempts to modeling QCLs, the common practice to account for nonlinear gain components is to complement the equation for the gain, g = gcΔn, gc is the gain cross-section, by a compression factor f. In this paper, improved (but still simple) models of the optical gain in QCL are proposed, which preserve the two-component gain structure. With these models, there is no need to solve the Hamiltonian with time-dependent potentials, so that extraordinary numerical loads can be avoided, but simultaneously the essential physics of the phenomena is kept. The improved gain models defined by Eqs. (12), (15) and (16) enable accounting for its nonlinear components while preserving the load-saving, scattering-like approach to light-matter interaction. It is also shown that as long as the populations and dc coherences are determined such that they account for the interaction with the optical field, the small-signal formulation of the gain gives its realistic estimate also for a large optical signal. This conjecture validates the use of non-equilibrium Green's function-based approaches, in which the interaction with the optical field is included through electron-photon selfenergies. The small-signal formulation of the gain can be used in this approach to monitor the saturation process, estimate the clamping flux and the light-current characteristic.

Threshold performance of pulse-operating quantum-cascade vertical-cavity surface-emitting lasers.

Quantum-cascade (QC) vertical-cavity surface-emitting lasers (VCSELs) could combine the single longitudinal mode operation, low threshold currents, circular output beam, and on-wafer testing associated with VCSEL configuration and the unprecedented flexibility of QCs in terms of wavelength emission tuning in the infrared spectral range. The key component of QC VCSEL is the monolithic high-contrast grating (MHCG) inducing light polarization, which is required for stimulated emission in unipolar quantum wells. In this paper, we demonstrate a numerical model of the threshold operation of a QC VCSEL under the pulse regime. We discuss the physical phenomena that determine the architecture of QC VCSELs. We also explore mechanisms that influence QC VCSEL operation, with particular emphasis on voltage-driven gain cumulation as the primary mechanism limiting QC VCSEL efficiency. By numerical simulations, we perform a thorough analysis of the threshold operation of QC VCSELs. We consider the influence of optical and electrical aperture dimensions and reveal the range of aperture values that enable single transversal mode operation as well as low threshold currents.

Optimization of gain region in mid-IR ( ≈ 5†µm) QCL.

Non-equilibrium Green's function (NEGF) formalism is used to optimize the gain region of a quantum cascade laser (QCL) tailored to emit radiation at ∼5 µm wavelength, originally designed by Evans et al. [Appl. Phys. Lett., 88,051105(2006)10.1063/1.2171476]. The optimization strategy uses electron-photon selfenergies to find characteristics of devices under the "operating conditions," i.e., interacting with the laser field. These conditions can be quite different from the one when the device is in no-lasing state and the unsaturated gain is being optimized. The saturation caused by the optical field can push the structure from strong to weak coupling conditions, what changes laser parameters in a non-linear manner. Moreover, the NEGF method does not require any phenomenological parameters (such as, e.g., the phase relaxation times), so the quantities dependent on these parameters are determined solely on physical grounds. The use of the above procedure for the structure under investigation shows that the increase of the quantum efficiency by 24% and the output power by 83% in comparison to the original design can be achieved when the widths of injection and extraction barriers are changed to their optimal values.

Light-enhanced incoherence of electronic transport in quantum cascade lasers.

Since their invention in the middle of the 1990s, quantum cascade lasers (QCLs) attract increasing theoretical interest stimulated by their widening applications. One of the key theoretical issues is the optimization of electronic transport which in most of these devices is governed by the injection barrier of QCL heterostructure. In the paper, the nonequilibrium Green's function formalism is used to study electronic transition through the injection barrier as a function of laser field in the cavity; for the increasing field, a crossover is observed from the strong coupling regime, in which electronic transport through the barrier is coherent, to the weak coupling regime, in which electronic transport gets incoherent. This crossover is characterized by gain recovery time, τrec, which takes sub-picosecond values for mid-IR QCLs operating at room temperature. This time is also important for the performance of devices under steady-state conditions; the maximum output power is obtained when the figure of merit, FOM = (g(0)/gth - 1)/gcτrec [g(0) is the linear response gain, gth is the threshold gain needed to compensate all losses, gc is the gain cross-section], reaches maximum. It is shown that the use of this optimization criterion can result in the structures essentially different from those which can be obtained when the optimized quantity is the linear response gain, g(0).