Exciton-polariton

Compared to the dispersion equation c2K2 = ew2, (1.81) introduces the dependence of e(a>) on K This is the spatial dispersion phenomenon studied first by Pekar.34 For molecular crystals spatial dispersion may be ignored, since the slope of the excitonic branch is often negligible near K ai/c. This is not the case for several ionic crystals, for which the spatial dispersion is strong enough for a new wave, corresponding to the excitonic branch, to be excited. New boundary conditions must then be found for the study of the reflectivity of the exciton-polariton system.35... 

The plane waves of a perfect 2D lattice diagonalize the electromagnetic interactions, giving rise to the excitonic dispersion through the Brillouin zone, and to the surface-exciton-polariton phenomenon around the zone center.148,126 The corresponding hamiltonian may be written as... 

FIGURE 6 Evolution of the intensity of the reflectance structures with in-plane orientation of the electric field (a) [10-10] orientation, (b) [-12-10] orientation [8], Note that the increase of Ais is accompanied by a decrease of Bu and makes it easier to detect A2S. Arrows indicate the average positions of transverse excitonic polaritons The eigenenergies, which are different for the two polarisations due to the spin exchange interaction, can be obtained from a lineshape fitting of the reflectivity spectra. 

When obtaining Eq. (357), we let fIt > flt at least by several times. Hence, instead of the exciton-phonon Hamiltonian (341), one can turn to the exciton-polariton Hamiltonian ... 

It was demonstrated above that in low-dimensional structures only exciton-polaritons from states with small wavevectors k < ko can spontaneously undergo radiative decay while conserving energy and momentum. A distribution of exci-tons in the energy band is expected to have a longer effective lifetime since only a small fraction of the occupied states have a radiative width. Studies of such... 

If the thickness of the surface layer in which a surface exciton-polariton is localized considerably exceeds the lattice constant of a crystal, the electric and magnetic field strength vectors, i.e. vectors E and H of a wave with energy hw in both media (in vacuum and in the crystal the crystal is assumed to be nonmagnetic so that the magnetic induction vector B = H), satisfy Maxwell s equations... 

Kinematic interaction of exciton-polaritons in crystalline organic microcavities... 

In this chapter we concentrate on nano-semiconductor systems, where it has become possible during the last 15 years to handle and control single excitons. More specifically we focus on excitons and exciton-polaritons in semiconductor QDs. This chapter presents first a theoretical background of the solid-state theory, the exciton and the coupling between the exdton and the photon (excitonic polariton). Optical properties of exciton polaritons in nanostructures and their photonic engineering are then discussed. 

After reviewing some solid state theory, we are now capable of modeling exdtons and exciton-polaritons in semiconductor nanostructures. We first study and model the exciton in general, then exdtons in QD-based nanostructures, and finally applications of QD excitons and exciton-polaritons. Details of exciton theory can be found in Dimmock (1967) and Fu and Willander (1999). 

By assuming small spatial variation of the excitation field within the QD, an effective permittivity is defined for the QD exciton polariton by writing... 

Andreani, L. C., Gerace, D., Agio, M. (2005). Exciton-polaritons and nanoscale cavities in photonic crystal slabs. Physica Status Solidi (B), 242, 2197-2209. 

Fu, Y., Thyldn, L., Agren, H. (2008). A lossless negative dielectric constant from quantum dot exciton polaritons. Nano Letters, 8,1551-1555. 

Ivchenko, E. L., Fu, Y, Willander, M. (2000). Exciton polaritons in quantum-dot photonic crystals. Physics of the Solid State, 42,1756-1765. 

Kavokin, A. (2007). Exciton-polaritons in microcavities Present and future. Applied Physics A, 9, 241-246. 

Zeng, Y, Chen, X.-S., Lu, W., Fu, Y. (2006b). Exciton polaritons of nano-spherical-particle photonic crystals in compound lattices. The European Physical Journal B, 49, 313-318. 

Depending on the substrate excitations which are coupled with light into the SP mode, one distinguishes surface plasmon polaritons, surface phonon polaritons, surface exciton polaritons, etc. In this section we shall consider surface plasmon polaritons in some detail. This type of electromagnetic wave was first discussed by Sommerfeld in connection with the propagation of radiowaves along the Earth s surface (Sommerfeld 1909). 

Another example is surface exciton polaritons on semiconductor surfaces. 

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