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

IEEE Journal of Quantum Electronics

Spectral hole burning and carrier-heating effect on the transient optical nonlinearity of highly carrier-injected semiconductors

Y. Nambu, Akihisa Tomita

Published Jan 1, 1994• 10 citations
Publisher

Abstract

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.>

DOI
10.1109/3.309856

Related papers

Observation of highly nondegenerate four-wave mixing in 1.5 mu m traveling-wave semiconductor optical amplifiers and estimation of nonlinear gain coefficient

Kazuro Kikuchi, Motoki KAKUI, Chung-En Zah +1 more

Nondegenerate four-wave mixing is measured in the 1.5 mu m traveling-wave semiconductor optical amplifier medium as a function of the pump-probe detuning frequency ranging from a few GHz to 400 GHz. It is found that two different sources are responsible for the four-wave mixing: the carrier density modulation and the nonlinear gain effect. The latter is clearly observed when the detuning frequency increases above 100 GHz. The nonlinear gain coefficient epsilon , which induces a gain grating through the pump-probe beating, is estimated to be 1.75*10/sup -23/ m/sup 3/. The change in the real refractive index associated with the nonlinear gain effect, which generates an index grating, is negligibly small. The relaxation time involved in the nonlinear gain effect is found to be less than 0.3 ps. These results support the role of the spectral hole burning rather than the carrier heating in the nonlinear gain effect.>

IEEE Journal of Quantum Electronics•Jan 1, 1992•132 citations

Four-wave mixing in quantum dot semiconductor optical amplifiers

Ahmed H. Flayyih, Amin Habbeb AL-Khursan

The theory of four-wave mixing (FWM) in the quantum dot (QD) semiconductor optical amplifiers (SOAs) is discussed by combining the QD rate equations system, the quantum-mechanical density-matrix theory, and the pulse propagation in QD SOAs including the three region of QD structure ground state (GS), excited state (ES), and wetting layer. Also, relations for differential gain, gain integral, and nonlinear susceptibility of both pump, probe, and signal pulses were discussed. Gain and differential gain have been calculated for QD structure. FWM efficiency and its components [spectral hole burning (SHB), carrier heating, and carrier density pulsation] are calculated. It is found that inclusion of ES in the formulas and in the calculations is essential since it works as a carrier reservoir for GS. It is found that QD SOA with enough capture time from ES to GS will reduce the SHB component, and so it is suitable for telecommunication applications that require symmetric conversion and independent detuning.

Applied Optics•May 6, 2013•14 citations

Spectral hole burning and light-induced band splitting in the gain region of highly excited semiconductors

A. E. Paul, Rolf H. Binder, S. W. Koch

A many-body analysis of spectral hole burning and light-induced band renormalization in the gain region of an initially inverted semiconductor is presented. The results are based on the numerical solution of the semiconductor Bloch equations, specialized to the case of noncopropagating pump-and-probe light fields. These equations account for coherent pump-probe scattering and include the Coulomb correlation between charge carriers. They also contain optical dephasing and carrier-carrier scattering rates that are computed within the random-phase approximation.

Physical review. B, Condensed matter•Mar 15, 1992•5 citations

Four-wave mixing and rabi oscillations in quantum-dot semiconductor optical amplifiers

Benjamin Lingnau, Marina Zajnulina, Kathy Lüdge

Using a self-consistent delay-differential-equation model for the description of the nonlinear light propagation in InAs/InGaAs quantum-dot-in-a-well semiconductor optical amplifiers, we analyze the amplifier in a four-wave-mixing setup in terms of the conversion efficiency. Our model allows us to extract the hierarchy of nonlinear effects that constitute the four-wave-mixing process. We show that spectral hole burning in the quantum-dot medium facilitates wavelength conversion over a spectral detuning of several THz, whereas the effect of carrier heating and global carrier-density pulsations is found to be negligible. Furthermore we show that for high optical field amplitudes the emergence of Rabi oscillations leads to a flattening of the conversion efficiency, potentially allowing for ultra-broadband wavelength conversion and frequency comb generation.

