Tail asymptotics of light-tailed Weibull-like sums

Abstract: We consider sums of n i.i.d. random variables with tails close to exp{−x^β} for some β > 1. Asymptotics developed by Rootzén (1987) and Balkema, Klüppelberg, and Resnick (1993) are discussed from the point of view of tails rather than of densities, using a somewhat different angle, and supplemented with bounds, results on a random number N of terms, and simulation algorithms

Laser feedback interferometry in multi-mode terahertz quantum cascade lasers

The typical modal characteristics arising during laser feedback interferometry (LFI) in multi-mode terahertz (THz) quantum cascade lasers (QCLs) are investigated in this work. To this end, a set of multi-mode reduced rate equations with gain saturation for a general Fabry-Pérot multi-mode THz QCL under optical feedback is developed. Depending on gain bandwidth of the laser and optical feedback level, three different operating regimes are identified, namely a single-mode regime, a multi-mode regime, and a tuneable-mode regime. When the laser operates in the single-mode and multi-mode regimes, the self-mixing signal amplitude (peak to peak value of the self-mixing fringes) is proportional to the feedback coupling rate at each mode frequency. However, this rule no longer holds when the laser enters into the tuneable-mode regime, in which the feedback level becomes sufficiently strong (the boundary value of the feedback level depends on the gain bandwidth). The mapping of the identified feedback regimes of the multi-mode THz QCL in the space of the gain bandwidth and feedback level is investigated. In addition, the dependence of the aforementioned mapping of these three regimes on the linewidth enhancement factor of the laser is also explored, which provides a systematic picture of the potential of LFI in multi-mode THz QCLs for spectroscopic sensing applications

Mode selection and tuning mechanisms in coupled-cavity terahertz quantum cascade lasers

We present a model for longitudinal mode competition in coupled-cavity (CC) terahertz (THz) quantum cascade lasers (QCLs) by using a scattering matrix method and multi-mode reduced rate equations (RREs). The dependence of the mode selection and tuning characteristics on various device parameters are systematically investigated, including the net waveguide loss, the optical length of the passive cavity, and the heat sink temperature for different relationship between the active and passive cavity lengths. The changes in eigenmode frequencies due to variations of device parameter are calculated before solving the RREs. The mode selection and tuning results obtained from solving the nonlinear RREs could be well explained by linear scattering matrix analysis. The mode tuning process simulated by the proposed model is compared with experimentally measured data, yielding good agreement. Comprehensive study of the influence of the key device parameters on the performance of CC THz QCLs provides potential design rules for single-mode operation with either wide frequency tunability or high stability

Correction to “Temperature-Dependent High-Speed Dynamics of Terahertz Quantum Cascade Lasers”

Corrections to author affiliation information is presented in the above named paper

Correction to "Mode Selection and Tuning Mechanisms in Coupled-Cavity Terahertz Quantum Cascade Lasers"

In [1], the affiliation for Andrew Grier was incorrect. The correct affiliation where his contribution was made is as follows: A. T. Grier was with the School of Electronic and Electrical Engineering, University of Leeds, LS2 9JT Leeds, U.K. (e-mail: [email protected])

Measurement of the emission spectrum of a semiconductor laser using laser-feedback interferometry

The effects of optical feedback (OF) in lasers have been observed since the early days of laser development. While OF can result in undesirable and unpredictable operation in laser systems, it can also cause measurable perturbations to the operating parameters, which can be harnessed for metrological purposes. In this work we exploit this ‘self-mixing’ effect to infer the emission spectrum of a semiconductor laser using a laser-feedback interferometer, in which the terminal voltage of the laser is used to coherently sample the reinjected field. We demonstrate this approach using a terahertz frequency quantum cascade laser operating in both single- and multiple-longitudinal mode regimes, and are able to resolve spectral features not reliably resolved using traditional Fourier transform spectroscopy. We also investigate quantitatively the frequency perturbation of individual laser modes under OF, and find excellent agreement with predictions of the excess phase equation central to the theory of lasers under OF