Density matrix model for polarons in a terahertz quantum dot cascade laser

Burnett, Benjamin A.; Williams, Benjamin S.

doi:10.1103/physrevb.90.155309

Cited by 22 publications

(35 citation statements)

References 51 publications

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“…Generally, this expression is complex, but for real r it coincides with the previous result, Equation (90). Thus, the expression for the confinement factor given in Equation (90) corresponds to the perturbative expression for both TE and TM modes in the case of real r , and is commonly also used for complex r where it can be seen as a real-valued approximation to the perturbative result.…”

Section: Transverse Magnetic Modesupporting

confidence: 59%

“…In the Schrödinger picture, we thus obtain v = d t Tr{rρ} = Tr{rd tρ }, which is also valid for the incoherent contribution induced by the Lindblad operator term in Equation (3). [90] Thus, I = q | v |/L corresponds to the current through an individual (single-carrier) quantum system, where L indicates the system length in the direction of current flow, and L /| v | is the transit time of the carrier through the system. Again, averaging over a large ensemble of identical systems, we obtain the macroscopic current density J f = n 3D q Tr{rd tρ }.…”

Section: Macroscopic Polarization and Current Densitymentioning

confidence: 99%

“…The incoherent contribution to the current density is given by [90] which yields with Equations (3) and (4)…”

Section: Incoherent Contributionmentioning

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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Section: Transverse Magnetic Modesupporting

confidence: 59%

Section: Macroscopic Polarization and Current Densitymentioning

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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“…Our density matrix solver is adapted from Ref. [19] to compute difference frequency susceptibility. Density matrix transport models have been applied to specific QCL systems since their conception [20][21][22][23][24], but analytic formulations become prohibitively cumbersome for designs consisting of more than 3-4 levels.…”

Section: Methodsmentioning

confidence: 99%

“…Density matrix transport models have been applied to specific QCL systems since their conception [20][21][22][23][24], but analytic formulations become prohibitively cumbersome for designs consisting of more than 3-4 levels. To address this limitation, generalized density matrix models have recently been presented for modeling of arbitrarily complex designs [19,25,26], with the further extensions of coherent optical response and spatial periodicity first made in Ref. [26].…”

Section: Methodsmentioning

confidence: 99%

Origins of Terahertz Difference Frequency Susceptibility in Midinfrared Quantum Cascade Lasers

Burnett

Williams

2016

Phys. Rev. Applied

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We present a density matrix-based transport model applicable to quantum cascade lasers which computes both linear and nonlinear optical properties coherently and nonperturbatively. The model is applied to a dual active-region mid-infrared quantum cascade laser which generates terahertz radiation at the difference frequency between two mid-infrared pumps. A new mechanism for terahertz generation is identified as self-detection, ascribed to the beating of current flow following the intensity, associated with stimulated emission. This mechanism peaks at optical rectification but exhibits a bandwidth reaching significantly into the terahertz range, which is primarily limited by the subpicosecond intersubband lifetimes. A metric is derived to assess the strength of self-detection in candidate active regions through experiment alone, and suggestions are made for improvement of the performance at frequencies below 2 THz.

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