Dipole coupling

In certain situations involving coherently interacting pairs of transition dipoles, the initial fluorescence anisotropy value is expected to be larger tlian 0.4. As mdicated by the theory described by Wyime and Hochstrasser [, and by Knox and Gtilen [, ], the initial anisotropy expected for a pair of coupled dipoles oriented 90° apart, as an example. 

Smith, S. L., Ihrig, A. M. Solvent Effects on H—F Couplings Dipole Orientation Requirements for Solvent Dependence of Coupling Constants. J. Chem. Phys. 46, 1181 (1967). 

Formulation using i-coupled dipole matrix elements The scattering amplitudes Sy can also be related to dipole matrix elements Dy which are defined on the basis of j/7-coupling and classified by the channel index y — For these dipole matrix elements one has [Hua80]... 

Formulation using fti-coupled dipole matrix elements... 

Quadrupole Couplings, Dipole Moments and the Chemical Bond. Discuss. Faraday Soc. 19, 14—29 (1955). 

The coupled dipole equations (CDE) have been used in calculating the optical properties of composite media, including larger particles, where the dipoles are arranged to mimic a more complicated system, such as those used in DDA [38], [39], as well as fractal structures [40], which could be applied to model aggregation, surface composition, or percolation. The general nature of the solution allows for calculation of optical properties, as well as enhanced Raman and electric fields at any point in space. 

The dynamics of the spin system is governed by the Hamiltonian which in addition to a term reflecting external radio-frequency (rf) manipulations displays dependencies on chemical shifts, scalar (electron-mediated) J coupling, dipole-dipole coupling, and quadrupolar coupling, i.e.,... 

V. Kerasek, O. Brzobohaty, P Zemanek, Longitudinal optical binding of several spherical particles studied by the coupled dipole method. J. Opt. A Pure Appl. Opt. 11 (2009) 034009. P.A.M. Dirac, The Principles of Quantum Mechanics, Oxford University Press, Oxford, 1958. 

The discussion, presented in Section IV, has been concentrated on analysis of the effect of quantum interference on spontaneous emission in a V-type three-level atom. With the specific examples we have demonstrated that spontaneous emission can be controlled and even suppressed by quantum interference. In this section, we extend the analysis to the case of coherently driven systems. We will present simple models for quantum interference in which atomic systems are composed of two coupled dipole subsystems. In particular, we consider interference effects in coherently driven V and A-type three-level atoms. Each of the three systems is represented by two dipole moments, p, and p2, interacting through the vacuum field. 

In general, the study of the scattered intensity by systems where multiple scattering is non-negligible is a difficult task. In order to resolve these difficulties we have used several approximations the particle size is assumed to be much smaller than the incident wavelength, so the Rayleigh dipole approximation is used to characterize the particle scattering. For the surface case, the perfect conductor approximation (PCA) ( = -go) for the substrate is applied. In both systems, the scattered field is calculated in the far-field approximation. For the purpose of this research, these approximations do not constitute serious restrictions and facilitate the numerical calculations. For real substrates (metallic or dielectric) and/or finite size particles, the main conclusions are unaffected [9]. The scattered intensity is calculated by means of the coupled dipole method (CDM) [10] for both the volume case and the surface case. In the latter, the PCA allows us to apply the image theory [11]. 

Light scattering and extinction by a single aggregate 3.2.1. Coupled dipole method (CDM)... 

The main results for non-spherical grains in theoretical modeling have been obtained using two popular munerical techniques the T-matrix approach and the coupled-dipole approximation. 

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