Electrodynamics of quasi-one-dimensional carbon structures: Waveguiding, nonlinear response, composites

The talk presents an overview of theoretical results on electrodynamics and transport properties of carbon nanotubes (NTs). Consideration is given in the microwave, the infrared and the visible regimes. The talk comprises linear electrodynamics of isolated NTs with the emphasis given to waveguiding properties, nonlinear transport and nonlinear optics of NTs, electromagnetic response properties of NT-based composites. Effective boundary conditions for the electromagnetic field and the electrostatic potential in NTs are stated on the nanotube surface providing thereby the most appropriate tool for solving electrodynamic problems involving NTs. A detailed analysis of the waveguiding in a single homogeneous NT is presented. Scattering of electromagnetic cylindrical waves by an isolated semi-infinite NT is considered. The differences between the scattering responses of metallic and semiconducting NTs are discussed. The high harmonic generation by an isolated metallic NT exposed to an intense ultrashort pulse is discussed and the phase matching for different harmonics in a rope of parallel aligned NTs in dependence on the angle of incidence is considered. The talk also discuss a foundation of quantum electrodynamics of nanotubes. The last issue is of interest in relation to recent idea to use nanoobjects in quantum networks that store and process quantum information being transmitted by entangled states of photons. The talk stresses the tight relation between traditional problems of classical macroscopic electrodynamics and electrodynamic problems of quasi-one-dimensional nanostructures. That allows extension to nanostructures of well-developed mathematical approaches and rich experience accumulated in the traditional electrodynamics. On the other hand, complicated conductivity low and pronounced nanoscale field inhomogeneity provide peculiar electromagnetic response of NTs irreducible to the response of macroscopic samples.