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Journal of the Optical Society of America B

Material and light-pulse parameter dependence of the nonlinear optical susceptibilities in the coherent χ^(3) regime in semiconductor quantum wells

Ryu Takayama, N. H. Kwong, I. Rumyantsev, Makoto Kuwata‐Gonokami, Rolf H. Binder

Published Dec 1, 2004• 6 citations
Publisher

Abstract

A detailed numerical study of the third-order nonlinear optical susceptibilities (χ(3)) of semiconductor quantum wells is presented. The dependence of χ(3) on material parameters (electron-hole mass ratio and exciton linewidths), on the light polarization configuration (co- and countercircularly polarized) and on the spectral configuration is discussed. The goal of this study is to map out the nonlinear phase shift per quantum well and a related figure of merit caused by quasi-resonant excitonic and biexcitonic nonlinearities induced by picosecond light pulses. The study is based on the dynamics-controlled truncation formalism and evaluated under the assumption that only 1s-heavy-hole excitons contribute to the nonlinearities. It includes all correlation effects (exciton–exciton scattering in the singlet and triplet channels and coherent biexciton formation in the singlet channel) that contribute within the coherent excitonic χ(3) regime.

DOI
10.1364/josab.21.002164

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A detailed numerical study of the third-order nonlinear optical susceptibilities (χ(3)) of semiconductor quantum wells is presented. The dependence of χ(3) on material parameters (electron-hole mass ratio and exciton linewidths), on the light polarization configuration (co- and countercircularly polarized) and on the spectral configuration is discussed. The goal of this study is to map out the nonlinear phase shift per quantum well and a related figure of merit caused by quasi-resonant excitonic and biexcitonic nonlinearities induced by picosecond light pulses. The study is based on the dynamics-controlled truncation formalism and evaluated under the assumption that only 1s-heavy-hole excitons contribute to the nonlinearities. It includes all correlation effects (exciton–exciton scattering in the singlet and triplet channels and coherent biexciton formation in the singlet channel) that contribute within the coherent excitonic χ(3) regime.
Summary form only given. The nonlinear optics near the fundamental absorption edge is commonly formulated in terms of a limited number of material parameters characterizing the strength of specific nonlinear processes. Once the nonlinear response function underlying these material parameters is known, one can optimize the relevant nonlinear optical effect for specific device applications. This study is focused on optical nonlinearities at quasi-resonant conditions in the picosecond-pulse regime, where excitonic correlations, such as biexcitonic resonances, contribute prominently to the physical processes. Using a microscopic theory, we have calculated systematically the parameter dependencies of some representative figures of merit, nonlinear phase shift /spl Delta//spl phi/ and differential transmissivity AT, which provide complementary information on the nonlinear susceptibility-/spl chi//sup (3)/:/spl Delta//spl phi//spl sim/Re/spl chi//sup (3)/, /spl Delta/T/spl sim/Im/spl chi//sup (3)/, approximately. We will show in detail how the various aspects of excitonic dynamics affect these quantities around the exciton resonance.
A theoretical study of the coherently coupled heavy-hole--light-hole optical Stark effect in semiconductor quantum wells is presented. Based on a detailed investigation of the various many-body contributions to the Stark shifts, we identify a parameter regime in which the existence of intervalence band coherences (analogous to the nonradiative Raman coherence in three-level atoms) can be inferred from the coherently coupled heavy-hole--light-hole excitonic optical Stark shift. The analysis is performed for the third-order nonlinear optical regime $({\ensuremath{\chi}}^{3}$ regime), and is based on the dynamics-controlled truncation (DCT) formalism. It includes the relevant optical selection rules, excitonic and two-exciton-correlation (e.g., biexcitonic) effects.
This dissertation addresses both fundamental aspects of Coulomb correlations in semiconductor quantum wells and more practical aspects of theoretical analysis of semiconductor optoelectronic devices. After introducing the subject, we present and evaluate a state-of-the-art theory of the third order coherent optical response of a semiconductor quantum well based on the Dynamics Controlled Truncation (DCT) scheme. Already in the third order (the so-called chi (3)) regime, semiconductors exhibit a number of many-body Coulomb correlation effects. Their manifestation in various multi-pulse experimental configurations, customarily used in ultrafast semiconductor spectroscopy, has been an important component of this thesis. Coherent optical effects in a semiconductor 3-band system based on the heavy-hole, light-hole and conduction bands were investigated. The quantum beats in the time-integrated differential transmission signal were analyzed and compared with experimental data obtained at the University of Iowa. Fundamental differences from corresponding quantum beats in atomic 3-level systems were found. Also, the analysis of experimental data (obtained at the University of Arizona) of the coupled