Quantum cascade lasers (QCLs) are unipolar semiconductor lasers first demonstrated in 1994. Since then, they have played a central role in advancing mid-infrared and terahertz photonics, becoming among the most reliable light sources in these regions of the electromagnetic spectrum. Their importance is further reinforced by their ability to generate self-starting optical frequency combs, whose investigation is motivated both by fundamental physics and by a wide range of applications, including molecular spectroscopy and free-space optical communications. This Roadmap provides a unified overview of current advances and emerging directions in QCL research. The chapters are organized into three main sections: device design and technology; frequency combs and pulse formation; and applications of QCLs. Each chapter reviews the relevant background, summarizes the current state of the art, and identifies key challenges and future directions within its specific research area.
The convergence of theoretical, technological, and experimental efforts across the QCL community will be crucial to fully unlocking the potential of these devices, driving advances toward long -standing goals such as on-chip comb integration, miniaturized mid-IR and THz photonic circuits, and roomtemperature operation. At the same time, cross-fertilization with concepts from microresonator physics and broadband photonics is expected to open new regimes of frequency-comb generation and pulse formation directly within semiconductor platforms.
Careful numerical optimization is crucial in particular for THz QCLs, since selective electron injection and extraction is hampered by the small energy separation between the two lasing levels. Fully quantitative design optimization requires modelling of the optical gain. This is achieved by selfconsistent carrier transport simulations, which consider the relevant scattering mechanisms based on microscopic models and thus do not require empirical or fitting parameters [1]. The development of these methods is largely driven by the ongoing efforts to improve THz QCLs for practical use, including the realisation of room temperature operation. For a classification of the different approaches, see figure 1. The development of the first THz QCL was assisted by the Monte Carlo (MC) technique [3], which is a semiclassical, Boltzmann-type carrier transport modelling approach based on stochastic evaluation of the scattering transitions between the quantized states (figure 1(a)). By considering the electron wavevector k associated with the free in-plane motion, MC fully accounts for intrasubband scattering and computes the k dependent electron distributions [1]. However, coherent carrier transport is not properly considered. Subsequently, a hybrid DM-MC scheme was developed to include resonant tunnelling into MC at least in rudimentary form [4] (figure 1(b)). Coherent and scattering transport are both fully considered in quantum transport methods (figure 1(c)) such as the nonequilibrium Green’s functions (NEGF) approach [1,5,6], which has been the method of choice for the development of recent THz QCL record temperature designs [6,7]. NEGF is the most general, but also the most computationally expensive of these approaches. Consequently, various k-resolved DMbased transport models have been introduced in an effort to balance rigor and numerical load [8][9][10].
For the existing carrier transport modelling approaches, there is always a trade-off between accuracy and versatility on one hand, and numerical efficiency on the other hand. For optimization tasks, semiclassical rate equation models are still widely used [11,12]. These are much faster than MC since the k dependence has been removed by suitable averaging of the scattering rates (figure 1(d)) [1,11]. Although accuracy can be improved by employing k-averaged hybrid (figure 1(e)) [13] and DM (figure 1(f)) [14] approaches instead, such reduced models are inherently limited since they do not account for intrasubband processes. Another strategy is to neglect computationally expensive carrier transport mechanisms. Besides omitting coherence effects in semiclassical models, also quantum transport approaches typically rely on approximations to make computations feasible: In particular, electronelectron scattering is often only treated in Hartree approximation, since its implementation as a twobody interaction considerably complicates computation [1,5,6,[8][9][10]13,14]. A further strategy for reducing the numerical load is to use an adapted basis set which is computationally favourable for a certain design. For example, localized wave functions based on artificially subdividing the heterostructure in scattering transport regions, separated by tunnelling barriers, have been employed in hybrid DM-MC [4] and reduced [13] models (figure 1(b),(e)). Especially for THz QCLs, the identification of tunnelling barriers can be ambiguous [10]. By using so-called EZ states, this problem is avoided at the cost of introducing an empirical threshold energy [15]. A general issue associated with any finite basis set is that the simulation result depends on the chosen basis since the completeness relation is not entirely fulfilled, impeding numerical comparison of different designs [1,5,10]. This issue has for example been avoided in NEGF by using a spatial grid for discretization rather than adapted basis functions, at the expense of a higher numerical load [1]. Besides the development of increasingly powerful simulation approaches, improved numerical QCL design and optimization will greatly rely on the growth of numerical resources and the use of refined optimization strategies [6,12,16].
To date, carrier transport models have mainly focused on calculating the unsaturated gain, while only few works have dealt with simulating the actual laser operation [1,5,13]. Such approaches are Figure 1 -We allow at most two figures that are roughly the size of
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