We predict the existence of rogue waves in Bose-Einstein condensates either loaded into a parabolic trap or embedded in an optical lattice. In the latter case, rogue waves can be observed in condensates with positive scattering length. They are immensely enhanced by the lattice. Local atomic density may increase up to tens times. We provide the initial conditions necessary for the experimental observation of the phenomenon. Numerical simulations illustrate the process of creation of rogue waves.

We discuss the properties of surface plasmons-polaritons in graphene and describe three possible ways of coupling electromagnetic radiation in the terahertz (THz) spectral range to this type of surface waves. (i) the attenuated total reflection (ATR) method using a prism in the Otto configuration, (ii) graphene micro-ribbon arrays or monolayers with modulated conductivity, (iii) a metal stripe on top of the graphene layer, and (iv) graphene-based gratings. The text provides a number of original results along with their detailed derivation and discussion.

We show that by enclosing graphene in an optical cavity, giant Faraday rotations in the infrared regime are generated and measurable Faraday rotation angles in the visible range become possible. Explicit expressions for the Hall steps of the Faraday rotation angle are given for relevant regimes. In the context of this problem we develop an equation of motion (EOM) method for the calculation of the magneto-optical properties of metals and semiconductors. It is shown that properly regularized EOM solutions are fully equivalent to the Kubo formula.

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We use an exact solution of the relaxation-time Boltzmann equation in a uniform ac electric field to describe the nonlinear optical response of graphene in the terahertz (THz) range. The cases of monolayer, bilayer, and ABA-stacked trilayer graphene are considered, and the monolayer species is shown to be the most appropriate one to exploit the nonlinear free electron response. We find that a single layer of graphene shows optical bistability in the THz range, within the electromagnetic power range attainable in practice. The current associated with the third harmonic generation is also computed.