Four-wave Mixing In Semiconductors Research Articles

Strongly nonresonant four-wave mixing in semiconductors

When semiconductors are optically excited above or slightly below the band gap, the linear and nonlinear responses originate predominantly from the interband polarization. Here, we demonstrate that intraband excitations, i.e., rapidly oscillating currents that originate from the electric-field-induced acceleration of electrons and holes, contribute strongly to transient four-wave mixing when it is performed with center frequencies near half the band gap frequency. Within a two-band model we show that the presence of several pathways arising from different combinations of inter- and intraband excitations and their interference give rise to characteristic signatures in time- and spectrally resolved signals. Our approach is based on the semiconductor Bloch equations and includes the dynamics of off-resonant electron-hole excitations on a microscopic level. The predicted significant broadening and structure appearing in the four-wave-mixing spectra are in good qualitative agreement with experimental results.

Generation of Non-Classical Light by Four-Wave Mixing in Semiconductors

We describe experiments to generate non-classical quadrature squeezed states of light by four-wave mixing in semiconductors. Squeezing can be achieved with either the diagonal or off-diagonal components of the third-order nonlinear susceptibility tensor. We have demonstrated squeezing by self-phase modulation in ZnS at 780 nm, and by cross-phase modulation in ZnSe at 960 nm. Possibilities for generating squeezed light in other materials by these techniques are discussed.

Quantum kinetics of femtosecond four-wave mixing in semiconductors

We calculate the transient degenerate four-wave mixing signal with ultrashort laser pulses within the self-consistent formulation of the quantum kinetics of electrons and holes in a semiconductor interacting with longitudinal-optical (LO) phonons. Our numerical calculation shows that the integrated four-wave mixing signal as a function of the delay time shows an effective exponential decay, which, however, is modulated by an oscillation with a characteristic energy given by ωLO[1 + (me/mh)]. This peculiar quantum beat is caused by the interference of the interband polarization components, which are connected through a LO-phonon transition in the conduction band.

Influence of electron–electron scattering on femtosecond four-wave mixing in semiconductors

The influence of electron–electron scattering processes on the time evolution of four-wave mixing signals for ultrashort excitation in the vicinity of the band edge is investigated. The validity of a Markovian approximation is carefully analyzed. The Markovian relaxation of the one-particle distribution is compared with non-Markovian results obtained from the solution of quantum-kinetic equations for two-point functions. In the non-Markovian case relaxation processes are slowed down.

Spectrally resolved four-wave mixing in semiconductors: Influence of inhomogeneous broadening.

Spectrally resolved four-wave mixing in semiconductors: Influence of inhomogeneous broadening.

Nature of nonlinear four-wave-mixing beats in semiconductors.

The nature of the beat modulations observed in nonlinear four-wave mixing in semiconductors is determined by spectral resolution of the time-integrated four-wave-mixing signals. Beats between close-lying bound-exciton resonances in CdSe are found to be described by macroscopic polarization interferences between two noninteracting two-level systems. Beats between heavy-hole excitons and light-hole excitons in GaAs quantum wells, on the other hand, are described by a three-level system, i.e., as a true quantum interference phenomenon.

Theoretical and experimental investigations of time-dependent degenerate four-wave mixing in semiconductors.

A recently developed theoretical approach to degenerate four-wave mixing (DFWM) in the Raman-Nath regime is extended to allow the analysis of pulsed DFWM experiments in laser-excited semiconductors. The full time-dependent carrier-density grating equation is solved numerically to allow the calculation of time-integrated diffraction efficiency spectra. The calculations are compared with the results of pulsed experiments performed on low-temperature CdS for a variety of excitation intensities. Qualitative agreement between experiment and theory is obtained, yielding insights into the dynamics of the nonlinear-optical properties underlying the excitation-dependent behavior of the scattering spectra.

Effects of coherent polarization interactions on time-resolved degenerate four-wave mixing

We report the first observation of coherent polarization interactions in dense media in time-resolved degenerate four-wave mixing in semiconductors. For near-resonant ultrashort-optical-pulse excitation, these interactions lead to a diffracted signal at negative delay times, with a slope half that for positive delay times. At higher intensities, two temporal maxima appear in the diffracted signal, in agreement with many-body theory.

Quantum theory of nondegenerate four-wave mixing in semiconductors.

Many semiconductor materials exhibit large optical nonlinearities in the spectral regime of the fundamental absorption edge.1 Most of these nonlinearities rely on the interactions among the generated electron-hole excitations. Since the carrier-carrier intraband scattering processes establish quasi-thermal equilibrium on a sub-picosecond timescale, most theoretical studies deal only with the incoherent optical properties of semiconductors. However, effects like multi-wave mixing are phase sensitive processes which require a more elaborate treatment of the light-light interaction mediated by the incoherent medium. In this paper we present a theory of multi-wave mixing for a highly excited semiconductor. The theory is based on the fact that pulsation of the total carrier density can induce mixing since the carrier response time is of the order of nanoseconds, even if the intraband carrier-carrier scattering occurs in fractions of a picosecond. In our theory we concentrate on the population pulsations, simplifying or ignoring the many-body Coulomb effects as much as reasonably possible without having a completely unrealistic model.

Raman-Nath theory of degenerate four-wave mixing in semiconductors.

Raman-Nath theory of degenerate four-wave mixing in semiconductors.

Degenerate Four-Wave Mixing In Semiconductors: Application To Phase Conjugation And To Picosecond-Resolved Studies Of Transient Carrier Dynamics

Semiconductors appear to have excellent potential as materials for phase conjugation via degenerate four-wave mixing (DFWM) because of the large variety of nonlinear optical mechanisms that may be invoked in them. When the optical wavelength is near or above the band gap, mobile particles such as free electrons and holes or free excitons may be created; in such cases, DFWM itself provides a powerful contact-free and nondestructive technique for the study of carrier transport and decay parameters, such as ambipolar diffusion coefficients and recombination times. In this article, we briefly review the various nonlinear mechanisms that may be used for DFWM, as well as the various DFWM and related transient grating experiments that have been performed for application to phase conjugation and to carrier dynamics studies.

Degenerate four-wave mixing near the band gap of semiconductors

We present a theoretical calculation and experimental data on the effective third-order susceptibilities χ(3) for degenerate four-wave mixing near the band gap of semiconductors. The closeness of the calculated and experimental values for the effective χ(3) in silicon at 1.06 μm indicates the utility of our simple calculation. The large values of χ(3) indicate the possibility of high-efficiency degenerate four-wave mixing in semiconductors, especially at longer wavelengths.