Exciton-related nonlinear optical absorption and refractive index change in GaAs–Ga1−xAlxAs double quantum wells

Miranda, Guillermo L.; Duque, C.A.

doi:10.1016/j.physb.2012.10.008

Cited by 19 publications

(4 citation statements)

References 28 publications

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“…For example, there are several papers (see e.g. [26,47,[71][72][73][74][75]) dedicated to analyzing the optical behavior of quantum dots by calculating the absorption coefficient, 𝜁, and the relative changes at the same order of the refractive index, ∆𝑛∕𝑛, for an incident linearly polarized light beam. For a transition (𝓀 𝑖 , 𝓁 𝑖 , 𝓃 𝑖 ) → (𝓀 𝑗 , 𝓁 𝑗 , 𝓃 𝑗 ), we can compute such quantities (at first order for simplicity) as functions of the energy 𝐸 𝛾 of the incident photon [26] by using a density matrix approach and a perturbation expansion method [76] Here, 𝜇 0 is the permeability of the vacuum, 𝜀 = 𝜀 0 𝑛 2 𝑟 = 𝜀 0 𝜀 𝑟 is the real part of the permittivity of the material (𝜀 0 is the permittivity of the vacuum, 𝜀 𝑟 is the static dielectric constant of the material and 𝑛 𝑟 = √ 𝜀 𝑟 is the refractive index of the medium), 𝜎 𝑣 is the carrier density, Γ 𝑖𝑗 = ℏ∕𝑇 𝑖𝑗 is the relaxation rate-is a damping-related Lorentzian term associated with exciton scattering losses in the system [73]-(𝑇 𝑖𝑗 is the time relaxation), ℳ 𝑎;𝑖𝑗 ≡ ⟨Ψ 𝑎;𝓀 𝑗 ,𝓁 𝑗 ,𝓃 𝑗 |𝑒𝑥| Ψ 𝑎;𝓀 𝑖 ,𝓁 𝑖 ,𝓃 𝑖 ⟩ is the dipole matrix element for 𝑥-polarized incident radiation (𝑒 is the elementary charge) and ∆𝐸 𝑎;𝑖𝑗 ≡ 𝐸 𝑎;𝓀 𝑗 ,𝓁 𝑗 ,𝓃 𝑗 − 𝐸 𝑎;𝓀 𝑖 ,𝓁 𝑖 ,𝓃 𝑖 is the energy gap between the levels.…”

Section: Conclusion and Final Remarksmentioning

confidence: 99%

Three-dimensional bound states of cylindrical quantum heterostructures with position-dependent mass carriers

Christiansen,

Lima

2023

Phys. Scr.

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We present a comprehensive spectral analysis of cylindrical quantum heterostructures by considering effective electronic carriers with position-dependent mass for five different kinetic-operator orderings. We obtain the bound energy eigenstates of particles in a three-dimensional cylindrical nanowire under a confining hyperbolic potential with both open and closed boundary conditions in the radial and the axial directions. In the present model we consider carriers with continuous mass distributions within the dot with abrupt mass discontinuities at the barriers, moving in a quantum dot that connects different substances. Continuity of mass and potential at the interfaces with the external layers result as a particular case. Our approach is mostly analytical and allows a precise comparison among von Roos ordering classes.

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Section: Conclusion and Final Remarksmentioning

confidence: 99%

Three-dimensional bound states of cylindrical quantum heterostructures with position-dependent mass carriers

Christiansen,

Lima

2023

Phys. Scr.

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“…where ω is the frequency of an incident photon, µ the permeability of vacuum. Dipole matrix element M j j can be written as the following expression [29] M j j = ψ j |q(z e − z h )|ψ j .…”

Section: Theory and Modelmentioning

confidence: 99%

Exciton optical absorption in asymmetric ZnO/ZnMgO double quantum wells with mixed phases*

et al. 2020

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The optical absorption of exciton interstate transition in Zn1 − xl Mg xl O/ZnO/Zn1 − xc Mg xc O/ZnO/Zn1 − xr Mg xr O asymmetric double quantum wells (ADQWs) with mixed phases of zinc-blende and wurtzite in Zn1 − x Mg x O for 0.37 < x < 0.62 is discussed. The mixed phases are taken into account by our weight model of fitting. The states of excitons are obtained by a finite difference method and a variational procedure in consideration of built-in electric fields (BEFs) and the Hartree potential. The optical absorption coefficients (OACs) of exciton interstate transition are obtained by the density matrix method. The results show that Hartree potential bends the conduction and valence bands, whereas a BEF tilts the bands and the combined effect enforces electrons and holes to approach the opposite interfaces to decrease the Coulomb interaction effects between electrons and holes. Furthermore, the OACs indicate a transformation between direct and indirect excitons in zinc-blende ADQWs due to the quantum confinement effects. There are two kinds of peaks corresponding to wurtzite and zinc-blende structures respectively, and the OACs merge together under some special conditions. The computed result of exciton interband emission energy agrees well with a previous experiment. Our conclusions are helpful for further relative theoretical studies, experiments, and design of devices consisting of these quantum well structures.

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“…Within the framework of the effective mass approximation, the Hamiltonian for exciton states in a In

_{x}

_{1 - x}

N/GaN QW under the effects of growth‐direction applied electric field (

\overset{F}{true} = F \overset{u_{z}}{true}

) and hydrostatic pressure is given by

\begin{matrix} right H & center = & left \sum_{i = normale, h} ([], - \frac{ℏ^{2}}{2 m_{i}^{*} false(P false)} \frac{\partial^{2}}{\partial z_{i}^{2}} + V_{i} false(z_{i}, P false)) \\ right & center & left - \frac{ℏ^{2}}{2 μ (P)} ((), \frac{\partial^{2}}{\partial ρ^{2}} + \frac{1}{ρ} \frac{\partial}{\partial ρ} + \frac{1}{ρ^{2}} \frac{\partial^{2}}{\partial ϕ^{2}}) \\ right & center & left + e F (z_{normale} - z_{normalh}) - \frac{e^{2}}{ϵ (P) r}, \end{matrix}

where

r = \sqrt{ρ^{2} + false(z_{e} - z_{h})^{2}}

is the electron–hole distance,

ρ

is the in‐plane electron–hole relative coordinate, and

z_{e}

(

z_{h}

) is the positions of the electron (hole) along the z ‐direction. In addition,

…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Exciton‐related optical properties in zinc‐blende GaN/InGaN quantum wells under hydrostatic pressure

Duque

Morales

2015

Physica Status Solidi (b)

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The exciton‐related optical absorption in zinc‐blende InGaN/GaN single quantum wells (QW) under hydrostatic pressure is studied. The energy states in the system are calculated within the effective mass approximation and a variational scheme, taking into account the effects of applied hydrostatic pressure an static electric field. The optical response is calculated in the framework of the two‐level model and the rotating wave approximation. The results are given as functions of the In molar fraction, the QW width, the hydrostatic pressure, and the electric field strength. It is found that a significant exciton‐related nonlinear absorption can be achieved in the range of photon energies around 100meV, for the kind of structures under study.

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Exciton-related nonlinear optical absorption and refractive index change in GaAs–Ga1−xAlxAs double quantum wells

Cited by 19 publications

References 28 publications

Three-dimensional bound states of cylindrical quantum heterostructures with position-dependent mass carriers

Three-dimensional bound states of cylindrical quantum heterostructures with position-dependent mass carriers

Exciton optical absorption in asymmetric ZnO/ZnMgO double quantum wells with mixed phases*

Exciton‐related optical properties in zinc‐blende GaN/InGaN quantum wells under hydrostatic pressure

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