International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD)•Jul 1, 2017•1 citation

Two-level description of gain and mixing susceptibilities in amplifying semiconductor materials

Bruno J. Thedrez, A. Jones, Robert Frey

Optical-intensity-dependent gain and mixing susceptibilities of amplifying semiconductor materials have been calculated using the density-matrix approach. The model, which takes intraband relaxation and carrier-injection rate into account, allows for numerical computation of these susceptibilities, whatever the medium saturation is. As a simplification, an equivalent two-level system is derived which represents the gain and nearly degenerate four-wave mixing susceptibilities. Such an equivalence, which leads to the same field-induced polarization as the conventional rate equation model, also connects the two-level (or rate equation) parameters to the real characteristics of the semiconductor material.>

IEEE Journal of Quantum Electronics•Aug 1, 1988•18 citations

Saturation of interband absorption in semiconductors

A. O. Melikyan, G. R. Minasyan

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.

Semiconductors•Apr 1, 2000•9 citations
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.>
Nondegenerate four-wave mixing is measured in the 1.5 mu m traveling-wave semiconductor optical amplifier medium as a function of the pump-probe detuning frequency ranging from a few GHz to 400 GHz. It is found that two different sources are responsible for the four-wave mixing: the carrier density modulation and the nonlinear gain effect. The latter is clearly observed when the detuning frequency increases above 100 GHz. The nonlinear gain coefficient epsilon , which induces a gain grating through the pump-probe beating, is estimated to be 1.75*10/sup -23/ m/sup 3/. The change in the real refractive index associated with the nonlinear gain effect, which generates an index grating, is negligibly small. The relaxation time involved in the nonlinear gain effect is found to be less than 0.3 ps. These results support the role of the spectral hole burning rather than the carrier heating in the nonlinear gain effect.>
The theory of four-wave mixing (FWM) in the quantum dot (QD) semiconductor optical amplifiers (SOAs) is discussed by combining the QD rate equations system, the quantum-mechanical density-matrix theory, and the pulse propagation in QD SOAs including the three region of QD structure ground state (GS), excited state (ES), and wetting layer. Also, relations for differential gain, gain integral, and nonlinear susceptibility of both pump, probe, and signal pulses were discussed. Gain and differential gain have been calculated for QD structure. FWM efficiency and its components [spectral hole burning (SHB), carrier heating, and carrier density pulsation] are calculated. It is found that inclusion of ES in the formulas and in the calculations is essential since it works as a carrier reservoir for GS. It is found that QD SOA with enough capture time from ES to GS will reduce the SHB component, and so it is suitable for telecommunication applications that require symmetric conversion and independent detuning.
A many-body analysis of spectral hole burning and light-induced band renormalization in the gain region of an initially inverted semiconductor is presented. The results are based on the numerical solution of the semiconductor Bloch equations, specialized to the case of noncopropagating pump-and-probe light fields. These equations account for coherent pump-probe scattering and include the Coulomb correlation between charge carriers. They also contain optical dephasing and carrier-carrier scattering rates that are computed within the random-phase approximation.
Using a self-consistent delay-differential-equation model for the description of the nonlinear light propagation in InAs/InGaAs quantum-dot-in-a-well semiconductor optical amplifiers, we analyze the amplifier in a four-wave-mixing setup in terms of the conversion efficiency. Our model allows us to extract the hierarchy of nonlinear effects that constitute the four-wave-mixing process. We show that spectral hole burning in the quantum-dot medium facilitates wavelength conversion over a spectral detuning of several THz, whereas the effect of carrier heating and global carrier-density pulsations is found to be negligible. Furthermore we show that for high optical field amplitudes the emergence of Rabi oscillations leads to a flattening of the conversion efficiency, potentially allowing for ultra-broadband wavelength conversion and frequency comb generation.
Optical-intensity-dependent gain and mixing susceptibilities of amplifying semiconductor materials have been calculated using the density-matrix approach. The model, which takes intraband relaxation and carrier-injection rate into account, allows for numerical computation of these susceptibilities, whatever the medium saturation is. As a simplification, an equivalent two-level system is derived which represents the gain and nearly degenerate four-wave mixing susceptibilities. Such an equivalence, which leads to the same field-induced polarization as the conventional rate equation model, also connects the two-level (or rate equation) parameters to the real characteristics of the semiconductor material.>
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.