Self-consistent Maxwell-Bloch model of quantum-dot photonic-crystal-cavity lasers

Cartar, William K.; Mørk, Jesper; Hughes, Stephen

doi:10.1103/physreva.96.023859

Cited by 37 publications

(32 citation statements)

References 90 publications

(116 reference statements)

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“…Many of these applications can be seen as refinements of well-established calculation methods for resonant structures, where now the QNMs provide explicit and precise definitions of parameters that would normally be inferred by fitting to calculation data or measurements. The close connection between the QNMs and the resonances in scattering matrices of general structures has been clarified [41,68,69], and QNMs have been used as inputs to laser models [71,72] and for the derivation of the so-called temporal CMT [67], including applications to switching in nonlinear materials [73]. Yang et al used QNM perturbation theory for sensing applications [74], and QNMs of resonators modeled with a nonlocal material response were presented in Ref.…”

Section: Practical Applicationsmentioning

confidence: 99%

Modeling electromagnetic resonators using quasinormal modes

et al. 2020

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We present a bi-orthogonal approach for modeling the response of localized electromagnetic resonators using quasinormal modes, which represent the natural, dissipative eigenmodes of the system with complex frequencies. For many problems of interest in optics and nanophotonics, the quasinormal modes constitute a powerful modeling tool, and the bi-orthogonal approach provides a coherent, precise, and accessible derivation of the associated theory, enabling an illustrative connection between different modeling approaches that exist in the literature.

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Section: Practical Applicationsmentioning

confidence: 99%

Modeling electromagnetic resonators using quasinormal modes

et al. 2020

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“…Several research groups use the fourth-order Runge-Kutta (RK) method to solve the Bloch equations. [55,60,239,264] As illustrated in Figure 17b, the method is strongly coupled since electric field and density matrix are discretized at the same time steps. The exact procedure is not always described in related work, but can be outlined as follows.…”

Section: Runge-kutta Methodsmentioning

confidence: 99%

“…Although the MB equations are sometimes solved in two or even three spatial dimensions, [53][54][55][56][57][58][59][60] the model is frequently reduced to a single spatial coordinate in order to minimize the numerical load. [49] This is usually achieved by assuming plane wave propagation in the Maxwell equations, Equation (44), or the corresponding propagation equations in SVAA, Equation (62).…”

Section: Reduction To 1d Modelmentioning

confidence: 99%

“…[303,310] Rate equation terms of the form Equation (9) with phenomenologically chosen parameters are frequently used to model incoherent transitions in QD systems. [60,121,248,344,346,347] For a more detailed modeling, it must be taken into account that important dissipative processes in QDs depend on the occupations of two or more states, and that Pauli blocking is not included in Equation (9). This can be addressed by using an empirical nonlinear rate equation model, [207,354] or based on a microscopic treatment.…”

Section: Quantum Dot Devicesmentioning

confidence: 99%

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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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“…In particular, PhC lasers based on line-defect waveguides are ideal candidates for energy efficient light sources in high density PhC integrated circuits [1,2]. Solving Maxwell equations by a finite-difference-timedomain (FDTD) technique is a rigorous, but extremely timeand memory-consuming approach to analyze PhC devices [3]. Furthermore, FDTD simulations are not always useful to shed light on the physics of the investigated structures.…”

Section: Introductionmentioning

confidence: 99%