Dipolar interactions retarded

The problem is to discuss the generalized polarizability ae(1.49) with the matrix a 1 not commuting with that of the dipolar interactions, 0. To show that the pure retarded interactions may be discarded in the dynamics of mixed crystals, we assume here that the coulombic interactions are suppressed in (ft. The interaction tensor is then reduced to its retarded term (1.74). Then the dispersion is given by (1.35) ... 

In what follows, we present in Section IV.A a theory of the effects of weak disorder on the retarded interactions of 2D strong dipolar excitons, and in Section IV.B we analyze the effects of stronger disorders on the coulombic interactions, calculating the density of states and absorption spectra in 2D lattices, in the framework of various approximations of the mean-field theory. 

The inter-particle distance dependence of the near-field coupling would therefore reflect the distance decay of the near-field itself. In other words, each particle senses the near-field due to the other particle. By varying the distance of the other particle and monitoring the LSPR response, the spatial profile of the near-field can be deduced. The plot of the LSPR red-shift as a function of inter-particle gap (surface-to-surface separation) shows a much more rapid decay of the near-field than predicted by the dipolar model. This is because the dipolar model does not take into account the multipolar interactions between the particles, which become increasingly important at smaller and smaller inter-particle gaps. Plasmon coupling is therefore a multipolar interaction and its true distance-dependence can be quantitatively reproduced only by a complete treatment that includes all modes of interaction (dipolar, quadrupolar, octupolar). Computational electrodynamics methods such as discrete dipole approximation (DDA) (see Chapter 2) and finite-difference-time-domain (FDTD), which include a full multipolar treatment in addition to finite-size retardation effects, fit experimental trends well. 

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