Electric field components

Any cavity contains an infinite number of electromagnetic modes. For radiation confined to a perfectly conducting cubical cavity of volume V= L, the modes are given by the electric field components of the fomi ... 

Electric field component of plane-polarized electromagnetic radiation. 

The interaction of electromagnetic radiation with matter can be explained using either the electric field or the magnetic field. For this reason, only the electric field component is shown in Figure 10.2. The oscillating electric field is described by a sine wave of the form... 

Again, ion tunnels have no electric-field component in the z-direction, and ions must be injected with some initial kinetic energy if they are to pass through the device. 

The tensor of the static first hyperpolarizabilities P is defined as the third derivative of the energy with respect to the electric field components and hence involves one additional field differentiation compared to polarizabilities. Implementations employing analytic derivatives in the Kohn-Sham framework have been described by Colwell et al., 1993, and Lee and Colwell, 1994, for LDA and GGA functionals, respectively. If no analytic derivatives are available, some finite field approximation is used. In these cases the P tensor is preferably computed by numerically differentiating the analytically obtained polarizabilities. In this way only one non-analytical step, susceptible to numerical noise, is involved. Just as for polarizabilities, the individual tensor components are not regularly reported, but rather... 

Any periodic distortion that causes polarization of a molecule can also cause interaction with the electric field component of radiation. An example is the asymmetric stretching vibration of the CO2 molecule, that creates a fluctuating dipole moment as shown below. 

The transverse electric field component, with azimuthal order v, is given by ... 

Not only the phase change but also the amplitudes of the parallel and perpendicular electric field components change upon reflection, and do so differently when an adsorbate is present. The associated variation, indicated as 3 ( can in principle be used as well, but is an order of magnitude smaller than dA. 

To handle the three-layer problem quantitatively, we write the z = 0 electric field components in terms of complex three-layer Fresnel coefficients ... 

The electric field term is most easily evaluated with one electric field component at a time. Taking the z component, we have... 

For weakly guiding structures, the second term can be neglected, and we obtain the standard Helmholtz equation in which individual components of the electric field intensity vector E remain uncoupled. For high contrast waveguides this is clearly not the case. The second term in Eq. (2) in which the transversal electric field components are mutually coupled must be retained. 

Figure 9. The comparison of mode fields of ring (left) and disk (right) microresonators. Outer radii of both microresonators are R = 50 pm, the height of the guiding layer is 1 pm, the ring width is also 1 pm. The refractive indexes of the substrate, the guiding layer and the superstate are 1.45, 1.59 and 1.0, respectively, the wavelength is 1.55 pm. Upper figures vertical electric field component lower figures horizontal (radial) electric field component.

Figure 2. The FDTD simulation results for the electric field components Ex (a) and (c) and the Poynting vector component (h) and Sx (d). The waveguide is along z axis, the dashed lines contouring the non-etched 0.6 pm thick region of the core.

Figure 12 shows intensity distribution of different electric field components on the plane touching the back-side of the nanosphere. Strong depolarization is clearly seen, as the incident wave is polarized along the y-axis. 

We may represent a beam of arbitrary polarization, including partially polarized light, by a column vector, the Stokes vector, the four elements of which are the Stokes parameters. In general, the state of polarization of a beam is changed on interaction with an optical element (e.g., polarizer, retarder, reflector, scatterer). Thus, it is possible to represent such optical elements by a 4 X 4 matrix (Mueller, 1948). The Mueller matrix describes the relation between incident and transmitted Stokes vectors by incident is meant before interaction with the optical element, and by transmitted is meant after interaction. As an example, consider the Mueller matrix for an ideal linear polarizer. Such a polarizer transmits, without change of amplitude, only electric field components parallel to a particular axis called the transmission axis. Electric field components in other directions are completely removed from the transmitted beam by some means which we need not explicitly consider. The relation between incident field components (E, E i) and field components ( l, E () transmitted by the polarizer is... 

In problems involving optically active particles it is usually more convenient to use the amplitude scattering matrix in the circular polarization representation. The transformation from linearly to circularly polarized electric field components is... 

For spheres sufficiently small that Rayleigh theory (Chapter 5) is applicable, or for arbitrarily shaped particles that satisfy the requirements of the Rayleigh-Gans approximation (Chapter 6), incident light with electric field components parallel and perpendicular to the scattering plane may be scattered with different amplitudes however, there is no phase shift between the two components. Hence, the amplitude scattering matrix has the form... 

The nonzero static electric field components are given by equations such as ... 

If A] is phase-free, as discussed in Section III, and in Ref. 15, there are no longitudinal electric field components. This also occurs if A,-3"1 is zero [17]. The B(3) field is then a Fourier sum over modes with operators a qaq and is perpendicular to the plane defined by A and /1<2>. The four-dimensional dual to this term is defined on a time-like surface, following Crowell [17], which can be interpreted as E under dyad vector duality in three dimensions. The ( field vanishes because of the nonexistence of the raising and lowering operators l3 , . The BM is nonzero because of the occurrence of raising and lowering... 

B. Electric Field Components in Bulk Rare (Optically Thin) Medium... 

Fig. 2. ATR equipment 0 is the angle of incidence. Eu (parallel) and Fy (perpendicular) denote the direction of the electric field components of the incident light with respect to the plane of incidence ((x, z) plane). Ey, and E denote the electric field components with respect to a coordinate system fixed on the IRE.

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