Bloch gain in quantum cascade lasers

Abstract

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...

Valence intersubband gain without population inversion

“…To the best of the author's knowledge, the first demonstration of lasing without inversion appeared in atomic optics and was based on quantum interference in Rb atoms [4]. Here we analyse a very different scenario in intersubband emitters [5][6][7]. This may turn out crucial in the search for room temperature THz qcl's.…”

Intersubband gain without global inversion through dilute nitride band engineering

“…3 Conventional designs emitting at a given frequency ប seem to have a maximum operating temperature T max Ϸ ប / k B . 4 The main difficulty at high temperatures is achieving population inversion and ISB lasing without inversion ͑LWI͒, [5][6][7] may be a solution for this microscopic bottleneck. ISB LWI has been realized experimentally by exploiting the nonparabolicity of the conduction subbands and local population inversion near k = 0 even though the lowest subband may have larger global occupation.…”

Wallplug efficiency of quantum cascade lasers: Critical parameters and fundamental limits

“…The model is based on a simple rate equation analysis of the active and injection regions. Although we are aware of the shortcomings of such a simplified approach, in particular, in the underestimation of the gain at weak inversion due to the presence of Bloch gain, 10 we claim that these limitations play a significant role only in "marginal" lasers, i.e., ones that rely on very weak population inversion and that therefore will not exhibit large wallplug efficiencies. In this first approach, we will neglect all thermal effect due to the device self-heating; as such, the efficiency must be interpreted as the one of a pulsed device, being also the upper bound to the efficiency of a device operating in continuous wave.…”