Semiconductor Maxwell-Bloch Equations Research Articles

Nonlinear Polariton Pulse Propagation in Bulk Semiconductors

Nonlinear propagation of optical pulses through an extended bulk semiconductor is investigated using the coupled semiconductor Maxwell-Bloch equations including excitation induced correlations. For short pulse excitation around the exciton resonance, the theory describes the development of polariton beats and their suppression at increasing input pulse intensities due to the coupling of single exciton states to the Coulomb-correlated continuum of two-exciton states. A comparison of the theoretical results with experimental observations for CdSe bulk material is presented.

Direct observation of an ac Stark splitting in semiconductor microcavities excited above the continuum onset

We study the coherent optical response of a very high-finesse microcavity with a single quantum well by means of degenerate subpicosecond pump-probe spectroscopy. The dynamics of the ac Stark effect versus Pump intensity is investigated upon tuning the empty-cavity;mode-below and above the exciton transition energy, at the exciton continuum onset. The evolution from a simple dynamical excitonic shift to a dynamical splitting is clearly observed in both eases. The qualitative, agreement with numerical calculations based on the semiconductor Maxwell-Bloch equations is good.

Transverse mode dynamics of VCSELs through space-time domain simulation

An approximation to the Maxwell-Semiconductor Bloch equations is used to model transverse mode dynamics of vertical-cavity surface-emitting lasers (VCSELs). The time-evolution of the spatial profiles of the laser field and carrier density is solved by a finite-difference algorithm. The algorithm is fairly general; it can handle devices of any shape, which are either gain or index guided or both. Also there is no a priori assumption about the type or number of modes. The physical modeling includes the nonlinear carrier dependence of the optical gain and refractive index and dispersion effects on the gain and the refractive index are also included.

Self-Induced Transmission on a Free Exciton Resonance in a Semiconductor

We observe coherent long-distance propagation of an optical pulse in resonance with the free exciton at high light intensities in an optically thick semiconductor. The experiments show pulse reshaping, pulse breakup, and a high degree of transmission. Microscopic calculations using the semiconductor Maxwell-Bloch equations yield good agreement with the experimental data.

Spatio-spectral dynamics and spontaneous ultrafast optical switching in VCSEL arrays

Microscopic simulations on the basis of semiconductor Maxwell-Bloch equations show that in the short-time spatio-temporal dynamics of large aspect vertical cavity surface emitting lasers (VCSEL) and coupled VCSEL-arrays microscopic and macroscopic effects are intrinsically coupled. The combination of microscopic spatial and spectral dynamics of the carrier distribution functions and the nonlinear polarization of the active semiconductor medium reveal spatio-spectral hole-burning effects as the origin of ultra-fast mode-switching effects. In coupled VCSEL-arrays the simulations predict the emergence of spontaneous ultra-fast spatial switching.

Doppler-Shifted Self-Reflection from a Semiconductor

We report the experimental observation of a self-reflected wave inside a dense saturable absorber. A femtosecond pulse saturates the absorption and causes a density front to penetrate into the semiconductor. The dielectric constant change across the boundary between areas of low and high densities results in internal reflection. Due to the front propagation the self-reflected light is shifted by the Doppler effect. The Doppler shift makes it possible to distinguish between surface reflection and self-reflection and is used to experimentally verify the dynamic nonlinear skin effect. The measurements are in agreement with our theory which is within the framework of the reduced semiconductor Maxwell-Bloch equations.

Quasiadiabatic following of femtosecond optical pulses in a weakly excited semiconductor

Using semiconductor Maxwell-Bloch equations, we analyze the response of an ensemble of $1s$ excitons driven by a femtosecond optical pulse beyond the traditional approach of slowly varying amplitudes and phases. For optical pulses of a given duration, we show that the off-resonance optical field can evolve into a stable soliton. Besides hyperbolic-secant solitons, we find a single soliton with nonzero asymptotics that is stable against low-amplitude perturbations and whose form is not affected by collisions.

Theoretical investigation of the excitonic semiconductor response for varyingmaterial thickness: Transition from quantum well to bulk

For semiconductor slabs with thicknesses varying from the two-dimensional to the three-dimensional limit the linear optical response is calculated numerically by solving the semiconductor Maxwell-Bloch equations. For short-pulse excitation the spatiotemporal dynamics of the electronic mode structure and the development of exciton-free boundary layers are discussed.

Theory of ultrafast spatio-temporal dynamics in semiconductor heterostructures

Non-stationary spatio-temporal effects in semiconductor heterostructures are investigated for optical excitation by solving the coupled Semiconductor Maxwell-Bloch equations where relaxation processes are treated on the level of quantum kinetic equations in the Markovian limit. Light propagation in quantum well waveguide structures and perpendicular to multiple quantum wells is analysed in the case of linear and nonlinear response.

