Effective boundary conditions for planar quantum dot structures

The effective-boundary condition method is extended to nanoscale mesoscopic systems. The (EBC’s) appear as a result of the two-dimensional (2D)-homogenization procedure and have the form of two-side anisotropic impedance boundary conditions stated on the structure surface. It has been shown that, unlike to macroscopic electrodynamics, the surface impedance tensor exhibits sharp oscillations at frequencies of optical transitions. The EBC method supplemented with well-developed mathematical techniques of classical electrodynamics creates unified basis for solution of boundary-value problems in electrodynamics of nanostructures. We have shown that the radiative lifetime of 2D array of spherical quantum dots (QD’s) drastically changes its dependence on QD radius in comparison with the case of a single QD in the range of radii smaller than Bohr radius.