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physica status solidi (a)

Four-Wave-Mixing in Radiatively Coupled Multiple-Quantum-Well Structures: A Model Study

S. Haas, T. Stroucken, A. Knorr, F. Jahnke, S. W. Koch

Published Nov 1, 1997• 2 citations
Publisher

Abstract

The influence of radiative coupling on the four-wave-mixing signals of multiple-quantum-well structures is investigated theoretically for excitation at the excitonic resonance. It is shown that amplitude and shape of the FWM signals depend strongly on the number of quantum wells N in the sample and on the periodicity of the structure. For a fixed delay time τ12, the signal amplitude of a Bragg structure increases quadratically with N due to constructive interference as long as the radiative decay rate Nγrad is small compared to the inverse delay time τ—112. For large N, if the enhanced radiative decay rate exceeds the inverse delay time, superradiant emission leads to a decrease of the observed signals with increasing N. The signals of anti-Bragg structures with an odd number of quantum wells decrease with increasing N due to destructive interference effects whereas anti-Bragg structures with an even number of quantum wells behave similarly to Bragg structures.

DOI
10.1002/1521-396x(199711)164:1<19::aid-pssa19>3.0.co;2-q

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The influence of radiative coupling on the four-wave-mixing signals of multiple-quantum-well structures is investigated theoretically for excitation at the excitonic resonance. It is shown that amplitude and shape of the FWM signals depend strongly on the number of quantum wells N in the sample and on the periodicity of the structure. For a fixed delay time τ12, the signal amplitude of a Bragg structure increases quadratically with N due to constructive interference as long as the radiative decay rate Nγrad is small compared to the inverse delay time τ—112. For large N, if the enhanced radiative decay rate exceeds the inverse delay time, superradiant emission leads to a decrease of the observed signals with increasing N. The signals of anti-Bragg structures with an odd number of quantum wells decrease with increasing N due to destructive interference effects whereas anti-Bragg structures with an even number of quantum wells behave similarly to Bragg structures.
A theoretical investigation of the effects of static disorder on the linear optical response and the degenerate four-wave-mixing signals of multiple quantum well Bragg structures is presented. It is shown that disorder leads to a finite radiative coupling strength of subradiant modes that are optically forbidden in the ideal structure. In the absorption spectrum, the subradiant modes appear as sharp resonances in the presence of barrier thickness fluctuations, whereas the disorder induced subradiant modes are inhomogeneously broadened in the presence of interface roughness. The decay of the time integrated four-wave-mixing signal at large delays is determined by the dephasing time of subradiant modes, whereas the initial fast decay is dominated by the superradiant mode. A free induction decay is observed in the presence of barrier thickness fluctuations. In contrast, even a small inhomogeneous broadening induces a photon-echo-like behavior for the subradiant modes, while the superradiant mode still exhibits a free induction decay.
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A theoretical investigation of the effects of static disorder on the linear optical response and the degenerate four-wave-mixing signals of multiple quantum well Bragg structures is presented. It is shown that disorder leads to a finite radiative coupling strength of subradiant modes that are optically forbidden in the ideal structure. In the absorption spectrum, the subradiant modes appear as sharp resonances in the presence of barrier thickness fluctuations, whereas the disorder induced subradiant modes are inhomogeneously broadened in the presence of interface roughness. The decay of the time integrated four-wave-mixing signal at large delays is determined by the dephasing time of subradiant modes, whereas the initial fast decay is dominated by the superradiant mode. A free induction decay is observed in the presence of barrier thickness fluctuations. In contrast, even a small inhomogeneous broadening induces a photon-echo-like behavior for the subradiant modes, while the superradiant mode still exhibits a free induction decay.
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Rapid superradiant decay of coherently excited excitons in thin quantum wells (QWs) on a time scale of approximately 10 ps has been theoretically predicted by several groups [1], however, the experimental observation of this ultrafast radiative recombination is still the subject of controversial discussions. A recent theoretical paper [2] concludes, that this radiative decay rate should be strongly enhanced in multiple QW (MQW) Bragg structures due to radiative coupling of excitons excited in different wells via the exchange of transverse photons.