| Summary: | <p>A detailed theoritical discussion based on an effective medium theory<br />
approach is presented for the surface phonon-polaritons and the corresponding<br />
attenuated total reflection (ATR) spectra of dielectric composites. Both ATR and<br />
the propagation of the surface polariton (SP) modes are govemed by the<br />
frequency-dependent effective permittivity which can be modeled and derived in<br />
accordance with the effective medium theory. In this work, four models (Maxwell-<br />
Garnett, Birchak, Polder van Santen and wagner models)for effective permittivity<br />
are considered to presenting the theoritical results with and without the<br />
implementation of the Wiener inequality imposed on effective permittivity.<br />
Generally, the effective permittivity for all models depends on the composite filling<br />
factor f. Derivation of the SP dispersion curves means first finding solutions of<br />
Maxwell's equations that decay away from the interface between air and the<br />
sample and second applying the usual electromagnetic boundary conditions to<br />
find the dispersion relation between the frequency and the wave vector k af the<br />
SP modes. Experimental detection of the SP modes is then suggested by the<br />
introduction of a prism so as to enable ATR measurements to be carried out in<br />
the Otto configuration, in which an air gap separates the prism from the sample<br />
by a distance d. The computed numerical results for the semi-infinite sample of<br />
the dielectric composite Ag-KCI lead to the conclusion tha~ the SP modes for<br />
some chosen values of f are all reciprocal for all models of effective permittivity in<br />
the sense that the change of wave vector direction does not change the<br />
frequency. It is also found that the implementation of the Wiener inequality on<br />
effective permittivity lead to the fact that the number of the SP modes reduces<br />
significantly. The numerical calculations for the associated ATR spectra of the<br />
sample are also presented which show that when the Wiener inequality is not<br />
imposed on effective permittivity then the strongest ATR dips for each model are<br />
obtained with different values of f. Meanwhile, the same value of f equally gives<br />
the srongest dips for ails models when the Wiener inequality is imposed on<br />
effective permittivity.</p>
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