Lower polariton branch

Stimulated Raman scattering at the lower extraordinary polariton branch was detected for scattering angles of 3.5° and 5° by Gelbwachs etal. 80> in an... 

This split-off discrete state rejoins, for cK co0, the exciton energy ha>0 it behaves qualitatively in the same way as the lower branch of the 3D polariton.33 35 For this reason we call it the 2D polariton. It is the projection of the exciton K> on this 2D polariton (radiatively stable) that constitutes (1) the finite limit value of the curves AK t) for t- oo (Fig. 3.8), and (2) the weight of the discrete peak in the spectrum PK((o) (Fig. 3.9). The transition, in the 2D polariton branch, between the photon and the pure exciton characters occurs around the value K0 = co0/c in an area of width AK = r0/c (with ro = 15cm 1). Thus, the 2D polariton may be considered as a photon mode trapped in the 2D lattice, where it acquires its own dispersion.115,116,126 Therefore, the 2D polaritons cannot be excited by free photons, but they may be coupled to evanescent waves, by ATR for example.115,116... 

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. 

The polaritonic state has a well-defined wavevector as long as Sq C q. However, Sq diverges (i) for q —> 0 for both branches, and (ii) for large q for lower polariton, since in both these cases vg — 0. Below we consider both these cases in detail. 

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. 

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... 

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.

Fig. 4.3. The dispersion of polariton in cubic crystals. Nongyrotropic crystals (a) The dependences of exciton and photon energy on wavevector, the retardation neglected (b) the same but with retardation taken into account. The symbols and L indicate longitudinal and transverse polarization of excitons (c) retardation neglected but dependence of the exciton energy on the wavevector taken into account here and in (d), (e), and (f) only the lower branch of the polaritons shown (d) the retardation and dependence of exciton energy on wavevector are taken into account. Gyrotropic crystals (e) Dispersion of excitons in the cubic gyrotropic crystals if retardation is neglected (f) the same when retardation is also taken into account Aq denotes the position of the bottom of the polariton energy.

The structure of the lowest energy polaritonic state in the presence of dissipation can be examined directly from the dispersion relation (10.22). In the absence of dissipation, for the lower branch this state is characterized by the energy E = E 0) and q - 0. In this approximation the photoluminescence from this state is directed strictly normal to the microcavity surface. If the dissipation is taken into account, for the same value of energy E = E 0) the wavevector becomes complex, q = q j- q". For small wavevectors, Ecav(q) = If, I (h q2/2fi),... 

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. 

The lower-energy part of the LP branch, however, corresponds to the polariton states T (10.52) in which the exciton and photon are strongly coupled (7 = 0.15 > A — e = 0.1 eV) with comparable weight contributions in Tp and Hie. A dramatic effect of the disorder is in the strongly localized character of the polaritonic eigenstates near the bottom of the LP branch, as illustrated in Fig. 10.7(a) (needless to say the same behavior is observed for the states near... 

FlG. 13.15. (a) Dispersion curve for cavity polariton and energy relaxation of Wan-nier-Mott excitons (b) coupling coefficient of the lower branch to cavity photon and to exciton. 

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