Extensive study of the linewidth enhancement factor of a distributed feedback quantum cascade laser at ultra-low temperature

Quantum cascade lasers (QCLs) are optical sources exploiting radiative intersubband transitions within the conduction band of semiconductor heterostructures.¹ The opportunity given by the broad span of wavelengths that QCLs can achieve, from mid-infrared to terahertz, leads to a wide number of applications such as absorption spectroscopy, optical countermeasures and free-space communications requiring stable single-mode operation with a narrow linewidth and high output power.² One of the parameters of paramount importance for studying the high-speed and nonlinear dynamical properties of QCLs is the linewidth enhancement factor (LEF). The LEF quantifies the coupling between the gain and the refractive index of the QCL or, in a similar manner, the coupling between the phase and the amplitude of the electrical field.³ Prior work focused on experimental studies of the LEF for pump currents above threshold but without exceeding 12% of the threshold current at 283K⁴ and 56% of the threshold current at 82K.5 In this work, we use the Hakki-Paoli method6 to retrieve the LEF for current biases below threshold. We complement our findings using the self-mixing interferometry technique⁵ to obtain LEFs for current biases up to more than 100% of the threshold current. These insets are meaningful to understand the behavior of QCLs, which exhibit a strongly temperature sensitive chaotic bubble when subject to external optical feedback.⁷