Refraction indices of spatially nonuniform magnetic systems and nanostructures from the first principles

Abstract

An equilibrium two-time temperature Green’s function (TTGF)-based, quantum statistical mechanical approach has been used to derive from the first principles an explicit expression for the tensor of “local” refraction indices of spatially nonuniform systems in weak external electromagnetic (EM) fields in the linear approximation with regard to the field magnitudes. Written in terms of the TTGF-based, first-principle tensorial dielectric and magnetic susceptibilities, the obtained formula for the local tensor of refraction indices (TRI) is applicable to any system, including individual nanoscale objects, such as quantum dots and wires, magnetic nanostructures, composite materials, or spatially nonuniform, bulk magnetic materials. An explicit expression for the space-time Fourier transform (STFT) of the dielectric susceptibility tensor used in TRI is derived in terms of STFTs of the charge density—charge density TTGFs, while the corresponding STFT of the magnetic susceptibility tensor also includes STFTs of the microcurrent—microcurrent TTGFs. The STFTs of the equilibrium TTGFs featuring in the susceptibilities, and thus necessary to calculate TRI, can be obtained by equilibrium quantum statistical mechanical means, modeling and simulations, or from experimental data. Two TRI regimes of significant interest for applications that can be realized in spatially inhomogeneous magnetic systems have been identified.