Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning

Gordon, Ariel; Wang, Christine Y.; Diehl, Laurent; Kärtner, Franz X.; Belyanin, Alexey; Bour, D. P.; Corzine, S.; Höfler, G. E.; Liu, H. C.; Schneider, Harald; Maier, Thomas; Troccoli, Mariano; Faist, Jérôme; Capasso, Federico

doi:10.1103/physreva.77.053804

Cited by 198 publications

(154 citation statements)

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“…The electron diffusivity can be reduced by lowering the temperature, and indeed temperature has a strong effect on the emission spectra of QCLs [33], although the effect is not yet well understood. In this work, we choose to manipulate the PG by adjusting the facet reflectivities.…”

Section: -11mentioning

confidence: 99%

“…When p = 1, the primary mode begins to lase at the frequency ω 0 = ω ba . As the pumping p is increased, the field and inversion can be solved for by the method of [33] as shown in Appendix E, the main results of which are stated here. We account for the population grating, but not the coherence grating which has been incorporated in recent work [56].…”

Section: B Population Gratingmentioning

confidence: 99%

“…However, since we are here dealing with two counterpropagating waves, we chose to more closely follow the approach in [33]. We make the following Ansätze:…”

Section: Appendix E: Theory: Single-mode Solutionmentioning

confidence: 99%

“…A QCL with one high-reflectivity facet and a sufficiently low reflectivity of the other facet should in principle emit an AM waveform, and we provide preliminary evidence that this is indeed the case, demonstrating a QCL whose sidebands are separated from the primary mode by 46 FSR. While the PG and PP have been known to be important in QCLs, in previous work their effects were treated separately [33]. Instead, we emphasize that one should think of the PG, a spatial modulation of the inversion, and the PP, a temporal modulation of the inversion, as working in tandem to create a phase-locked multimode state at low pump power.…”

Section: Introductionmentioning

confidence: 99%

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Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator

et al. 2016

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We report the observation of a clear single-mode instability threshold in continuous-wave Fabry-Perot quantum cascade lasers (QCLs). The instability is characterized by the appearance of sidebands separated by tens of free spectral ranges (FSR) from the first lasing mode, at a pump current not much higher than the lasing threshold. As the current is increased, higher-order sidebands appear that preserve the initial spacing, and the spectra are suggestive of harmonically phase-locked waveforms. We present a theory of the instability that applies to all homogeneously broadened standing-wave lasers. The low instability threshold and the large sideband spacing can be explained by the combination of an unclamped, incoherent Lorentzian gain due to the population grating, and a coherent parametric gain caused by temporal population pulsations that changes the spectral gain line shape. The parametric term suppresses the gain of sidebands whose separation is much smaller than the reciprocal gain recovery time, while enhancing the gain of more distant sidebands. The large gain recovery frequency of the QCL compared to the FSR is essential to observe this parametric effect, which is responsible for the multiple-FSR sideband separation. We predict that by tuning the strength of the incoherent gain contribution, for example by engineering the modal overlap factors and the carrier diffusion, both amplitude-modulated (AM) or frequency-modulated emission can be achieved from QCLs. We provide initial evidence of an AM waveform emitted by a QCL with highly asymmetric facet reflectivities, thereby opening a promising route to ultrashort pulse generation in the mid-infrared. Together, the experiments and theory clarify a deep connection between parametric oscillation in optically pumped microresonators and the single-mode instability of lasers, tying together literature from the last 60 years.

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Section: -11mentioning

confidence: 99%

Section: B Population Gratingmentioning

confidence: 99%

“…However, since we are here dealing with two counterpropagating waves, we chose to more closely follow the approach in [33]. We make the following Ansätze:…”

Section: Appendix E: Theory: Single-mode Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator

et al. 2016

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“…As a result, some way of locking the modes together must be employed. Yet all the numerous attempts [14][15][16] to mode-lock QCL had limited success, and the practical achievements did not match numerous theoretical predictions. This problem can be traced to the fact that the in the QCL the relaxation time between the upper and lower laser levels (often referred to a "gain recovery time"), τ 21 is measured in picoseconds, and is thus much shorter than the cavity round trip time τ rt that is typically about 50-100ps in a few mm long cavity.…”

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confidence: 99%

Coherent frequency combs produced by self frequency modulation in quantum cascade lasers

Khurgin

Dikmelik

Hugi

et al. 2014

Applied Physics Letters

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126

105

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One salient characteristic of Quantum Cascade Laser (QCL) is its very short τ ~ 1ps gain recovery time that so far thwarted the attempts to achieve self-mode locking of the device into a train of single pulses. We show theoretically that four wave mixing, combined with the short gain recovery time causes QCL to operate in the self-frequencymodulated regime characterized by a constant power in time domain and stable coherent comb in the frequency domain. Coherent frequency comb may enable many potential applications of QCL's in sensing and measurement.Quantum cascade lasers (QCL's) 1 are versatile sources of coherent radiation in the mid and far infrared regions of the spectrum, in which many chemical compounds have characteristic strong fundamental absorption lines. The atomic-like joint density of state character of intersubband transitions, combined with quantum engineering 2-4 , allows the development of QCLs with heterogenous active regions 5 covering a very large spectral range. Recently, by combining such broadband active regions with an external cavity 6 , continuous tuning over large spectral ranges have been achieved in the 8-10 and 3-5μm wavelength range 7 . However, these sources, tunable over hundreds of wavenumbers, require a cavity with moving components, naturally limiting their tuning speed as well as their compactness.In the last decade, a new approach to broadband spectroscopy has been proposed and implemented by the use optical frequency combs 8,9 . In a dual comb spectrometer 10-12 , two optical combs with slightly different mode spacing are beaten onto a fast detector. Since each pair of modes (one from each combs) can be made to beat at a slightly different frequency, a Fourier transform of the signal on the detector enables a direct reading of the optical spectrum. So far, such technique has been demonstrated using combs based on mode-locked lasers, in which the periodic time optical output, consisting of pulses spaced by the round-trip period of the cavity, ensures the periodicity of the comb optical spectrum.To reduce the power consumption and size, it would be very attractive to generalize this technique for semiconductor lasers. Furthermore, for many applications, it would be especially interesting to do so in the mid-infrared region of the spectrum, where many molecules have their strong fundamental absorption lines and where the generation of combs is more challenging 13 . However, in the conventional free-running multi-mode laser the modes are not evenly spaced due to material dispersion and the broadening of the individual modes prevent the generation of well-separated beat notes in the RF domain. As a result, some way of locking the modes together must be employed. Yet all the numerous attempts 14-16 to mode-lock QCL had limited success,

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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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Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning

Cited by 198 publications

References 23 publications

Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator

Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator

Coherent frequency combs produced by self frequency modulation in quantum cascade lasers

Optoelectronic Device Simulations Based on Macroscopic Maxwell–Bloch Equations

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