Media electromagnetic field

The signal is reflected from the product surface because there is an abmpt impedance change in the sensor at the air—product interface. Because the electromagnetic field extends outside the two sensor conductors, the sensor impedance depends on the dielectric constant of the surrounding medium. In... 

FIG. 7 Schematics of the SHG process at the surface of a sphere of a centrosymmetrical medium with a radius much smaller and of the order of the wavelength of light. The cancellation or the addition of the nonlinear polarization contribution is given explicitly and underlines the effect of the electromagnetic field and the surface orientation. 

To illustrate the use of the vector operators described in the previous section, consider the equations of Maxwell. In a vacuum they provide the basic description of an electromagnetic field in terms of the vector quantifies the electric field and 9C the magnetic field The definition of the field in a dielectric medium requires the introduction of two additional quantities, the electric displacement SH and the magnetic induction. The macroscopic electromagnetic properties of the medium are then determined by Maxwell s equations, viz. 

For electrochemistry, of course, the most important properties of the n, involve the electric field and potential in the system. In general, to find the electromagnetic field in a medium, one has to solve the basic equation... 

Fig. 4 Waveguide evanescent wave (EW) principle. Light is propagated through the waveguide (n ) and an electromagnetic field (called EW) is generated in the external medium (n2). The EW interacts with immobilized molecules that absorb energy, leading to attenuation in the reflected light of the waveguide...

These nonlinear phenomena, long known theoretically but only experimentally realizable with lasers as light sources, are based on the fact that the polarization of a medium, induced by a high-intensity electromagnetic field, is no longer proportional to the electric field vector C, but contains nonlinear contributions ... 

The adequate protein/polymer concentrations in feed for 3-D NPH exist for SPRi, because the evanescent electromagnetic field decays exponentially from the metal surface into the interacting medium as described above. The thickness of 3-D NPH-SA prepared over the concentration of 0.25/0.025% is too thick to monitor SPR interactions even at the center of spots. It is thought that different proteins have each optimum concentration for 3-D NPH immobilization method in the case of SPR measurements. 

The electromagnetic field is required to satisfy the Maxwell equations at points where e and ju, are continuous. However, as one crosses the boundary between particle and medium, there is, in general, a sudden change in these properties. This change occurs over a transition region with thickness of the order of atomic dimensions. From a macroscopic point of view, therefore, there is a discontinuity at the boundary. At such boundary points we impose the following conditions on the fields ... 

Our fundamental task is to construct solutions to the Maxwell equations (3.1)—(3.4), both inside and outside the particle, which satisfy (3.7) at the boundary between particle and surrounding medium. If the incident electromagnetic field is arbitrary, subject to the restriction that it can be Fourier analyzed into a superposition of plane monochromatic waves (Section 2.4), the solution to the problem of interaction of such a field with a particle can be obtained in principle by superposing fundamental solutions. That this is possible is a consequence of the linearity of the Maxwell equations and the boundary conditions. That is, if Ea and Efc are solutions to the field equations,... 

Once we have obtained the electromagnetic fields inside and scattered by the particle, we can determine the Poynting vector at any point. However, we are usually interested only in the Poynting vector at points outside the particle. The time-averaged Poynting vector S at any point in the medium surrounding the particle can be written as the sum of three terms ... 

We showed in Chapter 3 that a physically realizable time-harmonic electromagnetic field (E, H) in a linear, isotropic, homogeneous medium must satisfy the wave equation... 

We may also expand the scattered electromagnetic field (E5,H5) and the field (E H,) inside the sphere in vector spherical harmonics. At the boundary between the sphere and the surrounding medium we impose the conditions (3.7) ... 

The electromagnetic field (E H,) inside the sphere is obtained from (8.13) and the transformation (8.9). We saw in Chapter 4 that, for given , there are four unknown coefficients in the expansions for the fields when the sphere is nonactive optical activity doubles the number of coefficients, which are determined by applying the conditions (4.39) at the boundary between sphere and surrounding medium and solving the resulting system of eight linear equations. We are interested primarily in the coefficients of the scattered field ... 

The process of total reflection of an incident wave in an optically dense medium against the interface of an optically less dense medium turns out to be of particular and renewed interest with respect to the concepts of nontransverse and longitudinal waves. In certain cases this leads to questions not being fully understood in terms of classical electromagnetic field theory [26]. Two crucial problems that arise at a vacuum interface can be specified as follows ... 

Let us carefully note that the emergence of Beltrami field relations from the Hillion-Quinnez model, is not due to an ad hoc rendering of the EM field relations, but is a logically consistent result that follows from recognizing that any electromagnetic field in a homogeneous, isotropic medium in free space, away from charges and currents, can be expressed either in terms of the spinors fa, or in terms of the complex Hertz-vector II. 

For a monochromatic wave of frequency oa in an inhomogeneous and isotropic medium of refraction index n r), the electromagnetic field satisfies Eq. (1) with k given by... 

At present the density effect has been quite thoroughly studied both theoretically and experimentally. There are different ways of obtaining the calculation formulas for Se. In particular, we can make allowance for the effect the surrounding medium has on the electromagnetic field of a particle by making the substitution c2—c2/e(a>) in the formula for the relativistic differential cross section of energy and momentum transfer... 

Electromagnetic fields are all around us and are not necessarily evil. For instance, without these fields radios and televisions would not work, and cell phones would be useless. The garage door opener could not be used from the comfort of a car and the door would not automatically open. Electromagnetic energy is needed for day-to-day lives. It just so happens that some electronic devices may be sensitive to the fields. Fortunately, exposure of such devices to the fields can be reduced. As discussed earlier, shields, filters, and isolation techniques are useful tools that allow us to live in the EMI environment. It is a matter of determining the source of the interference, the tolerance level of the victim, and the medium that is providing a means of interaction between the two. All EMI problems require knowledge of all three factors for an effective solution. 

A three-layer, planar optical waveguide consists basically of a high-RI film with RI np that is sandwiched between two lower-refractive-index materials referred to as the substrate and the cover medium with RIs ns and c> respectively Fig. 2. If Maxwell s equations are solved for such a layered structure, the following solutions for the electromagnetic field [Pg.281]

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