Field amplitude

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

Using the above relationship between the electric and magnetic field amplitudes from equation (Bl.26.15)) ... 

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. 

The earliest appearance of the nonrelativistic continuity equation is due to Schrodinger himself [2,319], obtained from his time-dependent wave equation. A relativistic continuity equation (appropriate to a scalar field and formulated in terms of the field amplitudes) was found by Gordon [320]. The continuity equation for an electron in the relativistic Dirac theory [134,321] has the well-known form [322] ... 

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. 

Nonmonochromatic Waves (1.16) Diffraction theory is readily expandable to non-monochromatic light. A formulation of the Kirchhoff-Fresnel integral which applies to quasi-monochromatic conditions involves the superposition of retarded field amplitudes. 

As a consequence, field methods, which consist of computing the energy or dipole moment of the system for external electric field of different amplitudes and then evaluating their first, second derivatives with respect to the field amplitude numerically, cannot be applied. Similarly, procedures such as the coupled-perturbed Hartree-Fock (CPHF) or time-dependent Hartree-Fock (TDHF) approaches which determine the first-order response of the density matrix with respect to the perturbation cannot be applied due to the breakdown of periodicity. 

The results of Fig. 2 therefore show that for the chosen frequency, almost total dissociation is attainable for a range of field amplitudes and we can get more I + Br or I + Br (the desired selectivity) with simple cw fields employed in the FOIST scheme. We may therefore infer that considerable dissociation and selectivity (almost any branching ratio) may be achieved using the scheme (18,19) presented here. The extent of optimization however varies with field amplitude and at the two ends of the field range, the FOIST results do not provide much improvement over the maximum available from one of the pure vibrational states in the optimization manifold. It should however be noted that FOIST alone can provide which of the v=0, 1 or 2 is optimal for the chosen objective. 

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... 

Frequently correlations of local field amplitude and molecular type are ignored and a single family of solution local field factors is adopted. 

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 ... 

Since these field amplitudes are known to be solutions of Schrodinger s equation, the solutions of... 

Propagation in a medium of a coherent optical wave packet whose longitudinal and transverse sizes are both of a few wavelength and whose field amplitude can induce relativistic motion of electrons is a novel challenging topic to be investigated in the general field of the so-called relativistic optics [11]. Theory and simulation have been applied to this problem for a few decades. A number of experiments have been performed since ultrashort intense laser pulses became available in many laboratories. 

The Hamiltonian of helium, in the center of mass frame and under the action of an electromagnetic field polarized along the x axis, with field amplitude F and frequency w, reads, in atomic units,... 

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...

Fig. 9.9 The calculated mode profiles for (a) a surface plasmon mode propagating along a 50 nm thick Au film, with an excitation wavelength of X 800 nm (note the plasmon field amplitude within the Au film is multiplied by 10 for clarity), and (b) a silicon PWEF waveguide with silicon core thickness of 220 nm, for an input wavelength of X 1550 nm...

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