Electrodynamic coupling

This discussion of the hyperfine splitting of the hydrogen isotopes was still affected by some uncertainty originating in part from the inaccuracy in the value of the electrodynamic coupling constant a. 

This is described as electrodynamic coupling, central to this approach. The induced dipole moment is given by, P2 t) =, where e is the charge... 

The first two terms arise from alkalis 1 and 2 unassociated by electrodynamic coupling in the structure and the last term is due to those associated by such effect, a is the total number of alkali ions. and can be evaluated statistically assuming a priori probabilities of their distribution. When p and are known, conductivity behaviour may be examined with three adjustable parameters, namely A, and. An example of sodium-potassium silicate conductivities where excellent fits were obtained is shown in Figure 6.09. In the figure, conductivities normalised with respect to the maximum conductivity in the single alkali silicate glasses (at 150 °C), have been plotted. 

The considerable distinctions between optical spectra of a metal nanostmcture and corresponding bulk metal appear due to surface modes (plasmon-polariton resonances) in nanoparticles and size dependence of their optical constants. In the case of partially-ordered nanoparticle arrays these effects are of the collective nature because of strong electrodynamic coupling. The theoretical approach for regarding... 

To demonstrate the influence of longitudinal coherent interactions we have investigated the transmission and reflection spectra of ID photonic crystals based on close-packed silver nanosphere monolayers separated by thin solid dielectric films. The strongest spectral manifestation of longitudinal electrodynamic coupling was shown [2] to take place in the case of joint electron and photonic confinements. In order to achieve it we chose intermonolayer film thicknesses Im so that the photonic band gap and the metal nanoparticle surface plasmon band could be realized at close frequencies in the visible. 

This is described as electrodynamic coupling, central to this approach. The induced dipole moment is given by, />2(0 = e.X2(t), where e is the charge on ion 2, and X2(t) is the time-dependent displacement of ion 2. The equation of motion governing the displacement of ion 2 corresponds to that of a forced damped oscillator and is given by... 

The most effective approach to describe the optical properties of the arrays with short-range ordering is the statistical theory of multiple scattering of waves (STMSW) [5]. This approach considers electrodynamic coupling of spatially correlated scatterers as interference summation and subsequent averaging of... 

The investigation of electrodynamic coupling between molecules and metal nanoparticles, and therefore of the phenomena enumerated above, has exploited different levels of approximations so far. We can classify such approximations referring to two criteria. The first is the use of quantum electrodynamics (QED) versus classical electrodynamics to describe the coupling. The second is related to the levels of description used for the molecule and the metal nanoparticle. For this, three different options can be found in the literature ... 

The molecule is a classical oscillating charge density (usually a point dipole) and the metal nanoparticle is a continuous body characterized by the frequency-dependent dielectric function (see Chapter 1). This is by far the most common description of the metal-molecule electrodynamic coupling problem in the literature. Notably, sometimes even the metal nanoparticle is reduced to a polarizable dipole. Depending on the phenomenon under study, this may be acceptable or results in an oversimplification [50]. 

Finally, the whole system (molecule + metal nanoparticle) can be treated atomistically via TD-DFT or other quantum chemical methods. The interaction between the metal nanoparticle and the molecule are treated on the same foot as the intra-molecule and intra-nanoparticle ones. This method is therefore able to include much more than just the electrodynamics coupling, as it can include mutual polarization, chemical bonding, charge transfers (also in excited states). On the down side, at present this approach is limited to very small metal particles (a few tens of atoms, a few nm in size). Moreover, electrodynamics coupling is limited to the quasi-static limit, as standard molecular Hamiltonian includes only non-retarded Coulombic potential. Nevertheless, this method represents a fully ab initio approach to molecular plasmonics. 

We end this section by remarking that neglecting Etmg in the absorption does not allow to predict an interesting effects of the electrodynamics coupling between molecule and plasmon excitations the shifts of the absorption frequencies, of both the molecule and the plasmonics nanoparticle. 

Once again, for the purpose of studying the effects of electrodynamics coupling between a molecule and a metal nanoparticle, the classical dipole model for the molecule sets an intuitive framework [73], Scattering of light by a polarizable punctiform dipole can be seen as the emission of a dipole fitsc induced by the incident EM field at the frequency or. 

The scattering of light by a molecule close to a metal nanoparticle involves all the fields depicted in Fig. 5.1 Therefore, from the point of view of the electrodynamic coupling between the molecule and the metal nanoparticle, we can see the light scattering as a problem involving ... 

In the classification of models for metal-molecule electrodynamic coupling that we have done in Sec. 5.1, the model that we have described so far (a classical punctiform dipole close to a metal nanoparticle described as a continuous medium) is the simplest. While it has proven to be extremely useful, not only as a mean to grasp the basic physics of molecular plasmonics phenomena, but also to provide semi-quantitative and, sometimes, even quantitative results, it still remains a model empirical in nature. In this section we shall briefly describe models that goes beyond such an approach. 

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