Performance evaluation of numerical methods for the Maxwell–Liouville–von Neumann equations

Riesch, Michael; Tchipev, Nikola; Senninger, Sebastian; Bungartz, Hans‐Joachim; Jirauschek, Christian

doi:10.1007/s11082-018-1377-4

Cited by 23 publications

(18 citation statements)

References 20 publications

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“…To demonstrate the effect of the harmonic beatnote on the modulation of the QCL, numerical simulations based on the open-source software package mbsolve 28,29 were realised to investigate the electric field evolution in a structure reproducing the QCL characteristics. The simulation model is based on the full-wave Maxwell-Bloch (MB) equations 30,31 for the three-level system (i.e., without the rotating wave and slowly varying amplitude approximations), taking into account counterpropagating waves and spatial hole burning.…”

Section: Discussionmentioning

confidence: 99%

Ultrafast response of harmonic modelocked THz lasers

et al. 2020

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The use of fundamental modelocking to generate short terahertz (THz) pulses and THz frequency combs from semiconductor lasers has become a routine affair, using quantum cascade lasers (QCLs) as a gain medium. However, unlike classic laser diodes, no demonstrations of harmonic modelocking, active or passive, have been shown in THz QCLs, where multiple pulses per round trip are generated when the laser is modulated at the harmonics of the cavity's fundamental round-trip frequency. Here, using time-resolved THz techniques, we show for the first time harmonic injection and mode-locking in which THz QCLs are modulated at the harmonics of the round-trip frequency. We demonstrate the generation of the harmonic electrical beatnote within a QCL, its injection locking to an active modulation and its direct translation to harmonic pulse generation using the unique ultrafast nature of our approach. Finally, we show indications of self-starting harmonic emission, i.e., without external modulation, where the QCL operates exclusively on a harmonic (up to its 15th harmonic) of the round-trip frequency. This behaviour is supported by time-resolved simulations of induced gain and loss in the system and shows the importance of the electronic, as well as photonic, nature of QCLs. These results open up the prospect of passive harmonic modelocking and THz pulse generation, as well as the generation of low-noise microwave generation in the hundreds of GHz region.

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Section: Discussionmentioning

confidence: 99%

Ultrafast response of harmonic modelocked THz lasers

et al. 2020

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“…The exact procedure is not always described in related work, but can be outlined as follows. [260] First, the electric field is updated using the standard FDTD update step. Then, the update of the density matrix using the rulê ρ n+1 =ρ n + t (k 1 + 2k 2 + 2k 3 + k 4 )/6 (149) follows, where k 1 = F n (ρ n ), k 2 = F n+1/2 (ρ n + t k 1 /2), k 3 = F n+1/2 (ρ n + t k 2 /2), and k 4 = F n+1 (ρ n + t k 3 ).…”

Section: Runge-kutta Methodsmentioning

confidence: 99%

“…[52] Additionally, it can be executed efficiently in parallel, although the naive implementation will not yield the maximum performance and a more advanced approach must be used. [259,260] The major drawback is the introduced numerical dispersion which can only be avoided by using very fine discretization sizes. Otherwise, artifacts in the simulation results could be the consequence.…”

Section: Numerical Schemes For Maxwell's Equationsmentioning

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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“…fast recovery of the absorber inversion lifetime as well as ultra-strong coupling of the FSA to the optical field, generation of a pair of colliding pulses becomes possible. To verify our approach, we employ semi-classical models for both the gain and the absorber, which are based on the solution of the full Maxwell-Bloch equations [6]. Compared to the traditionally used "travelling wave" models, which treat the carrier dynamics via classical rate equations, our approach resolves the electromagnetic field in space and time, solves the quantum mechanical von Neumann equation to evaluate the light-matter interaction dynamics, while it also includes important effects known to play a role in quantum cascade lasers, such as dispersion, optical nonlinearities and spatial hole burning.…”

Section: Modelmentioning

confidence: 99%

“…Notably, we do not employ the commonly used rotating wave approximation which fails for large spectral pulse widths. Furthermore, with the goal for transparency and reproducibility of our results by experimental and theoretical groups alike, we have released our simulation framework as an open source program for the community to exploit [6,7]. ps) as fast as 3 times shorter than the cavity round trip time, CPML is possible and above all, is robust against variations of the experimental parameters.…”

Section: Modelmentioning

confidence: 99%