ISSN 0030-400X, Optics and Spectroscopy, 2009, Vol. 106, No. 4, pp. 627–631. © Pleiades Publishing, Ltd., 2009. Original Russian Text © V.V. Rumyantsev, S.A. Fedorov, 2009, published in Optika i Spektroskopiya, 2009, Vol. 106, No. 4, pp. 698–703. 627 1. INTRODUCTION At present, investigations of various optical proper- ties of thin films and layered crystalline systems have attracted considerable attention in condensed-matter physics [1–6]. The urgency of these investigations is caused, on the one hand, by the needs of semiconductor electronics in quasi-two-dimensional objects with a certain structure and by the progress in quasi-two- dimensional electrodynamics [7] and, on the other hand, by a considerable success in the study of multi- layer systems, in particular, of magnetic photonic crys- tals [3–5] and composite materials based on silicon and liquid crystals (see [1, 6, 8–11] and references therein). In [12, 13], we studied the propagation of electromag- netic waves localized in an ultrathin homogeneous film and found the dispersion laws that determine the rele- vant integral optical characteristics. At the same time, the up-to-date progress in nanotechnology and photon- ics [10, 11, 14], as well as the necessity of the creation of ultrathin composite materials, stimulates the investi- gation of more complex quasi-two-dimensional struc- tures than the structures studied in [12, 13]. This inves- tigation can be most easily performed for ultrathin films that consist of bands that differ from each other both in the composition and in the thickness. In this case, the methods developed previously in [15, 16] for the calcu- lation of the concentration dependence of polariton spectra can be used directly for the calculation of corre- sponding excitations. In this work, we studied the propagation of electro- magnetic excitation localized in a nonideal quasi-two- dimensional system, which, in the general case, is a topologically ordered ensemble of bands with a random number of defect bands. In these systems, the defect bands may differ from the basic ones (for an ideal peri- odic structure) in both the composition and thickness. These systems can be numerically simulated in some approximations; in this study, we use the virtual crystal approximation. This approximation [17, 18] consists of the replacement of the configuration-dependent param- eters of the Hamiltonian of the problem by their config- uration-averaged values. We studied the concentration dependence of the lowest photonic bandgap of a non- ideal layered quasi-two-dimensional Si/SiO 2 superlat- tice with two elements in the unit cell. 2. PROPAGATION OF LIGHT IN AN ULTRATHIN HOMOGENEOUS FILM In the case of an ultrathin film (with the thickness d on the order of the electronic excitation radius), the interaction of the electromagnetic field with the layer can only be macroscopically described based on model representations, for example, as, e.g., in [12]. Let us consider the propagation of a plane electro- magnetic wave with a frequency ω and a wave vector q in the plane of an ultrathin plate according to the phe- nomenological approach [12] without concretization of the microscopic structure of the material. The limiting case of this system is a layer of atoms or molecules lying in one plane. In this system, the distance between the neighboring atoms (molecules) is much smaller than the electromagnetic wavelength. The long-wave- length field (λ  d) outside the layer does not depend on the characteristics of the crystal structure and on the polarization distribution along the film thickness. It is described by the D’Alembert equation, and the sole nontrivial information about the effect of the layer on the electromagnetic field consists of the boundary con- ditions, which couples the field amplitudes from both sides of the layer. The latter circumstance allows us to PHYSICAL OPTICS Propagation of Light in a Quasi-Two-Dimensional Si/SiO 2 Superlattice with Variable Layer Thickness V. V. Rumyantsev and S. A. Fedorov Galkin Donetsk Physicotechnical Institute, National Academy of Sciences of Ukraine, Donetsk, 83114 Ukraine Received October 14, 2008 Abstract—The propagation of an electromagnetic excitation localized in a nonideal quasi-two-dimensional Si/SiO 2 system that constitutes a topologically ordered set of bands with a random number of defect bands is numerically simulated within the virtual crystal approximation. The defect bands differ from the basic layers (for an ideal periodic structure) in both the composition and the thickness. The concentration dependence of the lowest photonic bandgap of the nonideal layered Si/SiO 2 film is studied. It is found that the presence of foreign layers in this nonideal superlattice causes a considerable renormalization of its polariton spectrum. PACS numbers: 78.20.-e DOI: 10.1134/S0030400X09040250