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Journal of Optics

Kerr nonlinearity due to intersubband transitions in a three-level InAs/GaAs quantum dot: the impact of a wetting layer on dispersion curves

Ali Khaledi‐Nasab, Mohammad Sabaeian, Mostafa Sahrai, Vahid Fallahi

Published May 1, 2014• 18 citations
Publisher

Abstract

We report Kerr nonlinearity due to intersubband transitions in a three-level InAs/GaAs dome-shaped quantum dots (QDs) system. The impact of wetting layer and dot size on the electronic, linear and nonlinear optical properties is discussed. The results showed an overall shift of dispersion curves towards lower frequencies, pronounced reshaping of absorption and dispersion curves, and two orders of magnitude enhancement in Kerr nonlinearity due to the presence of a wetting layer.

DOI
10.1088/2040-8978/16/5/055004

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Results in Physics•Jan 1, 2016•12 citations
We report Kerr nonlinearity due to intersubband transitions in a three-level InAs/GaAs dome-shaped quantum dots (QDs) system. The impact of wetting layer and dot size on the electronic, linear and nonlinear optical properties is discussed. The results showed an overall shift of dispersion curves towards lower frequencies, pronounced reshaping of absorption and dispersion curves, and two orders of magnitude enhancement in Kerr nonlinearity due to the presence of a wetting layer.
In the past few years advance in nanofabrication techniques have made it possible to make well-like compound semiconductor structures of low nanometer size.In these structures,the state of the electron in the direction perpendicular to the length of the well is quantized with sufficiently large separation in energy levels and the motion of the electron parallel to the length is that of a quasi-free electron.One of the most remarkable properties of these one-dimensional electron system is that the optical transitions between the size-quantized subbands are feasible.The result shows there is a large optical nonlinearities in asymmetric quantum wells.The problem of optical saturation of intersubband absorption has recently attracted considerable attention.The problem is very important to the development of superlattice devices such as fast infrared detectors and(modulators) because one needs to know the range of input optical intensities for which linear operation is(possible.) The analytical expression of the linear and the third-order nonlinear optical intersubband absorption coefficients are obtained in Pschl-Teller wells using the density matrix formalism taking into account the(intrasubband) relaxation.Since there are two adjustable parameters κ and λ in Pschl-Teller wells,the shapes of the wells will change with the change of the parameters κ and λ,accordingly the linear and the third-order nonlinear optical absorption coefficients will change with the parameters κ and λ.It is shown that the optical absorption coefficient depends on the parameter,and the optical intensity strongly. The absorption saturation will occur with I increase.Numerical results are presented for a typical AlGaAs/GaAs Pschl-Teller well.
In recent years,the subject of optical nonlinearity in semiconductor quantum confined structures such as quantum wires and quantum dots has attracted a considerable attention because of their relevance for studying practical applications and as a probe for the electronic structure of media.It has been shown that the low dimensional quantum systems present very large nonlinear optical susceptibilities .Theoretically,most of the studies on quantum dots are focused on spherical quantum dots for simplicity.The shape of quantum dot depends on growth conditions.In fact,quantum dots are better described as thin disk or cylinder.In the present work third order nonlinear optical susceptibilities in disk shaped quantum dots due to resonant intersubband transition are analyzed by a compact density matrix approach.It has rarely been discussed in literatures.Firstly,we consider an electron moving in a quantum disk whose radius R is very large compared to its thickness d .For simplicity,we assume that the isotropic effective mass approximation is valid within the disk and that the inner potential is null while the outer confining potential is approximately infinite.Using the adiabatic approximation we solve the three dimensional Schrdinger equation and obtain the analytical expressions of wave functions and energy levels in cylindrical coordinates.Secondly,we consider the system is excited by an electromagnetic field with frequency ω. The electromagnetic field is incident with a polarization vector normal to the disk.We treat H′=ezE(t) as a perturbation term.By using the compact density matrix method,we derive a general formula for third order nonlinear optical susceptibilites employing a four level model in quantum disk.Finally,numerical results are illustrated for a typical GaAs quantum disk.We calculate the third order nonlinear optical susceptibilities as a function of the disk thickness.It is shown that the third order nonlinear optical susceptibilities in quantum disk are 10～100 times larger than that in quantum well for various disk thickness.Furthermore,if we choose an optimized thickness of quantum disk,we could obtain a quite large refractive index with a comparatively small absorption coefficient.Therefore,we suggest that the quantum dots would be an excellent system in the field of optical communications and optical switching.
We study theoretically the time evolution of nonlinear optical phenomena of a probe electromagnetic field pulse in intersubband transitions of a semiconductor quantum well structure under the influence of a pump electromagnetic field. More specifically, we take into consideration the effects of electron-electron interactions and consider the interaction of a two-subband system with rectangular electromagnetic fields. The spectral form of the linear absorption, dispersion, and nonlinear optical Kerr effect is described, from the time that the external field is applied up until the dynamics of the system has reached a steady state. In order to describe the dynamics of the system, the effective nonlinear Bloch equations are used, in which renormalized terms for the transition energy and the applied field have been added, due to the effects of electron-electron interactions. These equations are properly combined, and the differential equations of the density matrix elements for the several optical phenomena up to third order are derived. These are solved numerically in the whole time range up to the steady state for a GaAs/AlGaAs quantum well structure. We show that the form of the several optical spectra studied here has a significantly altered evolution over time, according to the value of the frequency of the pump field and of electron sheet density. Even in the case in which the spectral form in the steady state case is almost identical for two different sets of parameters, their evolution can be quite different, according to the precise value of these parameters.
A scheme for giant enhancement of the Kerr nonlinearity in linear triple quantum dot molecules is proposed. In such a system, the tunneling-induced transparency window obtained in double quantum dot molecules splits into two windows, due to the coupling with the third quantum dot. And most important, the Kerr nonlinearity can be enhanced by several orders of magnitude, compared with that generated in double quantum dot molecules. With proper detuning of the tunneling, giant Kerr nonlinearity accompanied by vanishing absorption can be realized, which opens the possibility to enhance self-phase modulation in tunneling controllable semiconductor nanostructures under conditions of low light levels. Quantitative analysis shows that the giant Kerr nonlinearity is attributed to the interacting double dark resonances induced by the tunneling between the triple quantum dots, therefore no extra laser fields are required.
A model of the dynamical equations of the density matrix describes double tunnelling between double quantum dot (QD) system states, this is to study Kerr nonlinearity in QD structure. Inhomogeneity in the QD system is included which is not included in earlier studies of Kerr nonlinearity in QDs. Possibilities of subluminal and superluminal light propagation and switching between them are examined. Double tunnelling is shown to obtain giant Kerr dispersion compared with single tunnelling. High conduction- and low valence-band tunnelling components are required to obtain high Kerr dispersion. Working with one tunnel component reduced Kerr dispersion and switching between subluminal and superluminal can be obtained and the EIT window can be removed.