Light-polarization and intensity dependence of higher-order nonlinearities in excitonic FWM signals

Buck, M.; Wischmeier, L.; Schumacher, Stefan; Czycholl, Gerd; Jahnke, F.; Voss, T.; Rückmann, I.; Gutowski, J.

doi:10.1140/epjb/e2004-00369-4

Cited by 14 publications

(19 citation statements)

References 26 publications

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“…The latter one is essential to reproduce the broad background on the high-energy side of the polariton resonances in the nonlinear transmission spectra. As a minor aspect, the biexciton binding energy is slightly underestimated by the truncation of the exciton basis, similar to the result in [26] for a QW system.…”

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confidence: 74%

“…In the coherent regime, excitonic and biexcitonic nonlinearities up to third order in the optical field can be consistently described in terms of the dynamicscontrolled truncation (DCT) formalism [19,20] which has been successfully applied in the past to QW systems [21,22,23,24,25,26]. We extend this formalism to layers with a finite thickness where the sample boundaries still provide a confinement potential for the electrons and holes.…”

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Coherent propagation of polaritons in semiconductor heterostructures: Nonlinear pulse transmission in theory and experiment

et al. 2005

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The influence of coherent optical nonlinearities on polariton propagation effects is studied within a theory-experiment comparison. A novel approach that combines a microscopic treatment of the boundary problem in a sample of finite thickness with excitonic and biexcitonic nonlinearities is introduced. Light-polarization dependent spectral changes are analyzed for single-pulse transmission and pump-probe excitation. The propagation of light pulses which are coupled to the excitonic resonances is a fundamental problem in semiconductor optics that has been the subject of intense experimental and theoretical research. The observations are dominated by the strong light-matter interaction and its interplay with the inherent many-particle Coulomb interaction of the electronic system. In the linear optical regime, exciton polaritons give rise to effects like polariton beating in the time-resolved pulse transmission [1] or yield strong modifications of excitonic transmission spectra, see e.g. [2,3,4]. In the nonlinear optical regime, incoherent saturation of the polariton resonances in transmission spectra [5,6] and in the amplitude and phase of the time-resolved transmission [7] as well as transmission changes in pump-probe experiments [8] have been studied.The above investigations are focused on samples where the thickness corresponds to a few exciton Bohr radii where polariton effects are most pronounced in the optical spectra. In this case the interplay of the induced excitonic polarization in the medium with the propagating light field is strongly influenced by sample surfaces which considerably complicates the theoretical description. In a frequently used phenomenological approach [9] the coupling of the exciton relative and center-of-mass (COM) motion at the sample boundaries is neglected. Then the exciton COM motion is subject to quantization effects in the confinement geometry while the exciton relative motion is approximated by the result of the infinitely extended medium. As a result of this approach, the solution of the wave equation for the electromagnetic field requires additional boundary conditions (ABCs) [9,10] which are, however, not uniquely defined. Unfortunately, in many situations the choice of ABCs can influence the theoretical predictions [11]. To avoid these ambiguities, the use of microscopic boundary conditions within a non-local semiconductor response has been discussed in Refs. [12,13] and recently applied to the linear optical regime [3,4,14]. The description of optical nonlinearities combined with a microscopic treatment of boundary conditions has been restricted so far to the quantum-well (QW) limit where propagation effects lead to radiative exciton broadening, which can be modified in radiatively coupled QWs. Furthermore, excitonic nonlinearities in QWs have been studied in connection with microcavity polaritons; for a review see [15]. In the opposite limit of the sample thickness approaching the bulk limit nonlinear pulse propagation effects [16,17] have been analyzed successfully with...

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Coherent propagation of polaritons in semiconductor heterostructures: Nonlinear pulse transmission in theory and experiment

et al. 2005

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“…The theory consistently includes all coherent third order (χ (3) ) nonlinearities and the resulting equations of motion are solved in a self-consistent fashion in the optical fields which includes a certain class of higherorder nonlinearities. 30,31,32 Correlations involving more than two excitons and those involving incoherent excitons are neglected. These effects are not expected to qualitatively alter the presented results for the considered coherent exciton densities of ∼ 10 10 cm −2 , especially for excitation well below the exciton resonance.…”

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“…1), we account for the dominant contributions to the QW response by evaluating the optically induced QW polarization in the 1s heavy-hole exciton basis. 29,31,32,34 We start from the coupled equations of motion for the field E k in the cavity modes with in-plane momentum k (treated in quasi-mode approximation 35 ) and the optically induced interband polarization amplitude p k in the embedded QW. We formulate our theory in the TE-TM basis for the optical fields in the cavity, Fig.…”

