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IEEE Journal of Quantum Electronics

Modeling of nonlinear absorption and refraction in quantum-well structures for all optical switching

Domenico Campi, P.J. Bradley, Riccardo A. Calvani, Renato Caponi

Published Apr 1, 1993• 13 citations
Publisher

Abstract

A realistic model of the electromagnetic response in excited, type-I semiconductor quantum wells is presented. A multisubband analysis of the room temperature band edge spectra, in which the plasma effects are determined through an iterative, numerical solution of a generalized Bethe-Salpeter equation, is introduced. The method allows the treatment of situations in which transitions higher than the first give sizeable contributions to the nonlinear optical properties, as in coupled quantum wells or in the propagation of TM modes within waveguides based on quantum confined structures. Further, the method accounts for the effects of finite quantum-well thickness and incorporates a phenomenological description of the width of the resonance lines. The behavior is compared to that exhibited by more idealized models introduced in earlier works, where single-subband, purely 2-D systems were treated. Computer generated spectra are compared with absorption spectra experimentally obtained for moderately strained InGaAs-InP QWs.>

DOI
10.1109/3.214500

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Journal of Applied Physics•Oct 1, 2012•8 citations
A realistic model of the electromagnetic response in excited, type-I semiconductor quantum wells is presented. A multisubband analysis of the room temperature band edge spectra, in which the plasma effects are determined through an iterative, numerical solution of a generalized Bethe-Salpeter equation, is introduced. The method allows the treatment of situations in which transitions higher than the first give sizeable contributions to the nonlinear optical properties, as in coupled quantum wells or in the propagation of TM modes within waveguides based on quantum confined structures. Further, the method accounts for the effects of finite quantum-well thickness and incorporates a phenomenological description of the width of the resonance lines. The behavior is compared to that exhibited by more idealized models introduced in earlier works, where single-subband, purely 2-D systems were treated. Computer generated spectra are compared with absorption spectra experimentally obtained for moderately strained InGaAs-InP QWs.>
Absorption spectra of strained InGaAs/InP quantum wells exhibit a single, unusually large exciton feature. 60% quenching is obtained for 4.3 mW Nd:YAG effective pump power at a wavelength of 1.064 mu m. A simple two-level formula fits well the behaviour at the exciton peak, and absorption spectra are reasonably approximated by a standard two-dimensional exciton model. Saturation intensities calculated with these techniques range around 200 W cm-2. Finally the Kramers-Kronig relations are used to calculate the associated refractive index change.
We review the nonlinear-optical effects observed at room temperature in semiconductor quantum-well structures photoexcited near the band gap. A comprehensive discussion of optical transitions in these microstructures is given, including excitonic effects and the specific features of room-temperature exciton resonances. Experimental investigations using continuous-wave, picosecond-, and femtosecond-laser sources are presented. They show extremely efficient nonlinear processes. In the case of excitations that are long compared with the exciton-ionization time, the induced changes in absorption and refraction do not depend on the wavelength or on the duration of excitation. These changes depend only on the density of absorbed photons and are interpreted in terms of electron–hole plasma screening and band filling. In contrast, for ultrashort excitation, nonlinear processes depend critically on the excitation wavelength. The selective generation of excitons is found to produce effects larger than a plasma of the same density. This unexpected result is shown to arise from the low temperature of the exciton gas before it interacts with the lattice and from the decrease of screening that is the reduced dimensionality of quantum-well structures.
Electro-optical effects, such as the Franz-Keldysh effect in bulk materials or the quantum confined Stark effect in quantum well structures, lead to strong optoelectronic nonlinearities which form the basis for optical modulators and optically bistable devices. They result from a modification of the optical absorption properties by an applied electric field and are particularly pronounced in the case of low dimensional semiconductors. We review theoretical modelling and computer simulations of such optoelectronic devices in particular for ZnSe based quantum well structures, where excitonic features dominate even at room temperature. The field dependent absorption spectra are calculated by a many-body theory including the full electron-electron interaction. The transition from the quantum confined Stark effect, which is found for well widths smaller than the exciton Bohr diameter, to the Franz-Keldysh effect, which corresponds to the limit of wide wells, is studied. Optical bistability and switching is found in R-SEED and D-SEED configurations, and the optimization of the device performance is discussed.
An examination of the contribution of excitons, compared to the continuum states, to the optical properties of GaAs/AlGaAs multiple quantum wells illuminates the mechanisms underlying nonlinear absorption and nonlinear refraction and yields information which is useful for optimizing devices which incorporate these materials. We have measured the absorption as a function of intensity at three different wavelengths—above the band edge, on the excitonic resonance, and far below the band edge—to separate the effects. We find that different well thicknesses have different saturation intensities both for excitonic and continuum absorption.
A nonequilibrium Green's-function TTT-matrix approach is presented for the consistent computation of semiconductor quantum-well optical spectra including strong Coulomb correlations in the coupled photon and carrier system. Numerical solutions of the Bethe-Salpeter-type equations yield good agreement with recent absorption and/or gain and emission experiments.
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.