Exciton-photon interaction

In the exciton-photon interaction, the translational molecular motions have negligible effects owing to the small amplitude of the translation compared to the optical wavelength. In contrast, the molecular rotations may cause an important variation of the transition dipole the librations may be strongly coupled to the incident photon via its coupling to the exciton. If DX(R) is the transition dipole of an a molecule in a unit cell, the first-order expansion in the libration coordinate 8 around the u axis will give... 

To the lowest order of exciton-photon interaction, we are looking for the excitonic solutions slightly perturbed by the photon continuum. For this case, we may put z = hu)0 in (1.33), so that for each excitonic wave vector K we obtain an equation providing a complex excitonic energy (h = 1) ... 

For a large value of rK, the golden rule" does not apply a more complete treatment of the exciton-photon interaction has been carried out126 for the wave vectors (c K /co) - 1 < (r0/coo)2/3. 

Several other charge carrier generation mechanisms involve excitons (1) field or thermal ionization of excitons, (2) exciton interaction with trapped carriers, (3) exciton-exciton interaction, and (4) exciton-photon interaction. 

Above we discussed the dispersion rule and radiative width of states in the special case of vectors P(k, p) perpendicular to the crystal plane. Other situations can be treated in the same manner. The dispersion for this case, as compared with those displayed in Fig. 4.5, will change. To calculate the dispersion of a polariton in a wide region of the it is necessary to take into account the terms proportional to A2 in the operator of the exciton-photon interaction. 

The appearance of an enhanced radiative width and renormalization of the exciton dispersion are the main effects arising in one- and two-dimensional structures under the influence of retardation (21). Qualitatively these effects are valid for Frenkel as well as for Wannier-Mott excitons. In contrast to 3D structure where in the exciton-photon interaction all three components of the momentum have to be conserved and as a result a picture with 3D polaritons arises, for structures of lower dimensionality only the in-plane momentum for 2D structures is conserved and only one component for the ID structure. An exciton in both cases is coupled to a continuum of photon states. There is no possibility of reversible strong... 

In (7.58) the exciton-photon interaction as well as scattering by phonons, is taken into account. The expression (7.58) is finite for an arbitrary ui. It corresponds to a result which would be obtained by summation of probabilities of photon absorption in all orders of perturbation theory, formulated with respect to the constant of the exciton-photon interaction. If in (7.58) we let the light velocity go to infinity, and thus if we neglect the retardation, the expression of (7.58) attains the form (7.55). 

Following the usual procedure (see Ch. 4), we write the Hamiltonian of the exciton-photon interaction near the anticrossing region in the form ... 

It consists of a lattice of N molecular sites spaced by distance a and comprises the exciton part (an is the exciton annihilation operator on the site n), photon part (bk is the photon annihilation operator with the wavevector k and a given polarization) as well as the ordinary exciton-photon interaction. The cavity photon energy ek is defined by eqn (10.44), e represents the average exciton energy, while en are the on-site exciton energy fluctuations. 

The exciton-photon interaction is written in such a form that 2y yields the Rabi splitting energy in the perfect system. We chose to use the same number N of photon modes, and the wavevectors k are discrete with 2ir/Na increments. Our approach is to straightforwardly find the normalized polariton eigenstates Tj) (i is the state index) of the Hamiltonian (10.50) and then use them in the site-coordinate representation ... 

So far, we have considered the Bose-Einstein condensation of Coulomb excitons and thus we neglected the influence of the retardation. Such a consideration is correct only for excitons with small (or zero) oscillator strengths. Thus the above-described consideration on the Bose-Einstein condensation can be applied, for example, to the case of triplet excitons, or to singlet excitons for which the exciton-photon interaction energy is smaller than the exciton level width, caused by, for example, scattering by phonons. 

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