Dipole free-space’ fields

The solutions can be labelled by their values of F and m.p. We say that F and m.p are good quantum. num.bers. With tiiis labelling, it is easier to keep track of the solutions and we can use the good quantum numbers to express selection rules for molecular interactions and transitions. In field-free space only states having the same values of F and m.p can interact, and an electric dipole transition between states with F = F and F" will take place if and only if... 

Figure 8.18. The phase of the scattered field, evaluated at the position of the source dipole, as a function of free-space wavenumber (cm-1).

Now let us examine what would happen to the response of the dielectric if we put an alternating voltage on the capacitor of frequency co. If CO is low (a few Hz) we would expect the material to respond in a similar manner to the fixed-voltage case, that is d (static) = e(co) = e(0). (It should be noted that eo, the permittivity of free space, is not frequency-dependent and that E(0)/eo = H, the static dielectric constant of the medium.) However, if we were to increase co to above microwave frequencies, the rotational dipole response of the medium would disappear and hence e(co) must fall. Similarly, as we increase co to above IR frequencies, the vibrational response to the field will be lost and e(co) will again fall. Once we are above far-UV frequencies, all dielectrics behave much like a plasma and eventually, at very high values, e(co)lto = 1. 

In resolving the apparent paradox of how an antenna with no charge (in free space) can have an electric-dipole moment, one can go back to definitions. In Ref. 14 the fields from a current distribution are evaluated by expanding... 

Figure 19.1 (A) 2D projection of the calculated local field intensity distribution around a pair of 15 nm diameter silver nanoparticles excited with Xi = 400 nm light polarized along the interpaiticle axis. The edge-to-edge particle separation is 2 nm and the free space incident light intensity Ej,x P taken to be unity. The local field intensity near the pair is shown in false color. The calculation was done using dipole-dipole approximation (DDA) method with each dipole unit being a square with sides of 0.2 nm. (B) Model of the photophysics of a molecule represented by a three level system and how the excitation and decay dynamics are affected by plasmon enhancement of radiative rates and the introducticm of a rate for quenching Icq of the excited state due to proximity to the metal surface. E (X ) and E (X2) are the field enhancements at the position of the molecule for the excitation and emission wavelengths respectively, kn and kMR represent the radiative and non-radiative decay rates of the molecule in the absence of plasmon enhancement.

The dielectric permittivity of a medium (relative to the permittivity of free space, 8q = 8.85 X 10 F/m) is given by e and measures the polarization of the medium per unit applied electric field. The dielectric loss factor arises from energy loss during time-dependent polarization and bulk conduction. The loss factor is written as a". The loss tangent or dissipation of the medium, tan<5 is defined by e"/e. The orientation of molecular dipoles has a characteristic time r. Typically is short early in the cure but grows large at the end of the cure. 

Thus, neglecting displacement currents, the electromagnetic field of an alternating magnetic dipole in free space is described as follows ... 

The vertical component of the magnetic field caused by the vertical dipole in free space, as follows from Chapter 1, can be presented as ... 

The leading terms in eqs. 8.13 and 8.14 describe the primary field of the magnetic dipole in a free space and the secondary field of induced currents when the skin effect can be neglected. The first term for the quadrature component is larger when an observation point is closer to the dipole. It means that the quadrature component of the current, which is proportional to frequency, is generated by the primary field only, and it is concentrated mainly near the dipole, i.e. within the internal area. 

Proceeding from results obtained for the step function we will consider to what extent type of excitation M(t) and moment of measuring t define conditions for which a field can be considered with sufficient accuracy as a quasistationary one, i.e. when it changes synchronously with the dipole moment in free space. 

Before discussing the conductivity of tissue, consider one of the simplest and most easily understood volume conductors sahne. The electrical conductivity of sahne arises from the motion of free ions in response to a steady electric field, and is on the order of 1 S/m. Besides conductivity, another property of saline is its electrical permittivity, s (S sec/m). This property is related to the dielectric constant, /c (dimensionless), by e = /cso, where Sq is the permittivity of free space, 8.854 x 10 S sec/m. Dielectric properties arise from bound charge that is displaced by the electric field, creating a dipole. They can also arise if the appHed electric field aligns molecular dipoles (such as the dipole moments of water molecules) that are normally oriented randomly. The DC dielectric constant of sahne is similar to that of water (about... 

In these expressions N is the number of dipoles per unit volume, e the electron charge, m the electron mass, T the damping constant, coq the resonance radian frequency of the harmonically bound electron, co the radian frequency of the field, and the permittivity of free space. Equations (12) and (13) are sketched in Fig. 1. The range of frequencies where increases with frequency is referred... 

---