(c) Dr Paul Kinsler. [Acknowledgements & Feedback]
This work was done within the semiconductor microstructures group at the University of Sheffield, and involved theoretical collaboration with Dr D. Whittaker (now at Toshiba Cambridge), and experimental contact with Dr T.A. Fisher (now at University of Western Australia). This widely respected group, has extensive experimental expertise and strong links to the III-V Central Facility which is based in Electronic and Electrical Engineering at Sheffield.
Some surprising results were obtained from measurements made on semiconductor microcavities at the Department of Physics, University of Sheffield. The high quality microcavities are designed within the group and fabricated at the UK Central Facility for III-V Materials (located within the Department of Electronic and Electrical Engineering). A microcavity is a micron sized optical cavity containing a number of quantum wells. These devices are made entirely from semiconductors, and measurements can be made either optically or electrically. The small size of the optical cavity combined with the two dimensional nature of the electronic states confined in the quantum wells ensure that quantum mechanical effects are very important. Reflectivity measurements of these samples showed unexpectedly narrow spectral lines corresponding to the polariton states inside the microcavity. These polariton quasi-particles are formed from coherent combinations of the photons and excitons in the system, where an exciton is a bound electron--hole pair, so an exciton-polariton is the coherent combination of an exciton trapped in the quantum well in the structure with a photon trapped in the microcavity. Narrow lines would give opportunities for better precision in opto-electronic devices based on these structures, so it was important to discover the reason, so it could be better exploited.
To start with I applied Greens function techniques to work out how to combine the spectral broadening from the exciton with the broadening caused by the cavity. The broadening of the exciton was assumed to be gaussian, in keeping with the nature of the alloy fluctuations causing it; whereas the cavity broadening was due to the finite lifetime of a photon in the optical microcavity, and had a Lorentzian lineshape. However, while this gave some spectral (FWHM) narrowing, due to the differing lineshapes, it was not enough to explain the results.
Next the dispersion of the cavity mode and the exciton needed to be taken into account. The exciton had dispersion because of its finite mass, and the cavity mode had dispersion because the Bragg-reflector mirrors were effectively parallel planes. Using a techinque developed by Halperin, we were able to explain the extra narrowing as a result of the dispersion of the exciton-polaritons, and after performing an error analysis, obtained excellent agreement with the experimental data. However, it was unclear exactly what the physical interpretation of this result was. This took a bit of careful thinking, but the result boils down to this: the dispersion tells you how the energy varies with the wavevector of an object, and in the "effective mass" approximation, you can define a lengthscale over which the objects wavefunction extends. The dispersion of the exciton-polaritons is a mixture of the exciton and photon dispersions, depending on the makeup of the coherent superposition which it is made of. Now think back to that exciton broadening, caused by the alloy fluctuations. These vary randomly in space, and the dispersion tells us the spatial extent of the exciton--polariton. An exciton--polariton, made "larger" by its photonic part, spreads over more alloy fluctuations -- and the more alloy fluctuations it sees, the better it sees the underlying average quantum well potential. This greater averaging leads directly to the better spectral resolution seen in the experiments.
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Date=20000223 19990316 19970511 Author=P.Kinsler