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Semiconductors

Saturation of interband absorption in semiconductors

A. O. Melikyan, G. R. Minasyan

Published Apr 1, 2000• 9 citations
Publisher

Abstract

The nonlinear absorption factors in a direct-gap semiconductor are calculated both for the pump and probe waves using the density matrix formalism. The key feature of the calculation is the consideration of the carrier dispersion. It is shown for the first time that the dispersion law defines the saturation behavior of the absorption factor. The intensity and frequency dependences of the absorption factors calculated differ significantly from those obtained previously. It is also shown that the conventional theory of nonlinear interband absorption based on the kinetic equations for carriers leads to the correct results only in the limit of small pump intensities.

DOI
10.1134/1.1187993

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The nonlinear absorption factors in a direct-gap semiconductor are calculated both for the pump and probe waves using the density matrix formalism. The key feature of the calculation is the consideration of the carrier dispersion. It is shown for the first time that the dispersion law defines the saturation behavior of the absorption factor. The intensity and frequency dependences of the absorption factors calculated differ significantly from those obtained previously. It is also shown that the conventional theory of nonlinear interband absorption based on the kinetic equations for carriers leads to the correct results only in the limit of small pump intensities.
Saturation properties of absorption, dispersion, and mixing susceptibilities in semiconductors have been described using the density matrix approach. This model, which takes into account both intraband thermalization and interband relaxation including Auger recombination, allows for numerical computation of the susceptibilities whatever the temperature and laser intensity are. As a simplification, an equivalent two-level system is derived which represents very well absorption and mixing susceptibilities for any laser wavelength, dispersion being correctly described by this model only when the pump frequency is close to or smaller than the band-gap energy. Such an equivalence is very easy to handle and allows for great simplification when the susceptibilities are introduced into the propagation equations.
Dispersive optical bistability has been observed in various direct-gap semiconductors. This effect is due to the dependence of the refractive index on the intensity I. A unified microscopic theory of the observed optical bistability in direct-gap semiconductors, such as GaAs is developed by calculating the complex, non-linear dielectric function for arbitrary free-carrier concentrations. The calculation, which includes many-body effects, consists in a very accurate numerical solution of the Bethe-Salpeter equation for the polarisation function. The resulting time-resolved spectra are discussed and are compared with experimental results.
Mechanisms for reduced interband absorption using intersubband coherence or intersubband coupling in semiconductor quantum wells are analyzed by exactly solving the density matrix equation. By placing some mild limitations on the diagonal density matrix elements, general analytic solutions are obtained without weak-field restrictions. Our solutions demonstrate reduced absorption, various nonlinear processes, and coupling-field-modulation of interband transitions. Our results agree well with previous results for three-level atomic systems, give insights into nonlinear mechanisms, and point out the importance of nonperturbative approaches to this class of problems.>
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.
An improved density-matrix theory is developed that can treat both spectral hole burning and carrier heating self consistently. Various intraband and interband relaxation terms characterized by different relaxation times and quasi-equilibrium distributions are introduced into the density-matrix equations within a relaxation-time approximation. Conservation of total number and energy densities of carrier systems in each band is considered to determine the quasi-equilibrium distributions. Formalism is applied to the calculation of the transient optical nonlinearity of highly carrier-injected semiconductors. Spectral hole burning and carrier-heating effects on the spectral and temporal characteristics are then clarified. In particular, the significant four-wave-mixing effect due to carrier heating is pointed out. An experiment that can be used to directly prove the existence of the carrier-heating effects on gain nonlinearity is also proposed.>
Optical interband excitonic absorption of semiconductor quantum wells (QW’s) driven by a coherent pump field is investigated on the basis of semiconductor Bloch equations. The pump field has a photon energy close to the intersubband spacing between the first two conduction subbands in the QW’s. An external weak optical field probes the interband transition. The excitonic effects and pump-induced population redistribution within the conduction subbands in the QW system are included. When the density of the electron–hole pairs in the QW structure is low, the pump field induces an Autler–Townes splitting of the exciton absorption spectrum. The split size and the peak positions of the absorption doublet depend not only on the pump frequency and intensity but also on the carrier density. As the density of the electron–hole pairs is increased, the split contrast (the ratio between the maximum and the minimum values) is decreased, because the exciton effect is suppressed at higher densities owing to the many-body screening.