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Influence of exciton-exciton correlations on the polarization characteristics of polariton amplification in semiconductor microcavities

2007

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Based on a microscopic many-particle theory we investigate the influence of excitonic correlations on the vectorial polarization state characteristics of the parametric amplification of polaritons in semiconductor microcavities. We study a microcavity with perfect in-plane isotropy. A linear stability analysis of the cavity polariton dynamics shows that in the co-linear (TE-TE or TM-TM) pump-probe polarization state configuration, excitonic correlations diminish the parametric scattering process whereas it is enhanced by excitonic correlations in the cross-linear (TE-TM or TM-TE) configuration. Without any free parameters, our microscopic theory gives a quantitative understanding how many-particle effects can lead to a rotation or change of the outgoing (amplified) probe signal's vectorial polarization state relative to the incoming one's.

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“…We start from the nonlinear equation for the optically induced interband polarization p ± (+, − label the circular polarization states) and perform a spatial Fourier decomposition of p ± and the exciting field E ± with respect to the in-plane wave vector k. We label the Fourier components with the subscripts s, f and p for probe (also called signal, with k = k s , assumed to be small but nonzero), background-free FWM (k = −k s ), and pump (k = 0) direction, respectively. The resulting equations are linearized in the weak probe field E ± s but solved self-consistently in the pump field E ± p [31,32]. The equations for p The nonlinear pump equation for p ± p (not shown) involves the same nonlinear processes.…”

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Large optical gain from four-wave mixing instabilities in semiconductor quantum wells

Schumacher¹,

Kwong²,

Binder³

2007

Europhys. Lett.

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PACS 71.35.-y -Excitons and related phenomena PACS 78.47.+p -Time-resolved optical spectroscopies and other ultrafast optical measurements in condensed matter PACS 42.65.Sf -Dynamics of nonlinear optical systems; optical instabilities, optical chaos and complexity, and optical spatio-temporal dynamicsAbstract.-Based on a microscopic many-particle theory, we predict large optical gain in the probe and background-free four-wave mixing directions caused by excitonic instabilities in semiconductor quantum wells. For a single quantum well with radiative-decay limited dephasing in a typical pump-probe setup we discuss the microscopic driving mechanisms and polarization and frequency dependence of these instabilities.In gaseous atomic or molecular systems and simple Kerr media, four-wave mixing (FWM) processes lead, among other things, to transverse optical instabilities (e.g., refs. [1][2][3][4][5]). The interest in these FWM instabilities has recently been renewed by the demonstration of their effectiveness for all-optical switching at very low light intensities [6,7]. In this Letter we argue on the basis of a microscopic many-particle analysis that FWM instabilities can occur via nonlinear excitonic processes in a single semiconductor quantum well (QW). Instead of studying spontaneous off-axis pattern formation induced by these instabilities, we investigate their role in a pumpprobe setup as illustrated in fig. 1. We find that the FWM instabilities can lead to large gain in the probe and (background-free) FWM directions that grows exponentially with the pump pulse duration, limited by the eventual buildup of incoherent exciton/biexciton densities. Our analysis shows that the materials conditions for observing these instability-induced gains, though quite stringent, appear to be obtainable in currently available highquality QW samples.FWM has been widely used in studies of microscopic processes in QWs (e.g.,). An example of FWM driven instabilities in semiconductors is the parametric amplification of exciton polaritons in planar QW microcavities [16][17][18][19][20][21][22][23]. In contrast to the microcavity, we focus on the "simple" system of a single QW. Using a microscopic many-particle theory we give a comprehensive stability analysis of the optical polarization field in- duced by a normally incident pump beam, treating all vectorial polarization state channels. In atomic systems, phase-space filling (PSF) nonlinearities drive the instabilities, and in microcavities it is the interaction between cocircularly (say, ++) polarized polaritons, related to the Hartree-Fock (HF) interaction and two-exciton (++) correlations [21][22][23]. We find that neither PSF nor excitonic interactions in the ++ channel are promising for instabilities in single QWs, mainly because of excessive excitationinduced dephasing (EID). Instead we show that instabilities and large probe gains can be produced in single QWs by virtual biexciton formation, which requires the pump to

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Light-polarization and intensity dependence of higher-order nonlinearities in excitonic FWM signals

Cited by 14 publications

References 26 publications

Coherent propagation of polaritons in semiconductor heterostructures: Nonlinear pulse transmission in theory and experiment

Coherent propagation of polaritons in semiconductor heterostructures: Nonlinear pulse transmission in theory and experiment

Influence of exciton-exciton correlations on the polarization characteristics of polariton amplification in semiconductor microcavities

Large optical gain from four-wave mixing instabilities in semiconductor quantum wells

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