Group velocity dispersion in terahertz frequency combs within a generalized Maxwell-Bloch framework

Abstract

As many molecules have their rotovibrational resonance frequencies in the mid-infrared or terahertz regime, efficient generation of corresponding frequency combs may lead to large progress in gas spectroscopy and sensing. Quantum cascade lasers (QCLs) are among the most promising candidates for a compact and cheap radiation source in this frequency range. This contribution presents a full-wave numerical solution of the Maxwell-Liouville-von Neumann equations, thus avoiding the limited applicability of the rotating wave approximation to moderate field strengths and spectral bandwidths. We include losses and chromatic dispersion of the optically active material in the QCL. The semiclassical approach uses the finite-difference time-domain (FDTD) method to derive update equations for the electric field, starting from the one-dimensional Maxwell equations. There, the optical full-wave propagation is coupled to the electronic quantum system via a polarization term that arises from the evolution of the density matrix. Furthermore, dispersion effects are considered through a classical polarization term and losses are introduced by a finite material conductivity. This work mainly focuses on the integration of group velocity dispersion (GVD) due to the bulk material and, if applicable, the waveguide geometry into the update equations. It is known to be one of the main degradation mechanisms of terahertz frequency combs, but has not yet been added to the existing full-wave solver. The implementation is carried out as Lorentz model and is applied to an experimentally investigated QCL frequency comb setup from the literature. The reported results are in good agreement with the experimental data. Especially, they confirm the need for dispersion compensation for the generation of terahertz frequency combs in QCLs.