Steady-state propagation of ultrashort optical pulses in semiconductor excitonic medium

The form-invariant coherent pulse propagation in semiconductors excited at the 1s-exciton resonance is studied analytically with the reduced semiconductor Maxwell–Bloch equations. The sech-shaped pulse solution for the electric field is presented. The effects of Coulomb interactions between excitons and spatial dispersion are discussed. Applications to CdS and CdSe crystals are made.

EXCITONIC SELF-INDUCED TRANSPARENCY IN SEMICONDUCTORS

The form invariant coherent pulse propagation in semiconductors excited at 1s-exciton resonance is studied analytically using the reduced semiconductor Maxwell-Bloch equations. The sech-shaped pulse solution for excitonic self-induced transparency (SIT) is presented, showing significant difference in comparison with the well known SIT solution for non-interacting two-level systems. In contrast to 2π pulses in atomic systems, the phenomenon of SIT of interacting excitons in semiconductors occurs for the pulses of area 1.07π. Possible applications of the SIT solitons in semiconductor all-optical switching devices are discussed.

Polariton solitons in semiconductors: Quantitative study

The reduced semiconductor Maxwell-Bloch equations are used to describe analytically dynamics of polariton solitons in semiconductor excitonic medium. Quantitative estimations of the conditions for the polariton soliton formation in CuCl and CdS crystals are performed.

Pulse propagation and many-body effects in semiconductor four-wave mixing

The semiconductor Maxwell-Bloch equations are solved to study the simultaneous influence of pulse propagation effects and Coulomb many-body interaction on the four-wave-mixing signal of semiconductors. Temporal and spatial modulations as well as the decay of time-resolved and time-integrated signals are analyzed for various excitation conditions. It is shown that propagation effects may significantly modify the line shapes depending on sample thickness and excitation conditions. In most cases the signal is more influenced by its own propagation than by the propagation of the input pulses. Exciton-polariton effects are recovered in the low intensity limit. For relatively thin samples an increased temporal decay is observed whereas for thicker samples the propagation effects lead to strong beats in real time. For higher intensities, where an echolike structure is generated, the competition of signal generation by the pump pulses and absorption by the semiconductor determines the output.

Optically induced excitation density flops in semiconductors

AbstractThe optically induced excitation density in a semiconductor multiple quantum well is experimentally observed to go through a maximum at sufficiently high excitation intensity. This is achieved by using the interaction of two copropagating ultrafast optical pulses to extract the temporal dependence of the optically induced polarization, which is proportional to the temporal derivative of the excitation density. Solutions to the Maxwell semiconductor Bloch equations show that the observations are a manifestation of Rabi flopping in semiconductors. The results confirm the presence of many‐body modifications to the Rabi flopping for the excitation conditions used in the experiment.

Theoretical analysis of ultrafast pump-probe experiments in semiconductor amplifiers

Pump-probe experiments in semiconductor amplifiers are analyzed theoretically. On the basis of Maxwell–Semiconductor–Bloch equations it is shown that the probe signal exhibits dominant oscillatory interference-like structures. These structures are superimposed on the pump and probe intensity dependent features. The calculations are qualitatively similar to experimental results.

Theoretical study of resonant ultrashort-pulse propagation in semiconductors.

Femtosecond-pulse propagation in resonantly excited semiconductors is investigated by numerically solving the semiconductor Maxwell-Bloch equations for plane waves. For excitation at the exciton resonance, it is shown that the pulse absorption exhibits a strongly nonlinear dependence on the input pulse area. Very long propagation distances for strong pulses are observed, but even when all dephasing processes have been neglected, no lossless propagation (self-induced transparency) was found. The influence of the electron-hole many-body effects, nonequilibrium carrier relaxation, and optical dephasing on the pulse-propagation dynamics is studied

Coherent Pulse Breakup in Femtosecond Pulse Propagation in Semiconductors

Coherent pulse breakup is observed for below-exciton resonance femtosecond excitation in a room-temperature GaAs/AlGaAs multiple quantum well waveguide using the cross-correlation technique. This pulse breakup is present only for large area pulses with durations less than the dephasing time of the closest exciton. For pulses longer than the exciton dephasing times, but with the same and even larger areas, the pulse breakup is not observed. The breakup is due to neither self-induced transparency nor temperoral soliton. Instead, calculations based on the coupled semiconductor Maxwell-Bloch equations show that coherent self-phase modulation during propragation drives the system out of the initial adiabatic following regime into oscillatory excitation density, and eventually, pulse shape modulations.

Propagation-induced escape from adiabatic following in a semiconductor.

Breakup of a below-resonance femtosecond pulse is observed in a room-temperature GaAs/AlGaAs multiple-quantum-well waveguide using cross-correlation techniques. The breakup is due to neither self-induced transparency nor temporal solitons. Instead, calculations based on the coupled semiconductor Maxwell-Bloch equations show that coherent self-phase-modulation during propagation drives the system out of the initial adiabatic following regime into excitation density oscillations and eventually pulse-shape modulations.