A topological insulator (TI), whose typical examples are Bi2Te3 and Bi2Se3, has bulk properties similar to those of conventional band insulators, but has a novel property in that its surface state is metallic. The surface state is expected to exhibit the quantum charge/spin Hall effect without an external magnetic field and the two interfaces of a TI in slab geometry have quantized Hall conductivities with opposite signs. The two sites correspond to a pair of quantum Hall layers (QHLS) in which the sign of the Hall conductivity in one layer is opposite to that in the other layer. This system can be considered as an alternating QHLS (AQHLS) and helicon like mode early are shown to occur [1]) for that. A similar system is expected to appear in bianisotropic photonic metamaterials, which are artificially engineered composite media in which the subwavelength features of the designed unit cells and coupling between them governs the macroscopic electromagnetic behavior. Exploiting these facts we can extrapolate some aspects of the phenomena interplay in metamaterials and TI nanolayered structures on the basis of similarities between Maxwell and Dirac equations. Mathematically [2], this is because, under some (rather general) conditions, the Maxwell equations for electromagnetic waves in an inhomogeneous dielectric medium can be reduced to the Dirac equations for charge carriers in TI subjected to an external electric potential. In the first part of the paper, we explore properties of the electromagnetic waves (EM) waves in a topological insulator layered structures and superlattice. According to the macroscopic Maxwell equations approach the dispersion laws of plasmon polaritons on the surface of topological insulator were obtained. The case of one-side and two-side excitation was considered. The condition of existence of the antiphase plasmon polaritons in the topological insulator film was obtained. The topological insulator Bi2Se3 based one-dimensional photonic crystal was studied. Due to the high bulk refractive index of Bi2Se3 it can be considered as high contrast photonic crystal. It was found that the spectrum of transmission of the system has very narrow frequency and angle peaks. The number of peaks on the angle scale depends on the number of photonic crystal layers. This photonic crystals can be used for the creation of collimated light and the design of unidirectional absorbers. Also there application for the design of optical sensors was considered. For superlattices in the long wavelength limit, we find a gapless EM mode, which is a known feature of conventional helicon waves. However, in marked contrast, the dispersion relation is linear instead of quadratic, and the mode is active for both circular polarizations. The model of the topological insulator superlattice, has two kinds of photonic bands, since the unit ―cell‖ has two ―sites.‖ Both photonic bands do not depend on the polarization direction. What should be emphasized is that one of the photonic bands has nowhere energy gaps, in spite of the presence of periodicity. The resulting photonic band structure is compared with a numerically calculated transmission spectrum. We explore the optical properties of periodic layered media containing left-handed metamaterials. This study is based on several analogies between the propagation of light in metamaterials and charge transport in TI. At an interface separating two dissimilar layered metal-dielectric media electromagnetic surface states can exist. Surface modes existing in such a structure can be considered as a generalization of the surface Tamm states well known for electronic systems. This state became gapless with Dirac cone spectrum like interface states of TI in the case of heterolayer of metamateria and normal media.We show that the photonic band-gap structure of a periodic system built of alternating left- and right-handed dielectric slabs contains conical singularities similar to the Dirac points in the energy spectrum of charged quasiparticles in TI in the case of a metamaterial periodic structure consisting of alternating layers of positive and negative refractive index with average zero refractive index. Such singularities in the zone structure of the infinite systems give rise to rather unusual properties of light transport in finite samples. Based on an analogy with electromagnetic metamaterials some aspects of electron matter waves in TI layered structures are analysed.