Surface polariton

T. Tamir, J. J. Burke, and G. I. Stegeman, Surface polariton-like waves guided in thin, lossy metal films, Phys. Rev. B 33, 5186-5201 (1986). 

Surface electromagnetic waves or surface polaritons have recently received considerable attention. One of the results has been a number of review articles1, and thus no attempt is made here to present a comprehensive review. These review articles have been concerned with the surface waves, per se, and our interest is in the use of surface electromagnetic waves to determine the vibrational or electronic spectrum of molecules at a surface or interface. Only methods using optical excitation of surface electromagnetic waves will be considered. Such methods have been the only ones used for the studies of interest here. 

We note that ionic crystals may have dielectric functions satisfying Eq. (4) for frequencies between their transverse and longitudinal optic phonon frequencies. SEW on such crystals are often called surface phonons or surface polaritons and the frequency range is the far IR. 

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.

We are very much indebted to Professor J. M. Turlet and Dr. J. Bernard for helpful discussions and for providing us with material included in this work. Many stimulating private communications with Dr. M. R. Philpott are acknowledged. Dr. R. Brown has performed very extensive numerical simulations to help explore various extensions of the mean-field theory. One of us (Ph. K.) acknowledges stimulating discussion and correspondence with Professors S. A. Rice and V. M. Agranovitch on the distinction between our monolayer elementary excitations and the usual surface polariton modes investigated by those authors. 

Khosravi H, Tilley DR, Loudon R (1991) Surface polariton in cylindrical optical fiber. J Opt Soc Am A 8 112-122... 

Knobloch, H., Brunner, H., Leitner, A., Aussenegg, F., and Knoll, W. (1993). Probing the Evanescent Field of Propagating Plasmon Surface-Polaritons by Fluorescence and Raman Spectroscopies Journal (rf Chemical Physics 98 10093-10095. 

Girlando A, Philpott MR, Heitmann D, Swalen JD, Santo R (1980) Raman spectra of thin organic Aims enhanced by plasmon surface polaritons on holographic metal gratings. J Chem... 

Bozhevolnyi SI, Vohnsen B, Smolyaninov II, Zayats AV (1995) Direct observation of surface polariton localization caused by surface-roughness. Opt Commun 117(5-6) 417 23... 

J. E. Sipe and G. I. Stegeman, Nonlinear Optical Response of Metal Surfaces. In Surface Polaritons Electromagnetic Waves at Surfaces and Interfaces, M. Agranovich and L. Mills, Eds., Elsevier, Amsterdam, 1982. 

Agranovich VM, Mills DL (1982) Surface polaritons - electromagnetic waves at surfaces and... 

A new imaging technique, surface-plasmon microscopy, has been developed by Rothenhausler and Knoll and applied to Langmuir-Blodgett films. Plasmon surface polaritons ( surface plasmons, or PSPs) are surface... 

When the frequency of the surface biphonon lies within the band of the surface polariton, Fermi resonance occurs and the dispersion curve of the po-lariton is subject to a number of essential changes (gaps appear, etc. (86)). Consequently, experimental research of surface polariton dispersion under these conditions could yield, like similar investigations of bulk polaritons, a great deal of interesting information, not only about the surface biphonons themselves, but about the density of states of surface phonons and the magnitude of their anharmonicity constants as well. 

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. 

Surface polaritons at the sharp interface between media... 

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... 

Observation of exciton surface polaritons at room temperature... 

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). 

During 1980-1981 the possibility of the existence of nonlinear surface polaritons of various types was predicted in the literature (18), (19)-(20). In particular, Tomlinson (19) and Maradudin (21) derived s-polarized surface polaritons at a plane interface between two dielectrics, one of which has an isotropic and linear (e1) dielectric constant whereas the dielectric constant of the other is that of a nonlinear uniaxial medium... 

Nonlinear p-polarized polaritons for b = 0 were considered under the same conditions (20). The papers cited revealed the dispersion laws of nonlinear waves of s and p types. Their most significant features are the non-monotonic dependence of the field amplitudes on z and the dependence of the frequencies of these waves on the field amplitude at the boundary (i.e. at z = 0). We do not go into details of the calculations here. We emphasize only that the transition layer, which can also be optically nonlinear, was ignored in these papers. Taking into account the nonlinearity in the transition layer results in the dependence of surface wave characteristics on the field at the interface, and this special case has been dealt with (22), (23) in connection with the problem of self-focusing of surface polaritons. 

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. 

Using this relation and also eqn (12.17) and assuming a boundary with vacuum, we obtain the dispersion relation for surface polaritons ... 

If the polarizabilities a are known, eqn (12.78) determines the surface polariton dispersion as a function of the isotopic composition of the mixture. 

Otto, A. (1975). Spectroscopy of Surface Polaritons by Attenuated Total Reflection. In Seraphin, B. O (Ed.), Optical Properties of Solids, New Developments. North-Holland, Amsterdam, p. 677. 

Agranovich, V. M. and Mills, D. L. (Eds.) (1982). Surface Polaritons - Electromagnetic Waves at Surfaces and Interfaces. North-Holland, Amsterdam. 

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