Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Multi-Wave Interactions in Semiconductors

Andrew E. Paul

Published Jan 1, 1992• 0 citations
OpenAlex

Abstract

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.

Related papers

Multiwave mixing in semiconductor laser media

Murray Sargent, Fenglei Zhou, S. W. Koch

This paper analyzes the interaction of a strong wave and one or two probe waves with an intrinsic semiconductor medium which is partially inverted by an injection current. The many-body interactions of the electron-hole excitations are described using recently developed generalized Bloch equations for semiconductors. Coupled-mode equations for the different light fields are derived and solved, and predict that the gain and the coupling coefficients experience asymmetric dips. These dips are generated by scattering of the strong field off carrier-density pulsations induced by the pump-probe interference.

Physical Review A•Nov 1, 1988•21 citations

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

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

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.

Quantum Optoelectronics•Jan 1, 1995•0 citations

Many-body effects in low-order optical nonlinearities of semiconductor quantum wells

Ilia Roumiantsev

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.

•Jan 1, 2003•0 citations

Picosecond Dynamics in Optically ExcitedSemiconductors: Exciton Dephasing,Ionization Equilibrium and Pauli Blocking

Rocharj Mondal

Excitons, the bound states of an electron and a hole, in semiconductors are interesting objects and they continue to attract attention of researchers from all over the world. Despite intense research on exciton physics over last three-four decades, many interesting phenomena related to the dynamics and the nonlinear optical properties of excitons in semiconductors and their nanostructures in the coherent and incoherent regimes are still to be explored. This thesis presents our effort to study the nonlinear optical properties as well as the exciton dynamics in coherent and incoherent regime in semiconductor nanostructures including GaAs quantum wells (QWs) and InAs quantum dots (QDs). We have set up several time-resolved and steady-state optical spectroscopic measurement techniques in our laboratory to carry out our study on excitons dynamics in semiconductor QWs and QDs. We work out a clear and detailed theory of the pump-probe signal taking account of all aspect of the measurement, namely, the lock-in detection, spectral selection by the monochromator and time-integration at the slow photodetector. We have used the formalism of optical Bloch equations conventionally used to analyse wave mixing experiments. Our analysis puts the pump-probe technique on the same footing as the wave mixing experiments. We show that pumpprobe experiments can be used to study both coherent and incoherent dynamics. We also present a clear physical picture of the measured signal using the Lorentz harmonic oscillator model. We report the investigation of the coherent exciton dephasing dynamics using pumpprobe reflectivity measurement in GaAs QWs for resonant excitation. Two GaAs/AlGaAs QWs with well thicknesses 8 nm and 17.5 nm are used. We found a strong dependence of the dephasing rate of the excitons with increasing exciton density due to exciton-exciton scattering. We found that the exciton dephasing rate of 8 nm QWs at low excitation density and at low lattice temperature is larger than the corresponding dephasing rate of the 17.5 nm QWs, possibly due to larger effect of inhomogeneous broadening. We also report that the dephasing rates for both QWs are linear with the sample temperature below the 30 K. We report the study of ionization equilibrium between the exciton and the electronhole plasma population in the temperature and pressure (excitation density) phase space. Non-resonant excitation of semiconductor creates a nonequilibrium state of electron-hole plasma. We investigate this ionization equilibrium using steady state photoluminescence and time-resolved excitation correlation PL measurements. We present a clear phase diagram (in temperature and carrier density phase space) of this ionization process.A clear density-dependent increase in the ionization ratio is observed and its connection with the Mott transition is discussed. Semiconductor nanocrystals and QDs are another important area of research, mainly due to their huge potential for device application. We present a simple model which combines carrier loss kinetics, detailed balance principle in thermodynamic equilibrium and Pauli exclusion principle to quantitatively explain the observed behaviour of the experimental data.

