It is well known [1-3] that optical properties of ionic crystals depend strongly on the shape and the size of the crystals. In the simplest case when a sample is a slab or a film with the optical thickness nd A, where n is the refractive index, d is the film thickness and is the light wavelength in vacuum, size effects were investigated both experimentally and theoretically. In infrared reflection - absorption (RA) spectra and in spectra of thermostimulated emission of infrared radiation by thin films deposited on a metal substrate only radiative surface polaritons were observed whereas in Raman spectra, in . contrast to infrared spectra, transverse and longitudinal optical phonons were observed [4-6J. At the optical thickness of films md << A the sample under investigation looks like the Fabri-Perot cavity. For such sample a set of bands Wm appears at the frequencies Wm < WTO and Wm < WLO in infrared RA and in thermostimulated emission spectra [6,7] . These bands correspond to radiative states of the electromagnetic field in a film, i.e. to cavity modes [6-9]. The shape of these bands, their frequencies and intensities are well described theoretically within the framework of linear crystal optics if macroscopic dielectric functions of a film and a substrate and experimental geometry are known [6,7]. It is well known that thermal vibrations of ions and electrons inside a substance of a cavity are accompanied by generation of an electromagnetic field at the frequency of these vibrations,and this electromagnetic field under certain conditions can leave the cavity if the cavity has a semitransparent wall. An analogous situation should also take place for surface (interface) vibrations of ions and electrons in the substance. They also should generate the electromagnetic field. Electromagnetic waves with q < k0 will be radiated into empty space, whereas those with q < k0 will be "tied" to the surface. As a rule surface polaritons of dielectric and semiconductor crystals and surface plasmon polaritons of metals are considered as nonradiative excitations because their wave vectors q are large than wave vector of light in a vacuum k0 . Nonradiative surface polaritons with q < k0, generated by thermal motion of surface atoms and electrons of crystals, can be converted into light by means of an ATR prism brought to the crystal surface [6,7] . The ATR prism placed near the surface of a crystal turn the nonradiative vibrational surface states of the crystal — vacuum interface with q < k0 into light absorbing (radiative) states. The presence of a prism near the crystal surface leads to a perturbation of surface polaritons and, as a result, to a considerable change in the dispersion law [6,7,10]. Radiative decay of these polaritons, i.e. their transformation into light, is detected experimentally. Thus, in addition to conventional anharmonic decay of elementary excitations in a crystal there exists an additional decay channel: a radiative channel. Namely due to the radiative instability of polaritons their interaction with the external electromagnetic field, i.e. light, is possible. In this report we consider radiative eigen states of plasmon excitations in cavity structures "ATR prism — gap — metal", "vacuum — dielectric film — metal substrate" and in "ATR prism — gap — dielectric film — metal substrate" structure.