Theory of gain spectra for quantum cascade lasers and temperature dependence of their characteristics at low and moderate carrier concentrations

Gorfinkel, Vera; Luryi, Serge; Gelmont, Boris

doi:10.1109/3.541687

Cited by 84 publications

(46 citation statements)

References 11 publications

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“…On the theoretical model side, neglecting all other scattering processes except for optical phonon scattering leads to an overestimate of the gain. The magnitude of the gain measured in this work is much larger than the one predicted only for non-parabolicity 18 and the shape of the gain curve is clearly different. In our model, although inclusion of the non-parabolicity was important to achieve a good correspondence between the shape of the experimental data and the theory, the key ingredient needed to predict both the dispersive shape and the right magnitude of the gain curve is the Bloch component of the second-order gain and not the non-parabolicity.…”

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confidence: 50%

“…On the basis of a comparison of laser characteristics, laser operation without global population inversion between subbands was already reported 17 and was attributed to the combined effect of nonparabolicity and a hot-electron distribution in the lower state 18 . However, no measurement of the gain curve was carried out in this experiment, preventing a definitive interpretation of these results.…”

mentioning

confidence: 99%

“…To demonstrate experimentally the existence of Bloch gain in QCL structures while excluding other phenomena that were predicted to also yield gain without global population inversion between subbands, such as non-reciprocity 16 and local k-space inversion due to non-parabolicity 17,18 , a spectrally resolved gain measurement is carried out in a specially designed QCL. On the basis of a comparison of laser characteristics, laser operation without global population inversion between subbands was already reported 17 and was attributed to the combined effect of nonparabolicity and a hot-electron distribution in the lower state 18 .…”

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Bloch gain in quantum cascade lasers

et al. 2007

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Esaki and Tsu's superlattice 1 , made by alternating two different semiconductor materials, was the first one-dimensional artificial crystal that demonstrated the ability to tailor semiconductor properties. One motivation of this work was the realization of the Bloch oscillator 2,3 and the use of its particular dispersive optical gain 4,5 to achieve a tuneable source of electromagnetic radiation. However, these superlattices were electrically unstable in the steady state 6 . Fortunately, because it is based on scatteringassisted transitions, this particular gain does not arise only in superlattices, but also more generally in semiconductor heterostructures 7,8 such as quantum cascade lasers 9 (QCLs), where the electrical stability can be controlled 10 . Here, we show the unambiguous spectral signature of Bloch gain in a special QCL designed to enhance the latter by exhibiting laser action in the condition of weak to vanishing population inversion.In solids, electrons have a fixed relation between momentum and energy: they move along energy bands, as known from condensed-matter theory. When an electric field is applied they are accelerated but the lattice forces a periodic motion at a definite Bloch frequency. This phenomenon is known as Bloch oscillations, and the idea was successfully used by Zener to explain the dielectric breakdown 3 . However, in usual solids the strong scattering due to impurities and carrier-carrier interaction prevents the observation of such oscillations, as the lattice constant is too short to allow the electrons to complete even one oscillation cycle. In superlattices, the lattice constant can be chosen and a subtle engineering may allow electrons to achieve a few oscillations before scattering. As this phenomenon is fascinating from a condensed-matter point of view, it also opens new perspectives for optics because charge oscillations naturally couple to radiation and offer a way to emit coherent radiation.Therefore, the important question is whether these oscillations can be self-sustained and provide optical gain. First, Ktitorov 4 and then Ignatov and Romanov 5 addressed the problem theoretically with Boltzmann equations and succeeded in providing a definitive signature for Bloch oscillations in superlattices in terms of a particular spectral response: the Bloch oscillations are found to amplify the electromagnetic field (optical gain) on the low-energy side of the oscillation frequency, whereas they absorb photons on the high-energy side. This particular shaped gain-Bloch gain-is the main feature of the Bloch oscillator. A series of experiments 11-13 using pulsed ultrafast techniques have successfully shown the existence of Bloch oscillations as electrons are pumped in a higher energy band and collectively oscillate over their dephasing time. However, the Bloch gain extends to zero frequencies and the structure becomes unstable in the steady state, so far preventing the observation of net gain in superlattices, although some evidence in photocurrent 14 and more recently in absorpt...

