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Physical review. B, Condensed matter

Degree and state of polarization of the time-integrated coherent four-wave mixing signal from semiconductor multiple quantum wells

Shekhar Patkar, A. E. Paul, Wei E. I. Sha, Jeremy A. Bolger, Arthur L. Smirl

Published Apr 15, 1995• 23 citations
Publisher

Abstract

All four of the Stokes parameters of the time-integrated degenerate four-wave mixing signal from a GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As multiple quantum well are measured as a function of the relative angle between the linear polarizations of the pump and the probe and of the incident fluence, thus completely characterizing the polarization state of the signal. The degree to which the signal is polarized, the ellipticity, and the orientation of the polarization ellipse are found to be strongly dependent on the orientation of the incident polarizations and on fluence. The principal features can be qualitatively understood in terms of a simple model that includes density-dependent dephasing and local-field corrections.

DOI
10.1103/physrevb.51.10789

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Applied Physics Letters•Jul 10, 1995•5 citations
All four of the Stokes parameters of the time-integrated degenerate four-wave mixing signal from a GaAs/{\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}As multiple quantum well are measured as a function of the relative angle between the linear polarizations of the pump and the probe and of the incident fluence, thus completely characterizing the polarization state of the signal. The degree to which the signal is polarized, the ellipticity, and the orientation of the polarization ellipse are found to be strongly dependent on the orientation of the incident polarizations and on fluence. The principal features can be qualitatively understood in terms of a simple model that includes density-dependent dephasing and local-field corrections.
The complete polarization state of the degenerate four-wave mixing signal from a GaAs/AlxGa1-xAs multiple quantum well is determined by time resolution of all four of its Stokes parameters as a function of the relative angle between the two linear input polarizations. The degree of ellipticity and the orientation of the polarization ellipse are both observed to vary dramatically in time, and the temporal evolution is found to depend strongly on the orientation of the input polarizations. These time-resolved results are shown to be consistent with previous measurements of the time-integrated Stokes parameters and to provide new constraints for physical models. The results are shown to be qualitatively consistent with a phenomenological model requiring the inclusion of both many-body interactions and biexcitonic effects.
In degenerate four-wave-mixing (DFWM) experiments the polarization of the incident laser pulses can have a strong influence on the measured signal. For GaAs quantum wells a number of DFWM experiments were performed by using either parallel or perpendicular polarization of the incident laser pulses. Experimentally, it turned out that some characteristic features of the signal differ appreciably for the two configurations. In particular, different dephasing times, phase shifts of the quantum beats, different time-resolved behavior (echoes versus free-induction decay), and intensity dependence of the measured signal have been reported.1–3
Dual-channel spectral interferometry is used to measure the ellipticity, the orientation of the polarization ellipse, and the sense of rotation of the four-wave-mixing signal from a GaAs-AlGaAs multiple quantum well. Each parameter is observed to oscillate dramatically at the heavy-hole-light-hole quantum beat frequency. During each beat period (in the strong quantum beat regime), the ellipticity oscillates twice between linear and almost-circular polarization, the orientation of the polarization ellipse rotates through a complete 180 degrees , and the sense of rotation changes from left- to right-circular polarization.
A dual-channel version of spectral interferometry is used to completely characterize the extremely weak ultrashort coherent four wave mixing (FWM) emission from multiple quantum wells (MQWs) by time resolving the polarization state, as well as the scalar amplitude and phase. The amplitudes and the phases of the x and y components of the coherent FWM emission are found to exhibit systematic (but distinct) variations with excitation fluence, time delay between the two incident pulses, detuning of the laser wavelength from the heavy hole (hh) exciton, and the orientation of the input polarizations. From these, a self consistent picture of the temporal dynamics of the amplitude, phase and polarization state is obtained that delineates the roles of many body effects, such as local field corrections, excitation-induced dephasing and biexcitons, in determining the excitonic dynamics.
Recent transient four-wave-mixing experiments in the two-pulse photon-echo configuration performed on GaAs quantum wells have yielded the surprising result that in some samples the T2{\mathit{T}}_{2}T2​ time obtained from the polarization decay can be shorter for cross-polarized input fields than for parallel input fields. A concomitant change from photon-echo to free-induction-decay behavior has also been observed. A phenomenological model is presented which explains these observations by means of a disorder-induced coupling of the ${\mathrm{\ensuremath{\sigma}}}^{+}$ and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}$ exciton transitions which is inhomogeneous in coupling strength. Such coupling also leads to a remarkable change in the light-hole--heavy-hole exciton quantum beat phase as a function of pulse delay for a critical relative orientation of the polarization of the incident pulses. Experimental observations of this effect are presented to support the validity of the model.
We report measurements of the polarization and time-averaged intensity of four-wave mixing signals from GaAs quantum wells as functions of the pump beam polarizations, laser photon energy, and optical injection density, the latter covering a range of higher levels than has previously been reported. Excitation of heavy-hole excitons produced a sin2 variation of the signal intensity as the pump beam polarizations changed from parallel to perpendicular, while injection of light-hole excitons led to an approximately cos2 dependence. The tuning dependence of the heavy-hole-exciton signal revealed a low-energy signal which is attributed to biexcitons. The dominance of this signal for perpendicular polarization causes the observed sin2 variation of the heavy-hole-exciton signal.