•Sep 1, 2015•0 citations

Multiwave mixing in semiconductor media

Murray Sargent, Stephan W. Koch

We consider an intrinsic semiconductor medium subject to an injection current, an arbitrarily intense electromagnetic wave, and one or two non-saturating waves. We assume that the saturating wave intensity is constant throughout the interaction region and ignore transverse variations. We further assume that the carrier–carrier scattering is sufficiently fast that the carriers are described approximately by Fermi-Dirac distributions. We find that the probe-wave propagation is described by Beer’s law or coupled-mode equations. These equations are determined by a Fourier expansion technique highly developed for two-level atoms. The absorption and coupling coefficients experience asymmetric dips generated by pump scattering off carrier-density pulsations induced by the pump–probe interference. These effects are reminiscent of coherent-dip phenomena well-known in two-level systems but differ significantly in form.

Annual Meeting Optical Society of America•Jan 1, 1988•0 citations

Sub-relaxation and sub-dephasing dynamics of light-induced polarization in semiconductors.

B. Fluegel

Using laser pulses of duration comparable to semiconductor relaxation and dephasing times, the coherent phenomena common to two-level systems have been demonstrated in II-VI and III-V semiconductors. These light-matter interactions are characterized by electrons and holes in their initially excited states and/or a macroscopic polarization that persists after the excitation. A nonthermal carrier distribution was observed in bulk CdSe, demonstrating the extremely fast energy relaxation possible when carrier-LO-phonon scattering is included. Quantum-confined CdSe microcrystallites were then employed to limit the available decay avenues. The one and two-pair transitions were characterized, and using spectral hole-burning, energy relaxation was shown to be substantially slower than in bulk. Dipole dephasing remained very rapid. Persistent macroscopic polarization was demonstrated in semiconductors through pump and probe experiments conducted on time scales faster than the inverse linewidth of the exciton. In the first set of experiments, it was found that the exciton optical Stark shift deviates from that predicted by a steady-state theory. The shift is smaller than expected and lasts longer than the pump pulse. Both effects are explained by free evolution of the exciton's polarization. Transient exciton bleaching is observed and shown to be a result of adiabatic following. In a second study of coherent polarization, spectral oscillations at negative delay times were studied. Oscillations were measured in a wide variety of semiconductors, temporally preceding several different pump-probe phenomena. By comparison with a semiclassical theory, it was shown that spectral oscillations in the spectral region of the exciton are evidence of persistent exciton polarization. Oscillations in the band are due to four wave mixing of the pump and probe beams.