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Bloch gain in quantum cascade lasers

et al. 2007

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“…[7][8][9][10][11][12][13] On the other hand, GaAs/ AlGaAs cascade structures may play an important role in producing stimulated radiation in the far-infrared region, which is also the topic of recent investigations, both experimental 14 -16 and theoretical. 17,18 The rapid experimental development has stimulated interest in theoretical work to explain the physical processes involved, [19][20][21] including the principles of carrier transport in devices, and hence, indicate routes to optimized layer design for improved output characteristics. Theoretical studies to date have mainly addressed the optimization of the active region structure and the electron-LO phonon scattering rates, so as to maximize the population inversion.…”

Section: Introductionmentioning

confidence: 99%

Self-consistent scattering theory of transport and output characteristics of quantum cascade lasers

Indjin

Harrison

Kelsall

et al. 2002

Journal of Applied Physics

121

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Electron transport in GaAs/AlGaAs quantum cascade lasers operating in midinfrared is calculated self-consistently using an intersubband scattering model. Subband populations and carrier transition rates are calculated and all relevant electron-LO phonon and electron-electron scatterings between injector/collector, active region, and continuum resonance levels are included. The calculated carrier lifetimes and subband populations are then used to evaluate scattering current densities, injection efficiencies, and carrier backflow into the active region for a range of operating temperatures. From the calculated modal gain versus total current density dependencies the output characteristics, in particular the gain coefficient and threshold current, are extracted. For the original GaAs/Al 0.33 Ga 0.67 As quantum cascade structure ͓C. Sirtori et al., Appl. Phys. Lett. 73, 3486 ͑1998͔͒ these are found to be gϭ11.3 cm/kA and J th ϭ6Ϯ1 kA/cm 2 ͑at Tϭ77 K͒, and gϭ7.9 cm/kA and J th ϭ10Ϯ1 kA/cm 2 ͑at Tϭ200 K͒, in good agreement with the experiment. Calculations shows that threshold cannot be achieved in this structure at Tϭ300 K, due to the small gain coefficient and the gain saturation effect, also in agreement with experimental findings. The model thus promises to be a powerful tool for the prediction and optimization of new, improved quantum cascade structures.

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“…Photonics 2016, 3, 30 7 of 15 dependence on the electron temperature for the gain cross-section and the inversion reduction factor using the non-parabolic subbands theory of [13]. The thermal backfilling loss coefficient ℎ was calculated according to [14] with the lattice temperature replaced by the electron temperature.…”

Section: Dealing With Hot Electrons and Stark Detuningmentioning

confidence: 99%

Modeling the Electro-Optical Performance of High Power Mid-Infrared Quantum Cascade Lasers

2016

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Performance modeling of the characteristics of mid-infrared quantum cascade lasers (MIR QCL) is an essential element in formulating consistent component requirements and specifications, in preparing guidelines for the design and manufacture of the QCL structures, and in assessing different modes of operation of the laser device. We use principles of system physics to analyze the electro-optical characteristics of high power MIR QCL, including thermal backfilling of the lower laser level, hot electron effects, and Stark detuning during lasing. The analysis is based on analytical modeling to give simple mathematical expressions which are easily incorporated in system-level simulations of defense applications such as directed infrared countermeasures (DIRCM). The paper delineates the system physics of the electro-optical energy conversion in QCL and the related modeling. The application of the performance model to a DIRCM QCL is explained by an example.

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Theory of gain spectra for quantum cascade lasers and temperature dependence of their characteristics at low and moderate carrier concentrations

Cited by 84 publications

References 11 publications

Bloch gain in quantum cascade lasers

Bloch gain in quantum cascade lasers

Self-consistent scattering theory of transport and output characteristics of quantum cascade lasers

Modeling the Electro-Optical Performance of High Power Mid-Infrared Quantum Cascade Lasers

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