The interaction of light with matter has triggered the interest of scientists for long time. The area of plasmonics emerges in this context through the interaction of light with valence electrons in metals. The random phase approximation in the long wavelength limit is used for analytical investigation of plasmons in three-dimensional metals, in a two-dimensional electron gas and finally in the most famous two-dimensional semi-metal, namely graphene. We show that plasmons in bulk metals as well as in a two-dimensional electron gas originate from classical laws, whereas, quantum effects appear as non-local corrections. On the other hand, graphene plasmons are purely quantum modes and, thus, they would not exist in a “classical world”. Furthermore, under certain circumstances, light is able to couple with plasmons on metallic surfaces, forming a surface plasmon polariton, which is very important in nanoplasmonics due to its subwavelength nature. In addition, we outline two applications that complete our theoretical investigation. Firstly, we examine how the presence of gain (active) dielectrics affects surface plasmon polariton properties and we find that there is a gain value for which the metallic losses are completely eliminated resulting to lossless plasmon propagation. Secondly, we combine monolayers of graphene in a periodic order and construct a plasmonic metamaterial that provides tunable wave propagation properties, such as epsilon-near-zero behavior, normal and negative refraction.

In this paper, we study propagation of surface waves at a boundary of an amplifying isotropic medium and hyperbolic metamaterial. We demonstrate that the gain material can be used to counterbalance the losses in hyperbolic medium. We show that the gain-loss balance can be maintained even in the presence of nonlinear saturation leading to the surface wave amplification.

Wave polarization contains valuable information for electromagnetic signal processing; hence, the ability to manipulate it can be extremely useful in photonic devices. In this work, we propose designs solely comprised of one of the emerging and interesting two-dimensional media; Black Phosphorus. Due to substantial in-plane anisotropy, the simplest possible structure: a single slab of Black Phosphorus, can be very efficient and for manipulating the polarization state of electromagnetic waves. We propose Black Phosphorus films that filter the fields along one direction, or achieve large magnetic-free Faraday rotation, or convert linear polarization to circular; these slabs can be employed as  components in numerous mid-IR integrated devices.