Kz dispersion

The dispersion curve for the k) of Equation (5.22) is more complicated than Figure 5.2, since kx, ky and kz can have different values. The convention is to show the energies at various selected points in the Brillouin zone. These are labeled as T, M, K and X, and are called symmetry points. 

Problems arise to get informations about the diffusion coeffients Ky and Kz. If equation (3.4) is interpreted as Gaussian distribution, a lot of available dispersion data can be taken into consideration because they are expressed in terms of standard deviations of the concentration distribution. Though there is no theoretical justification the Gaussian plume formula is converted to the K-theory expression by the transformation /11/ 

Further tests and previous experiences in other geographic locations confirmed that minimum Kz is a relevant (and often neglected) parameter to model properly the dispersion during weak wind and very stable conditions. Unfortunately no general value for minimum Kz can be defined, while proper values depend on season and local climatology, as well as on numerical diffusion in the advection scheme. 

FIGURE 2. Projection of the deduced Fermi surface of T12201 onto the ab-plane. The magnitude of the c-axis warping has been increased three-fold to emphasise the 8 loci where kz dispersion vanishes. The Brillouin zone has also been simplified as to accommodate the full aZ>-plane projection. 

A planar cavity provides no in-plane confinement (perpendicular to the growth axis) and just as for electronic states in QWs photons have only in-plane dispersion. Photons are quantized along the cavity as the mirrors force the axial wave vector kz in the medium to be 2n/L. Hence the cavity photon energy is approximately 

For simplicity we treat the microcavity with an optically active material as a slab of width Lc bounded by two perfect mirrors. Let the 2-ax is be directed normal to the cavity plane, with z = 0 corresponding to the middle of the microcavity. The eigenmodes of the empty microcavity are characterized by a two-dimensional (in-plane) wavevector q, and the values of the wavevector in the -direction are quantized, with kz = tt/Lc for the lowest energy eigenmode. The mode which we will consider is polarized in the xy plane, and is normal to the photon wavevector q. Its dispersion is given by  

We would like now to focus on initial conditions for the electron ensemble immediately after the optical excitation. The laser pulse may excite electron-hole pairs in the middle of the Wannier-Stark ladder, lower or above which within the miniband picture corresponds to excitation of electrons in the middle, bottom or top of the miniband, correspondingly. We assumed that all electrons were initially distributed in k-space in accordance with the normal distribution /(A J=(l/V2 o-i ) exp(-( -( j)2/2<7t2) where (k is the average k, and [Pg.201]

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