heavy-hole-light-hole optical Stark shift revealed evidence of intervalence band coherences, an analog of Raman coherences in atomic 3-levels systems. A scheme for realization of electromagnetically-induced transparency (EIT) based on the interference of excitonic and biexcitonic coherences was proposed. Corresponding experiments performed at the University of Oregon showed indeed a considerable coherent reduction of excitonic absorption. Furthermore, an extension of the chi(3) analysis revealed an energy renormalization of the biexciton, in good agreement with the corresponding experiment. A microscopic analysis of polarization dynamics in time-resolved four-wave mixing signals was performed, revealing interesting implications for the biexciton dephasing in addition to the significance of many-body correlations. In the case of four-wave mixing in semiconductor microcavities, our theoretical analysis in conjunction with experimental data obtained at the University of Tokyo gave us indications for a significant shortcoming of the second Born approximation (2nd BA) applied to two-exciton Coulomb correlations in a thin semiconductor quantum well, in agreement with the general knowledge of the qualitative failure of the 2nd BA in systems with short-range interaction in two dimensions. We also analyzed a novel all-optical switching technique based on the nonlinear polarization rotation. Apart from identifying the many-particle processes relevant for the switch operation in the chi(3) regime, we proposed ways to further optimize the switch.
In order to optimize opto-electronic applications of semiconductor nanostructures, a deep understanding of optical nonlinearities is essential.One fundamental method currently used within this field of research is ultrafast optical spectroscopy.This work presents a theoretical study of optical nonlinearities in semiconductor quantum wells in the coherent time regime.The theory is based on the equations of motion for the coherent exciton and biexciton transition amplitudes.These equations are derived using two different ways: Heisenberg equations of motion in combination with the dynamics-controlled truncation theory and alternatively the non-equilibrium Green´s function technique. For the coherent regime both approaches are equivalent and can be used to formulate a coupled set of equations for the coherent excitation dynamics that is correct up to the third order in the optical field.In contrast to the dynamics-controlled truncation theory the non-equilibrium Green´s function technique allows the inclusion of incoherent scattering processes into the description.The theory is evaluated to describe pump and probe as well as four-wave-mixing experiments with ZnSe quantum wells.Numerical calculations for the coherent control of the macroscopic polarization andthe dependence of transient four-wave-mixing on the light-polarization and intensity are both in good agreement with experiments.In order to correctly describe elevated excitation conditions for the latter investigation, the theory is self-consistently extended such that the included excitonic and biexcitonic nonlinearities contribute up to arbitrary order in the optical field.
The paper presents a description of two-pair correlations in an electron-hole system in laser-excited direct-gap semiconductors in terms of the exciton-boson formalism. The dependence of the states of quasi-particles on their angular momentum orientation is properly taken into account following group theory rules. It is shown for the example of heavy hole excitons in GaAs quantum wells that Coulomb two-exciton correlations include effective repulsion between excitons with nonzero total momenta and effective attraction between excitons with zero total momenta. They generate exciton and biexciton nonlinearities, respectively, in the exciton-biexciton system. The Heisenberg equations of motion derived are applied to four-wave mixing in the coherent mode. Two components of Coulomb two-exciton correlations were found to generate coherent four-wave mixing either separately, one at the cocircular and the other at the perpendicular-linear polarization of applied pulses, or jointly at parallel-linear polarization. General equations are obtained for the amplitude of four-wave mixing signals with time resolution in these polarization configurations, which, in the limit of ultranarrow pulses, reduce to analytic functions of time and excitation and sample parameters. These equations are used to analyze signal characteristics in every polarization configuration. The results give a correct picture of biexciton effects and the polarization dependence of coherent four-wave mixing in GaAs quantum wells.
Summary form only given. While the conceptual realization of "3-level effects" in semiconductors is usually based on one-particle states given by the band structure of the system, we propose the realization of "3-level effects" in semiconductors based on many-particle states. Specifically, we study the quantum coherences related to excitons and biexcitons. Our analysis is based on the dynamics-controlled trunction (DCT) formalism and includes quantum correlations and quantum coherences within the 3rd-order nonlinear optical response. Within the /spl chi//sup (3)/ regime, only one-pair (excitonic) and two-pair (two-exciton) quantum coherences occur. We restrict the analysis to 1s-hh and 1s-lh excitons which dominate the nonlinear response. Results are shown for ZnSe quantum wells.