Electric field amplituded

In this fonn it is clear that k leads to an attenuation of the electric field amplitude with distance (i.e. absorption). 

The time-averaged force, equation (Cl.4.3), consists of two tenns tire first tenn is proportional to tire gradient of tire electric field amplitude tire second tenn is proportional to tire gradient of tire phase. Substituting equation (Cl.4.4) and equation (Cl.4.5) into equation (Cl.4.3), we have for tire two tenns. 

When infrared radiation with electric field amplitude Eo impinges on the film-covered substrate, some is reflected from the ambient/film interface while some is transmitted into the film and then reflected at the film/substrate interface. Some of the radiation reflected at the film/substrate interface is reflected back into the film at the film/ambient interface. However, some is transmitted into the ambient (see Fig. 4). The reflection coefficient (r) for the film/substrate system is calculated by summing the electric field amplitudes for all of the waves reflected into the ambient and then dividing by the electric field amplitude Eo) of the incident radiation. 

In view of the result just found, it is interesting to contrast exact and approximate behaviour of the density n(x F) [eqs. p.5) and (2.17), respectively]. Some insight into the nature of the approximations contained in our treatment is gained through the inspection of Table 1, which collects Fermi-level energy values calculated for several electron occupation numbers and two different electric field amplitudes. The entries have... 

Table 1. Fermi-level energy Ef predicted for the harmonic-well model = 1. a.M.) for different electron numbers (2iV ) and different electric field amplitudes E (a.u.).

In ellipsometry two parameters are determined. These are A, the phase angle between the leading and trailing components in Fig. 27.24, and the ratio of the electric field amplitudes E and E, which defines the second parameter, /. IE I/IEJ = tan /. A and r may be recorded as functions of other experimental variables, such as potential and time. 

In the theoretical section above, the nonlinear polarization induced by the fundamental wave incident on a planar interface for a system made of two centrosymmetrical materials in contact was described. However, if one considers small spheres of a centrosymmetrical material embedded in another centrosymmetrical material, like bubbles of a liquid in another liquid, the nonlinear polarization at the interface of a single sphere is a spherical sheet instead of the planar one obtained at planar surfaces. When the radius of curvature is much smaller than the wavelength of light, the electric field amplitude of the fundamental electromagnetic wave can be taken as constant over the whole sphere (see Fig. 7). Hence, one can always find for any infinitely small surface element of the surface... 

Here E and E are electric field amplitudes on the surface and in vacuo interrelated by the Fresnel formulae c0 is the velocity of light in vacuo x°jf (K,susceptibility tensor defined by the equation ... 

Since adsorbed molecules are exposed both to the incident and reflected light waves whose electric field amplitudes are interrelated by the Fresnel formulae, the vectors in s- and -polarizations appear as ... 

The two important properties of the waveguide mode are its cross-sectional electric field amplitude profile A(x,y) and the effective index /VelT. Here x and y are the coordinates in the plane perpendicular to z, the waveguide propagation direction. The electric field at any point along the waveguide is given by... 

Fig. 9.8 Cross section of a silicon slot waveguide consisting of two 180 nm x 250 nm silicon channels, separated by a 50 nm gap. The solid line represents a line plot of the electric field amplitude of the horizontally polarized TE mode, taken along the horizontal midline of the waveguide...

The factor 1(0) in Eq. (7.2) is a function of 8 and the polarization of the incident light these features are discussed shortly. However, we first examine the remarkable amplitude, polarization, and phase behaviors of the electric fields [from which 1(0) is derived] and the magnetic fields of the TIR evanescent wave. The field components are listed below, with incident electric field amplitudes Aps and phase factors relative to those of the incident E field s phase at z = 0. (The coordinate system is chosen such that the x-z plane is the plane of incidence. Incident polarizations p and s are parallel and perpendicular to the plane of incidence, respectively.)... 

Figure 1. Schematic view of the one-dimensional layered structure. The vertical lines denote discontinuities of refractive index distribution. The monochromatic plane wave is incident in the y direction with the electric field amplitude The amplitudes of reflected and transmitted waves are ref and, respectively.

The loss of observable THG in the far field with tight focusing of the beam in homogenous normal dispersion media can be described with the paraxial wave equation [Equation (4.2)] assuming slow spatial variation of electric field amplitudes along the beam propagation direction (z direction). The solution of the paraxial wave equation for the amplitude of third harmonic (A3 J can be written as follows (Boyd 1992) ... 

Fig. 2 Diffraction image of an entrance-slit element. Abscissa z is distance in Rayleigh widths ordinate E is proportional to electric-field amplitude.

When a light wave with an electrical field amplitude E is incident on a dye solution which is non-absorbing in the spectral region of this light wave, a dipole moment is induced in each dye molecule ... 

A variant of IRRAS is polarization modulation IR reflection absorption spectroscopy (PM-IRRAS). In this method, the polarization of the IR beam incident on the sample is modulated between parallel and perpendicular polarization. When the sample is metallic, only the parallel-polarized light yields signals from adsorbed molecules, because the electric field amplitude of perpendicular-polarized light vanishes at the metal surface. This statement is the basis for the metal surface selection rule 100,109). When the medium above the sample (gas or liquid phase) is isotropic, both polarizations are equivalent. The PM-IRRAS method thus enables the measurement of signals from adsorbates on a metal surface in the presence of an absorbing gas or liquid phase. 

The importance of these equations is the following.In optics, U may represent a complex electric field amplitude and V its conjugate. If U results from a large number of coherent sources or scatterers, each endowed with a time lag xa, one has... 

Thus, the linear polarizability a (responsible for the value of the refractive index n) can be treated as an electric field amplitude-dependent quantity, i.e., aeff = a + (3-yEo)/4. Remembering that the light intensity is proportional to the square of the field amplitude, this means that the third-order nonlinearity leads to the linear dependence of the refractive index on the light intensity and that, for example, the phase of the propagating beam is modified at high light intensities due to this dependence. 

The magnitude of E1,0 can be calculated from Fresnel s law. If the electric field amplitude as a function of distance z is expressed per unit of incident electric field amplitude, E 0, of the perpendiculary polarized electromagnetic wave, then ... 

In the absence of noise, the system [179] describes the generation of a singlemode laser field interacting with a homogeneously broadened two-level medium [180]. The variables and parameters of the Lorenz system can be interpreted in terms of a laser system as q is the normalized electric field amplitude, the normalized polarization, q3 the normalized inversion, a = fe/y1 r = A+l, b = 72/71, with k the decay rate of the field in the cavity, yj and y2 the relaxation constants of the inversion and polarization, and A the pump parameter. Far-infrared lasers have been proposed as an example of a realization of the Lorenz system [162]. A detailed comparison of the dynamics of the system (42) and a far-infrared laser, plus a discussing the validity of the Lorenz system as laser model, can be found in Ref. 163. 

---