Dipole, oscillating

In 1930, London [1,2] showed the existence of an additional type of electromagnetic force between atoms having the required characteristics. This is known as the dispersion or London-van der Waals force. It is always attractive and arises from the fluctuating electron clouds in all atoms that appear as oscillating dipoles created by the positive nucleus and negative electrons. The derivation is described in detail in several books [1,3] and we will outline it briefly here. 

In order to illustrate some of the basic aspects of the nonlinear optical response of materials, we first discuss the anliannonic oscillator model. This treatment may be viewed as the extension of the classical Lorentz model of the response of an atom or molecule to include nonlinear effects. In such models, the medium is treated as a collection of electrons bound about ion cores. Under the influence of the electric field associated with an optical wave, the ion cores move in the direction of the applied field, while the electrons are displaced in the opposite direction. These motions induce an oscillating dipole moment, which then couples back to the radiation fields. Since the ions are significantly more massive than the electrons, their motion is of secondary importance for optical frequencies and is neglected. 

Since the charge becomes coupled with the oscillating field, q undergoes a periodic acceleration which we represent by ap. Next we borrow a relationship from electromagnetic theory to describe the field produced by an oscillating dipole such as the molecule we have described ... 

Next we look for a substitution for the acceleration experienced by the charge. A convenient device for doing this originates from considering the oscillating dipole produced by the driving field. Since /a = aE, we can describe the periodic (subscript p) dipole moment of a molecule by... 

This oscillating dipole will radiate a secondary wave of the same frequency, which may be observed along the direction OP making an angle 6 with the direction (x-axis) of the incident wave. The scattered wave will be polarized in the plane defined by P and the 2 -axis. The electric intensity Es c of the scattered wave will depend on the acceleration of the induced electric moment, i.e., on d pldC-. Specifically the amplitude o.sec of the wave scattered in the direction OP will depend on the amplitude of (1/c ) d pldt ) calculated from Eq. (14), on the projection of the moment perpendicular to the direction P in the plane, and inversely on the distance r from the scatterer. Thus,... 

This shows that there are now oscillating dipoles at frequencies (coi + CO2) and (cOi — CO2), which give rise to SFG and difference frequency generation (DFG), respectively. When C0i = C02, Eq. (5.7) becomes ... 

When the oscillating electric held of an incident light ray interacts with a molecule, a small oscillating dipole moment is induced in the molecule as a consequence of its polarisability, a. Polarisability itself is a measure of the change in the dipole moment of a molecule induced by an electric held, and in the simplest case, where the electric held E and induced dipole moment p are in the same direction ... 

The molar absorption coefficient, e(2), expresses the ability of a molecule to absorb light in a given solvent. In the classical theory, molecular absorption of light can be described by considering the molecule as an oscillating dipole, which allows us to introduce a quantity called the oscillator strength, which is directly related to the integral of the absorption band as follows ... 

We present here a condensed explanation and summary of the effects. A complete discussion can be found in a paper by Hellen and Axelrod(33) which directly calculates the amount of emission light gathered by a finite-aperture objective from a surface-proximal fluorophore under steady illumination. The effects referred to here are not quantum-chemical, that is, effects upon the orbitals or states of the fluorophore in the presence of any static fields associated with the surface. Rather, the effects are "classical-optical," that is, effects upon the electromagnetic field generated by a classical oscillating dipole in the presence of an interface between any media with dissimilar refractive indices. Of course, both types of effects may be present simultaneously in a given system. However, the quantum-chemical effects vary with the detailed chemistry of each system, whereas the classical-optical effects are more universal. Occasionally, a change in the emission properties of a fluorophore at a surface may be attributed to the former when in fact the latter are responsible. 

On the other hand, the radiated intensity of such oscillating dipoles is proportional to d T/dr f, so that we can write ... 

From classical electromagnetic theory (Jackson, 1975) for an oscillating dipole, the power radiated from the dipole oscillator is given by... 

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