Polaritons approximations

Then the approximate solutions of (1.33) are generally complex. However, in the case of the polariton, these solutions are still real, owing to the geometry of the system A photon emitted by the infinite 3D lattice is necessarily reabsorbed in other words, the exciton is not coupled to a continuum of photons (in which it is irreversibly diluted), but it is coupled to discrete photons with well-defined wave vectors, with subsequent undamped oscillations, which are the essence of the polariton. The situation is dramatically different when emission occurs in a... 

Figure 4.22. Polariton solutions for a 3D mixed crystal in the mean-polarizability approximation (4.117). In strong local field (A3), one obtains a resonance of the virtual crystal cAwA + cBwB another solution, strongly shifted, exists at low frequencies. On the contrary, in weak local fields (A,), the frequencies of the pure A and B crystals, slightly shifted, are solutions. We note that for cB - 0, one of the solutions tends, for any strength of the local field A, to ojb, which is the frequency of B unshifted by the interaction with the lattice A.

Unlike ISS, the electro-optic effect (or its inverse) can occur only in noncentrosymmetric media and in general does not lead to any real material excitation. However, if there are low-frequency IR-active modes in the crystal, they may be excited impulsively [36, 59]. Such phonons couple strongly to IR radiation to form mixed modes called polaritons. Impulsive stimulated polariton scattering can be described approximately by coupled equations of motion for the polarization contributions P, and due to ionic motions (i.e., phonons) and electronic motions, respectively [9, 60] ... 

G 1, X3 , Yl, ZJ , X3, Y03, Zl and Y P = 1- We here have introduced a normalization denominator although Tr 0M Wo 0 — 1 for all 0. This is because after expressing the 0M s in terms of polariton operators we want to make explicit use of their Bose character, which is valid however only approximately. 

Here rjji = exp(—27T l j/N). Since the f s and tit s obey bosonic commutation relations up to corrections 0(1/N), one sees from (28c) that Z = 0 + 0(1 /N), i.e., within the bosonic quasi-particle approximation, the action of a phase flip Zi cannot be calculated. However one can draw the conclusion that a single-atom phase error only contributes in first order of 1/N. From the other equations one recognizes an important property if we assume that the initial state Wo is an ideal storage state, i. e., without bright polariton excitations, we find that after tracing out the bright polariton states only decoherence contributions of order 0(1/IV) survive, e.g.,... 

Another scheme to calculate and interpret macroscopic nonlinear optical responses was formulated by Mukamel and co-workers [112 114] and incorporated intermolecular interactions as well as correlation between matter and the radiation field in a consistent way by using a multipolar Hamiltonian. Contrary to the local field approximation, the macroscopic susceptibilities cannot be expressed as simple functionals of the single-molecule polarizabilities, but retarded intermolecular interactions (polariton effects) can be included. 

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),... 

In the preceding derivation of the frequencies of surface polaritons and surface excitons the boundary conditions were applied at a sharp boundary without surface currents and charges. In this simplest version of the theory the so-called transition subsurface layer has been ignored however, this layer is always present at the interface between two media, and its dielectric properties differ from the dielectric properties of the bulk. Transition layers may be of various origins, even created artificially, e.g. by means of particular treatment of surfaces or by deposition of thin films of thickness dphenomenological theory it is rather easy to take account of their effects on surface wave spectra in an approximation linear in k (15). 

Harrick [156] and Hansen [99] gained insight into the physics of the ATR spec-tram of a layered stracture and derived formnlas for the penetration depth and the contribntion of the surface layer to the net absorption. Electric field analysis has also been employed to explain the phenomena of SEWs [132, 157, 158] and the excitation of surface polaritons [159, 160], In addition, EEA has been shown to be a basis for an approximate estimation of the molecular orientation (Section 3.11). However, as will be shown below, the MSEEs cannot be used to compare the spectral contrast for the same film in different optical systems. 

In this section, the reader will first be introduced to the general properties of polaritons at the interface of two media and within a layer. Then, following Vinogradov [26] and Ruppin [23], the results of a quasi-static treatment will be discussed to gain insight into the physical nature of the absorption bands observed in the IR spectra of ultrathin films. For further detailed discussion of both the theoretical and experimental aspects of the polariton theory and its approximations, several reviews [12-14] and monographs [15, 16, 24] are recommended. Modifications of polaritons in superlattices are considered in Refs. [27-29]. 

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