Dynamics of a broad-band quantum cascade laser: from chaos to coherent dynamics and mode-locking

Columbo, L.; Barbieri, Stefano; Sirtori, Carlo; Brambilla, Massimo

doi:10.1364/oe.26.002829

Cited by 39 publications

(31 citation statements)

References 44 publications

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“…For QCLs, the MB equations have primarily been used to study ultrashort pulse generation by mode‐locking and the closely related formation of coherent instabilities, as well as the generation of frequency combs . In detail, it has been found that coherent multimode instabilities result in the emergence of sidebands around the original longitudinal mode, giving rise to broadband multimode operation .…”

Section: Application To Optoelectronic Devicesmentioning

confidence: 99%

Optoelectronic Device Simulations Based on Macroscopic Maxwell–Bloch Equations

Jirauschek

Riesch

Tzenov

2019

Advcd Theory and Sims

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Due to their intuitiveness, flexibility, and relative numerical efficiency, the macroscopic Maxwell-Bloch (MB) equations are a widely used semiclassical and semi-phenomenological model to describe optical propagation and coherent light-matter interaction in media consisting of discrete-level quantum systems. This review focuses on the application of this model to advanced optoelectronic devices, such as quantum cascade and quantum dot lasers. The Bloch equations are here treated as a density matrix model for driven quantum systems with two or multiple discrete energy levels, where dissipation is included by Lindblad terms. Furthermore, the 1D MB equations for semiconductor waveguide structures and optical fibers are rigorously derived. Special analytical solutions and suitable numerical methods are presented. Due to the importance of the MB equations in computational electrodynamics, an emphasis is placed on the comparison of different numerical schemes, both with and without the rotating wave approximation. The implementation of additional effects which can become relevant in semiconductor structures, such as spatial hole burning, inhomogeneous broadening, and local-field corrections, is discussed. Finally, links to microscopic models and suitable extensions of the Lindblad formalism are briefly addressed. of a lower bandgap material than the adjacent layers, which restricts the free electron motion in that layer to the in-plane directions and gives rise to quantized energy states in growth direction. As a consequence of the further restriction of the energy spectrum and the even stronger carrier localization, additional improvement can be expected from 2D or 3D confinement, resulting in quantum wire/dash and quantum dot (QD) structures, respectively. Indeed, QD [1][2][3] and quantum dash [4] lasers and laser amplifiers have been shown to exhibit excellent characteristics. In Figure 1, the formation of quantized states in quantum wells, wires, and dots is schematically illustrated. The term quantum dash refers to an elongated nanostructure, that is, some kind of short quantum wire. By contrast, the term nanowire does not necessarily indicate strong quantum confinement. For example, in nanowire lasers, the nanowire geometry typically serves as a single-mode optical waveguide resonator, while the active region is based on a heterostructure or quantum well, as in a conventional laser diode. [5,6] Semiconductor optoelectronic devices usually rely on electron-hole recombination, that is, optical transitions between conduction and valence band states. The associated resonance wavelength is largely determined by the semiconductor bandgap, which establishes a lower bound on the transition energy. Thus, the coverage of a certain spectral region depends on the existence of suitable semiconductor materials, which for example restricts the availability of practical optoelectronic sources and detectors in the mid-infrared and terahertz regions. An alternative concept is based on intersubband devices, which employ so-called i...

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Section: Application To Optoelectronic Devicesmentioning

confidence: 99%

Optoelectronic Device Simulations Based on Macroscopic Maxwell–Bloch Equations

Jirauschek

Riesch

Tzenov

2019

Advcd Theory and Sims

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“…The realization, nearly 13 years ago, of frequency combs in high-Q monolithic microresonators filled with Kerr media [3] raised an enormous attention because of its potential for miniaturization and chip-scale photonic integration, and stimulated a great deal of activities [4][5][6]. More recently, another system relevant for photonic integration, namely the quantum cascade laser (QCL) emerged as a source of frequency combs [7][8][9][10][11][12]. Close to its lasing threshold, the dynamics of a QCL is governed by a cubic nonlinearity similar to the one of Kerr cavities.…”

Section: Introductionmentioning

confidence: 99%

“…A relevant point is that while in the passive case frequency combs need an external field providing the necessary energy intake, in active systems like the QCL frequency combs are generated in a free-running setup [7,[9][10][11][12][13]. The generalized LLE also contemplates a novel configuration, to our knowledge never analysed before, in which a ring QCL is driven by an external coherent field (QCL with injected signal).…”

Section: Introductionmentioning

confidence: 99%

Soliton dynamics of ring quantum cascade lasers with injected signal

et al. 2020

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Nonlinear interactions in many physical systems lead to symmetry breaking phenomena in which an initial spatially homogeneous stationary solution becomes modulated. Modulation instabilities have been widely studied since the 1960s in different branches of nonlinear physics. In optics, they may result in the formation of optical solitons, localized structures that maintain their shape as they propagate, which have been investigated in systems ranging from optical fibres to passive microresonators. Recently, a generalized version of the Lugiato–Lefever equation predicted their existence in ring quantum cascade lasers with an external driving field, a configuration that enables the bistability mechanism at the basis of the formation of optical solitons. Here, we consider this driven emitter and extensively study the structures emerging therein. The most promising regimes for localized structure formation are assessed by means of a linear stability analysis of the homogeneous stationary solution (or continuous-wave solution). In particular, we show the existence of phase solitons – chiral structures excited by phase jumps in the cavity – and cavity solitons. The latter can be deterministically excited by means of writing pulses and manipulated by the application of intensity gradients, making them promising as frequency combs (in the spectral domain) or reconfigurable bit sequences that can encode information inside the ring cavity.

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“…60 for a review till year 2005). More recently the RNGH instability has gained popularity as it has been invoked in order to understand the hot topics of spontaneous frequency-comb formation and self modelocking in quantum-dot and quantum-cascade lasers 19,20,24,61,62 .…”

mentioning

confidence: 99%

Coherent master equation for laser modelocking

et al. 2020

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Modelocked lasers constitute the fundamental source of optically-coherent ultrashort-pulsed radiation, with huge impact in science and technology. Their modeling largely rests on the master equation (ME) approach introduced in 1975 by Hermann A. Haus. However, that description fails when the medium dynamics is fast and, ultimately, when light-matter quantum coherence is relevant. Here we set a rigorous and general ME framework, the coherent ME (CME), that overcomes both limitations. The CME predicts strong deviations from Haus ME, which we substantiate through an amplitude-modulated semiconductor laser experiment. Accounting for coherent effects, like the Risken-Nummedal-Graham-Haken multimode instability, we envisage the usefulness of the CME for describing self-modelocking and spontaneous frequency comb formation in quantum-cascade and quantum-dot lasers. Furthermore, the CME paves the way for exploiting the rich phenomenology of coherent effects in laser design, which has been hampered so far by the lack of a coherent ME formalism.

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Dynamics of a broad-band quantum cascade laser: from chaos to coherent dynamics and mode-locking

Cited by 39 publications

References 44 publications

Optoelectronic Device Simulations Based on Macroscopic Maxwell–Bloch Equations

Optoelectronic Device Simulations Based on Macroscopic Maxwell–Bloch Equations

Soliton dynamics of ring quantum cascade lasers with injected signal

Coherent master equation for laser modelocking

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