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Quantum Optoelectronics

Pulse Propagation and Many-body Effects in Semiconductor Four Wave Mixing

A. Schulze, A. Knorr, S. W. Koch

Published Jan 1, 1995• 0 citations
Publisher

Abstract

The simultaneous influence of pulse propagation and Coulomb many-body interaction in Four Wave Mixing experiments is theoretically studied using the Semiconductor-Maxwell-Bloch equations. In this framework, the propagation of the optical fields and the microscopic interaction of the light with the semiconductor are treated consistently. The Maxwell equation is used as a reduced wave equation and the many-body Coulomb interaction are treated at the level of a screened Hartree-Fock approximation including phenomenological decay terms. We have analyzed the interplay of the propagation and Coulomb effects by calculating the Four Wave Mixing signal (FWMS) for different sample lengths and various excitation conditions, i.e, for pulses with different intensities at the exciton and in the continuum.

DOI
10.1364/qo.1995.qthe14

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The simultaneous influence of pulse propagation and Coulomb many-body interaction in Four Wave Mixing experiments is theoretically studied using the Semiconductor-Maxwell-Bloch equations. In this framework, the propagation of the optical fields and the microscopic interaction of the light with the semiconductor are treated consistently. The Maxwell equation is used as a reduced wave equation and the many-body Coulomb interaction are treated at the level of a screened Hartree-Fock approximation including phenomenological decay terms. We have analyzed the interplay of the propagation and Coulomb effects by calculating the Four Wave Mixing signal (FWMS) for different sample lengths and various excitation conditions, i.e, for pulses with different intensities at the exciton and in the continuum.
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This dissertation considers multi-wave interactions in bulk semiconductors. Non-equilibrium Green's functions are used to derive an appropriate set of equations describing the interaction of a light field with a semiconductor. Many-body effects lead to the screening of the Coulomb potential in these equations, as well as, carrier-carrier scattering. The carrier-carrier scattering is studied within the context of the carrier Boltzmann equation which contains the dynamically screened Coulomb potential. The relation between carrier scattering and optical dephasing is also made. The carrier scattering rates are then used in the equations describing a two beam pump-probe experiment. The resulting equations are solved numerically for both passive and active systems, and effects such as spectral hole burning, coherent light scattering, and light induced band splitting are studied. Considering three CW beams (pump and two probes) allows for the study of four-wave mixing in semiconductors. By considering CW fields, the semiconductor may be treated in the quasi-equilibrium approximation allowing for greater detail in the treatment of the light field. The resulting probe absorption yields asymmetries which result in an asymmetric four-wave mixing spectrum. The four-wave mixing spectrum is then used to study the amount of squeezing in the light field exiting the cavity in a four-wave mixing experiment.
Summary form only given. Four-wave mixing processes in semiconductor quantum wells have been studied intensively for many years, because they allow for a detailed investigation of ultrafast many-body processes such as quantum correlations and quantum coherences. From a theoretical point of view one can roughly divide the existing approaches into two categories: (i) fully microscopic theories based on the bandstructure and on Coulomb interactions between electrons and holes, and (ii) phenomenological few-level models.
Many-body Coulomb interactions dominate nonlinear optical properties of semiconductor structures in many respects. Resulting effects show up most distinct in the temporal evolution of transient four-wave mixing signals. The simplest example in systems with homogeneously broadened absorption is the static exchange interaction, which prevents the occurrence of pure free polarization decay and gives rise to an additional interaction induced signal. For inhomogeneous broadening one obtains photon echo-like behaviour. The temporal duration of the signal, however, is not determined by the width of the inhomogeneous broadening, as is predicted by theory if interaction effects are neglected, but is much smaller due to exciton-exciton interaction. Additional to the static interaction effects electron-electron correlations give rise to laser induced renormalization and dephasing processes which depend sensitively on the polarizations of the driving fields. These effects are analyzed on the basis of quantum-kinetic equations, which allow to describe the temporal evolution of the nonlinear polarizations. Numerical results are presented for various excitation conditions and material systems.