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Journal of Applied Physics

Effect of Coulomb interaction on nonlinear (intensity-dependent) optical processes and intrinsic bistability in a quantum well under the electric and magnetic fields

İbrahim Karabulut

Published Mar 1, 2011• 17 citations
Publisher

Abstract

The effect of the electrostatic Coulomb interaction on the line shape related to the intensity-dependent intersubband optical processes in a Si δ-doped quantum well is studied using the density matrix formalism. The electronic structure of the quantum well is calculated from the self-consistent numerical solution of the coupled Schrödinger–Poisson equations. The line shape function is considerably modified by the optical intensity and the electric and magnetic fields. Moreover, we demonstrate the existence of the optical bistability for appropriate values of the optical intensity and also the control of the optical bistability with the electric and magnetic fields. It is also found that the intersubband relaxation time plays an important role in determining the optical bistability region.

DOI
10.1063/1.3553641

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The effect of the electrostatic Coulomb interaction on the line shape related to the intensity-dependent intersubband optical processes in a Si δ-doped quantum well is studied using the density matrix formalism. The electronic structure of the quantum well is calculated from the self-consistent numerical solution of the coupled Schrödinger–Poisson equations. The line shape function is considerably modified by the optical intensity and the electric and magnetic fields. Moreover, we demonstrate the existence of the optical bistability for appropriate values of the optical intensity and also the control of the optical bistability with the electric and magnetic fields. It is also found that the intersubband relaxation time plays an important role in determining the optical bistability region.
The problem of saturation of intersubband absorption and optical rectification in asymmetric quantum wells is discussed theoretically using the density matrix formalism. The effects of the electron-electron interaction are taken into account. It is shown that near the resonance the spectral shapes of the nonlinear optical absorption coefficient and the nonlinear optical rectification coefficient are very similar. In the absence of the electron-electron interaction the spectral responses are nearly Lorentzian. The electron-electron interaction plays an important role in heavy doped systems. In structures with large spatial separation of the ground and the excited states wave functions, the depolarization effect is small and the absorption spectrum is affected mainly by the electrostatic Coulomb interaction. This interaction shifts the absorption peak to higher energy by an amount depending on the intensity of the incident light and leads to the significant distortion (asymmetry) of the line.
Abstract We study the nonlinear intersubband optical absorption of a single Si δ‐doped GaAs sheet placed in the middle of a GaAs quantum well and subjected to an electric field. The Schrödinger and Poisson equations are solved self‐consistently for various electric field strengths. The self‐consistent solutions provide us with the correct confining potential, the wave functions, the corresponding subband energies and the subband occupations. The nonlinear optical intersubband absorption spectra are discussed within the framework of the density matrix formulation for various electric field strengths, well widths, and sheet thicknesses in which Si atoms are distributed uniformly. We include both the depolarization and exciton shifts in calculations. The depolarization effect not only shifts the peak value but also makes the nonlinear absorption spectrum strongly asymmetric with the increasing intensity of the optical field. The blue‐shift associated with the depolarization shift is decreased when the intensity is increased. The absorption line shape becomes more asymmetric at smaller well widths and thicker doping layers. The electric field restores the symmetry of the absorption line shape at larger well widths and thinner doping layers, but it decreases the peak value of the line shape. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An intrinsic optical bistability in a double quantum well is described theoretically. The effect is based on the resonant tunneling of electrons against the electric-field force (the counterfield electron transfer) and is driven and controlled by far-ir radiation exciting an intersubband transition. The theory relies on the density-matrix technique and takes into account optical intersubband excitation, interwell tunneling, the relaxation of populations and polarizations, and the mean-field effects of the transferred electron charge (shifts of the levels and changes of matrix elements). Hysteresis-type curves are obtained for both the charge-transfer probability and the optical absorption as functions of the light intensity. The theory shows the effect to be readily observable under realistic conditions, with the exciting-light intensity as low as 50 W/cm2{\mathrm{cm}}^{2}cm2.
We theoretically investigate the nonlinear intersubband response, in particular the intrinsic optical bistability (IOB), of quantum well (QW) structures embedded into layered systems. A semiclassical approach is employed based on the plane-wave approximation, the transfer-matrix formalism, the sheet model, and the density-matrix formalism developed to calculate the two-dimensional nonlinear intersubband electron conductivity and the IOB. A variety of presented numerical results demonstrate the importance of inhomogeneity of spatial distribution of radiation intensity induced by multiple radiation reflection for the IOB in layered structures. It is shown that knowing the radiation intensity distribution in the area occupied by QWs, in part standing-wave patterns, are crucial for understanding of IOB pictures. The IOB in systems of one, two, three, five, and ten QWs is investigated. The multistability phenomenon is addressed.
We present self-consistent calculations of the energy levels in an asymmetric coupled quantum-well structure coupled to a CO2 laser source which is nearly resonant with an intersubband transition. Solving Schrödinger’s and Poisson’s equations concurrently with a set of rate equations, it is shown that intrinsic optical bistability can be achieved. The bistability arises from charge transfer and a subsequent, self-consistent shift of the energy levels which feeds back to the absorption rate. Using realistic parameters, an on-off intensity ratio of 4:1 at switching powers of a few 100 kW/cm2 is predicted at about 10-μm wavelength.
In this study, the effects of the external fields (electric and tilted magnetic fields) and well parameters on the optical absorption coefficients in GaAs/GaAlAs multiple (five) quantum wells under the applied electric and tilted magnetic fields has been investigated theoretically. Firstly, the energy eigenvalues and eigen functions of an electron confined in multiple quantum wells are calculated by analytically from Schrödinger equation using the transfer matrix method within the effective mass approximation, Secondly, the linear, nonlinear and total intersubband optical absorptions in GaAs/GaAlAs multiple quantum wells system are studied within the compact density-matrix approach. It is shown that the parameters such as strenghts of the external fields and θ-tilted angle values not only shift the peak positions in absorption spectrum but also considerably modify their potential heights. In generally, electronic and optical properties of the quantum wells are very sensitive to the applied external fields and well parameters. Therefore, we can conclude that the effect of the external fields can be used to tune and control the optical properties of interest in the range of the far-infrared electromagnetic spectrum.