•Jan 1, 1992•0 citations
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.
This paper analyzes the interaction of a strong wave and one or two probe waves with an intrinsic semiconductor medium which is partially inverted by an injection current. The many-body interactions of the electron-hole excitations are described using recently developed generalized Bloch equations for semiconductors. Coupled-mode equations for the different light fields are derived and solved, and predict that the gain and the coupling coefficients experience asymmetric dips. These dips are generated by scattering of the strong field off carrier-density pulsations induced by the pump-probe interference.
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.
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.
Excitons, the bound states of an electron and a hole, in semiconductors are interesting objects and they continue to attract attention of researchers from all over the world. Despite intense research on exciton physics over last three-four decades, many interesting phenomena related to the dynamics and the nonlinear optical properties of excitons in semiconductors and their nanostructures in the coherent and incoherent regimes are still to be explored. This thesis presents our effort to study the nonlinear optical properties as well as the exciton dynamics in coherent and incoherent regime in semiconductor nanostructures including GaAs quantum wells (QWs) and InAs quantum dots (QDs). We have set up several time-resolved and steady-state optical spectroscopic measurement techniques in our laboratory to carry out our study on excitons dynamics in semiconductor QWs and QDs. We work out a clear and detailed theory of the pump-probe signal taking account of all aspect of the measurement, namely, the lock-in detection, spectral selection by the monochromator and time-integration at the slow photodetector. We have used the formalism of optical Bloch equations conventionally used to analyse wave mixing experiments. Our analysis puts the pump-probe technique on the same footing as the wave mixing experiments. We show that pumpprobe experiments can be used to study both coherent and incoherent dynamics. We also present a clear physical picture of the measured signal using the Lorentz harmonic oscillator model. We report the investigation of the coherent exciton dephasing dynamics using pumpprobe reflectivity measurement in GaAs QWs for resonant excitation. Two GaAs/AlGaAs QWs with well thicknesses 8 nm and 17.5 nm are used. We found a strong dependence of the dephasing rate of the excitons with increasing exciton density due to exciton-exciton scattering. We found that the exciton dephasing rate of 8 nm QWs at low excitation density and at low lattice temperature is larger than the corresponding dephasing rate of the 17.5 nm QWs, possibly due to larger effect of inhomogeneous broadening. We also report that the dephasing rates for both QWs are linear with the sample temperature below the 30 K. We report the study of ionization equilibrium between the exciton and the electronhole plasma population in the temperature and pressure (excitation density) phase space. Non-resonant excitation of semiconductor creates a nonequilibrium state of electron-hole plasma. We investigate this ionization equilibrium using steady state photoluminescence and time-resolved excitation correlation PL measurements. We present a clear phase diagram (in temperature and carrier density phase space) of this ionization process.A clear density-dependent increase in the ionization ratio is observed and its connection with the Mott transition is discussed. Semiconductor nanocrystals and QDs are another important area of research, mainly due to their huge potential for device application. We present a simple model which combines carrier loss kinetics, detailed balance principle in thermodynamic equilibrium and Pauli exclusion principle to quantitatively explain the observed behaviour of the experimental data.
We consider an intrinsic semiconductor medium subject to an injection current, an arbitrarily intense electromagnetic wave, and one or two non-saturating waves. We assume that the saturating wave intensity is constant throughout the interaction region and ignore transverse variations. We further assume that the carrier–carrier scattering is sufficiently fast that the carriers are described approximately by Fermi-Dirac distributions. We find that the probe-wave propagation is described by Beer’s law or coupled-mode equations. These equations are determined by a Fourier expansion technique highly developed for two-level atoms. The absorption and coupling coefficients experience asymmetric dips generated by pump scattering off carrier-density pulsations induced by the pump–probe interference. These effects are reminiscent of coherent-dip phenomena well-known in two-level systems but differ significantly in form.
Using laser pulses of duration comparable to semiconductor relaxation and dephasing times, the coherent phenomena common to two-level systems have been demonstrated in II-VI and III-V semiconductors. These light-matter interactions are characterized by electrons and holes in their initially excited states and/or a macroscopic polarization that persists after the excitation. A nonthermal carrier distribution was observed in bulk CdSe, demonstrating the extremely fast energy relaxation possible when carrier-LO-phonon scattering is included. Quantum-confined CdSe microcrystallites were then employed to limit the available decay avenues. The one and two-pair transitions were characterized, and using spectral hole-burning, energy relaxation was shown to be substantially slower than in bulk. Dipole dephasing remained very rapid. Persistent macroscopic polarization was demonstrated in semiconductors through pump and probe experiments conducted on time scales faster than the inverse linewidth of the exciton. In the first set of experiments, it was found that the exciton optical Stark shift deviates from that predicted by a steady-state theory. The shift is smaller than expected and lasts longer than the pump pulse. Both effects are explained by free evolution of the exciton's polarization. Transient exciton bleaching is observed and shown to be a result of adiabatic following. In a second study of coherent polarization, spectral oscillations at negative delay times were studied. Oscillations were measured in a wide variety of semiconductors, temporally preceding several different pump-probe phenomena. By comparison with a semiclassical theory, it was shown that spectral oscillations in the spectral region of the exciton are evidence of persistent exciton polarization. Oscillations in the band are due to four wave mixing of the pump and probe beams.