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Journal of the Optical Society of America B

Optical absorption saturation of semiconductor quantum dots

David A. B. Miller, D. S. Chemla, Stefan Schmitt-Rink

Published Jan 1, 1986• 0 citations
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Abstract

We have analyzed theoretically the optical absorption saturation of semiconductor microcrystallites so small that they show strong quantum confinement in all three dimensions [quantum dots (QDs)]. We show that saturation of the lowest energy excited state becomes extremely simple to describe even including excitonic effects. Such QDs exhibit novel physical properties, including very large optical absorption per unit volume, that make QDs very attractive nonlinear media.

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We have analyzed theoretically the optical absorption saturation of semiconductor microcrystallites so small that they show strong quantum confinement in all three dimensions [quantum dots (QDs)]. We show that saturation of the lowest energy excited state becomes extremely simple to describe even including excitonic effects. Such QDs exhibit novel physical properties, including very large optical absorption per unit volume, that make QDs very attractive nonlinear media.
Quantum dot (QD)-based semiconductor optical amplifiers offer unique properties compared with conventional devices based on bulk or quantum well material. Due to the bandfilling properties of QDs and the existence of a nearby reservoir of carriers in the form of a wetting layer, QD semiconductor optical amplifiers may be operated in regimes of high linearity, i.e. with a high saturation power, but can also show strong and fast nonlinearities by breaking the equilibrium between discrete dot states and the continuum of wetting layer states. In this paper, we analyse the interplay of these two carrier populations in terms of a simple rate equation model. Based on the steady-state and small-signal properties of the model, we analyse and discuss the optical modulation response and the four-wave mixing properties of QD semiconductor optical amplifiers, in particular emphasizing the role of ultrafast gain dynamics.
Transient optical nonlinearities of semiconductor quantum dots in the strongly confined regime are studied, in which the exciton, biexciton and magnetic field effects are taken into account. The photo induced band-to-band electronic transitions are considered from both the heavy-hole (hh) and light-hole (lh) valence bands to the lowest (1s) exciton state below the fundamental absorption edge. The time dependent perturbation technique for a three-level system, under the near band gap resonant excitation regime, has been employed; with the incorporation of the relaxation and dephasing mechanisms phenomenologically. The induced polarization is calculated from where the real and imaginary parts of the third-order nonlinear optical susceptibility, responsible for the occurrence of nonlinear refraction and nonlinear absorption respectively, have been derived. The temporal and detuning spectra of nonlinear refraction and absorption; and their dependence on density of biexcitons and a moderately strong magnetic field, have been analyzed. It is observed that the nonlinear refraction and nonlinear absorption enhance with increasing magnetic field in small CdS quantum dots.
Density matrix approach has been employed to analyze the pump-probe spectroscopic absorption spectra of small semiconductor quantum dots (QDs) under strong confinement regime with sizes smaller than the bulk exciton Bohr radius such that the Coulombic interaction energy becomes negligible in comparison to the confinement energy. The average time rate of absorption has been obtained by incorporating the radiative and nonradiative decay processes as well as the inhomogeneous broadening arising due to nonuniform QD sizes. The analytical results are obtained for QDs duly irradiated by a strong near resonant pump and broadband weak probe. Numerical estimations have been made for (1) isolated QDs and (2) QD-arrays of GaAs and CdS. The results agree very well with the available experimental observations in CdS QDs. The results in case of GaAs QDs can lead one to experimentally estimate absorption/gain spectra in the important III-V semiconducting mesoscopic structures.
Nanometer-size crystals abbreviated to semiconductor nanocrystals are known as zero-dimensional dots. Their optical properties have been characterized by the quantum confinement effect and the lowest excited states show blue shifts depending on their size. Quantum dots are sharply different from other low-dimensional quantum structures, such as quantum wells and quantum wires, because they are made of as small as 103~106 atoms. Considerable fraction of atoms face the surface or the interface of quantum dots in the surrounding materials, so that the energy of quantum dots is expected to be easily modified by the surroundings.
I recent years, significant attention has been given to nonlinear optical phenomena, such as nonlinear optical absorption and dispersion, derived from a driven quantum transition of semiconductor nanostructures, such as semiconductor quantum wells, quantum disks and mainly quantum dots. An important issue that is widely studied is the effect of probe electromagnetic field intensity on the total (nonlinear) absorption coefficient and on the total (nonlinear) index of refraction. Some of the phenomena that are commonly found for large electromagnetic field intensities are the creation of a strong dip in the absorption spectrum near or at resonance (the so-called bleaching effect), negative absorption near or at resonance that leads to optical gain and the change of the slope of the total index of refraction near or at resonance from negative to positive that changes the behavior of the system from fast to slow light. Unfortunately, these phenomena do not exist and are artifacts of a common abuse of the theoretical methodology for the study of the total absorption coefficient and the total index of refraction. The main error is that the total absorption coefficient and the total index of refraction was initially derived from density matrix equations using perturbation theory and includes first-order (linear) as well as third-order (nonlinear) terms. This method gives correct results for small electromagnetic field intensities and it leads to saturation of absorption and dispersion in this regime. However, for larger intensities it gives the misleading results mentioned above due to either failure of the order of perturbation theory considered in the derivation of the total absorption coefficient and the total index of refraction or even failure of perturbation theory at all in the treatment of the problem. In this work, we revisit the problem of the total absorption coefficient and the total index of refraction in a symmetric semiconductor quantum dot structure (we choose the example of a core-shell quantum dot) under a strong probe field excitation. We use the two-level model, solve the relevant density matrix equations under the rotating wave approximation and under steady state conditions, and obtain the correct form of the nonlinear optical susceptibility that is then used for the derivation of the formulae of the total absorption coefficient and the total index of refraction under the interaction with a strong probe field. Actually, the commonly used perturbation theory formulae can be obtained by our formulae using a series expansion and keeping terms up to second order in electric field amplitude. We also derive the electronic structure of the quantum dot system by solving numerically the time-independent Schrodinger equation, under the effective mass approximation, using the potential morphing method and obtain the energy difference and the electric dipole matrix element for the relevant transitions of the quantum dot system. Then, for the specific quantum dot system we compare the results of the total absorption coefficient and the total index of refraction for the two methodologies (the perturbation result and our result) for different electromagnetic field intensities.