Exciton surface polaritons

Observation of exciton surface polaritons at room temperature... 

A theory of 2D excitons and polaritons is presented for this type of surfaces, with continuity conditions matching 2D states their 3D counterparts in the bulk substrate, investigated in Sections I and II. This leads to a satisfactory description of the excitations (polaritons, excitons, phonons) and their theoretical interactions in a general type of real finite crystals A crystal of layered structure (easy cleavage) with strong dipolar transitions (triplet states do not build up long-lived polaritons). 

To explain the observed width, it is necessary to look for strong surface-to-bulk interactions, i.e. large magnitudes of surface-exciton wave vectors. Such states, in our experimental conditions, may arise from virtual interactions with the surface polariton branch, which contains the whole branch of K vectors. We propose the following indirect mechanism for the surface-to-bulk transfer The surface exciton, K = 0, is scattered, with creation of a virtual surface phonon, to a surface polariton (K / 0). For K 0, the dipole sums for the interaction between surface and bulk layers may be very important (a few hundred reciprocal centimeters). Through this interaction the surface exciton penetrates deeply into the bulk, where the energy relaxes by the creation of bulk phonons. The probability of such a process is determined by the diagram... 

Figure 3.15. Diagram of a nonlocal surface-exciton transfer, corresponding to the optical creation of a surface exciton followed by its relaxation to the bulk. The essential virtual stage is the scattering of a surface phonon (K 0) and the creation of a surface polariton with a large wave vector (K 0), producing large interaction energies with the bulk. 21 Then relaxation in the bulk is ultrafast.

In the experimental study of surface excitons various optical methods have been used successfully, including the methods of linear and nonlinear spectroscopy of surface polaritons. A particularly large body of information has been obtained by the method of attenuated total reflection of light (ATR), introduced by Otto (1 2) (Fig. 12.1) to study surface plasmons in metals. Later the useful modification of ATR method also was introduced by Kretschmann (3) (the so-called Kretschmann configuration, see Fig. 12.2). The different modification of ATR method has opened the way to an important development in the optical studies of surface waves and later was used by numerous authors for investigations of various surface excitations. 

Phenomenological theory of surface Coulomb excitons and polaritons... 

As a matter of fact, as can be seen from eqn (12.17), the limit k —> oo is consistent with the sum t (u>) + e2(w) approaching zero, which in the particular case of the boundary with vacuum (ei = 1, e2 = e) agrees with eqn (12.12). The result of this limiting transition confirms once more the remark made above, viz. that surface polaritons for large values of k transfrom into Coulomb surface excitons. The dispersion law for Coulomb surface excitons at a sharp boundary and without taking spatial dispersion into account has the form... 

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). 

As stressed earlier, the transition from surface polaritons to Coulomb surface excitons corresponds to the limiting transition c —> oo. For p-polarized waves it yields the dispersion relation... 

The macroscopical surface excitons obtained when retardation is taken into account, i.e. surface polaritons, cannot spontaneously transform into bulk emitted photons. Therefore, surface polaritons are sometimes said to have zero radiation width (it goes without saying that a plane boundary without defects it implies). At the same time the Coulomb surface excitons and polaritons in two-dimensional crystals possess, as was shown in Ch. 4, the radiation width T To(A/27ra)2, where A is the radiation wavelength, a is the lattice constant, and To the radiative width in an isolated molecule. For example, for A=500 nm and a = 0.5 nm the factor (A/2-7Ta)2 2x 104, which leads to enormous increase of the radiative width. For dipole allowed transitions To 5x10 " em, so that the value of T 10 cm-1 corresponds to picosecond lifetimes r = 2-kK/T x, 10 12s. 

Macroscopic surface excitons and polaritons in isotopically mixed crystalline solutions... 

Figure 2.19. Profile of isoenergetic surfaces of the polariton states slightly below the bottom of the excitonic band, in the crystal model (2.139) including the modification (2.140).

For a polariton whose photonic component is predominant, at a few thousands reciprocal centimeters below 0, the isoenergetic surfaces are roughly spherical. Then, for E < , they change to ellipsoids compressed along the b axis, the excitonic component of the polariton becoming predominant. Thus, from a fraction of a reciprocal centimeter below E0, the polariton density of states shows a variation as (E — E0) 2 ... 

As illustrated in Fig. 2.8 of Section II, the general reflectivity lineshape shows (1) a sharp rise of the bulk 0-0 reflectivity (Section II.B.C) at E00, corresponding to the b coulombic exciton with a wave vector perpendicular to the (001) face (2) a dip, corresponding to the fission in the surface of a bulk polariton into one 46 -cm 1 phonon and one b exciton at E°° + 46 cm"1 (3) two vibrons E200 and E1 00 immersed in their two-particle-state continua with sharp low-energy thresholds. On this relatively smooth bulk reflectivity lineshape are superimposed sharp and narrow surface 0-0 transition structures whose observation requires the following ... 

The emission of the surface exciton, coupled to the bulk polaritons, may also be calculated using the above scheme, which, here also, coincides exactly with the quantuum-mechanical results. Instead of the lorentzian emission (3.20), we obtain an emission proportional to... 

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