Upper polariton branch

In contrast with the region cK > cu, the region cK < a> shows no analogy with the 3D case. Instead of a complete upper polariton branch, a new phenomenon appears, which may be represented, equivalently, either as a radiatively unstable exciton (3.19)—(3.20) or as scattering by the exciton-contaminated continuum states (3.21)—(3.22). 

In this section we examine the solutions of Maxwell s equations for a system with a broad and dispersionless electronic resonance. We show that these conditions result in the appearance of the end-points of the lower and upper polariton branches. These end-points restrict the intervals in which the polariton states have well-defined wavevectors. This consideration is applicable, in particular, to the disordered system of J-aggregates since each J-aggregate chain possesses rather narrow electronic transitions instead of broad dispersion (Fig. 10.3). The disorder present in the system does not influence the following arguments, since for small-cavity photon wavevectors, the system can be treated as effectively homogeneous. 

Just such a situation takes place for microcavity dispersion at the bottom of the lower and upper polariton branches in a microcavity with a = h/2M where M is the effective mass of the cavity polariton. Of course, specific features of the low-energy wavepackets stem from the fact that the polariton dispersion near the... 

Now let us consider the wavevector broadening of the upper polariton states for large q. At large wavevectors the upper polariton dispersion curve tends to that of the cavity photon, and 5q 7o(A2e63/2/cj2h c3) Rabi splitting, for large q the upper cavity polariton branch contains the coherent states only. 

FlG. 10.5. The dispersion curves of the coherent polaritonic states (solid lines) and of uncoupled cavity photons and the molecular excitation (dashed lines). The crosses show the end-points of the part of the spectrum with well-defined wavevector. On the right, the broadened line of the molecular resonance is shown. The inset shows the excitonic weights (10.26) for upper ( cix ) 2) and lower ( cix ) 2) polaritonic branches. Reprinted with permission from Agranovich et al. (15). Copyright 2003, American Physical Society. 

Figure3.43 (a) Schematic representation ofthesefdrffiactionlMO-pump FWM experimental setup, (b) Two-pulse spectrally resolved FWM spectrum from bulk ZnO obtained by using ft polarization at a delay time of 0.01 ps. The dotted lines show the polariton dispersion A denotes the lower A polariton branch and B and C represent the mixed branches due to the upper A/lower B and upper B/lower C polaritons, respectively. (After Ref [211].)...

Figure 1 Phonon-polariton dispersion in LiTa03. The solid lines describe the dispersion of the upper and lower branches of the polariton, the dashed line describes the dispersion of light at frequencies below the phonon resonance, and the dotted line describes the dispersion of light at frequencies above the phonon resonance.

From this macroscopic consideration it is seen that the states for which the wavevector is not a good quantum number do not form in a certain vicinity of q = 0 for both branches, and for q > q lx for the lower branch. In other words, the states with the well-defined wavevector exist in the intermediate region of the wavevectors only q n < q < qitlx for the lower branch, and q > q Pn for the upper branch. However, in contrast to the case of vanishing q, one can say that for q A> 1 the coherent polaritonic states do not form at all. The excited states from this part of the spectrum are not resonant with the cavity photon, and as a result no hybridization happens. Instead, these excited states are similar to the localized excited states in a non-cavity material, i.e. they are to be treated just as incoherent excited states. 

In this section we completely ignored the damping of the molecular and the cavity photon states. In other words, the cavity polariton wavevector was treated as a good quantum number. Therefore, based on the results of the previous Section, we conclude that the relations we have obtained are only applicable for the wavevectors q n < q < qmax for the lower branch, and q > q n for the upper branch. 

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