Electromagnetic field strength

This part of our chapter has shown that the use of the two variables, moduli and phases, leads in a direct way to the derivation of the continuity and Hamilton-Jacobi equations for both scalar and spinor wave functions. For the latter case, we show that the differential equations for each spinor component are (in the nearly nomelativistic limit) approximately decoupled. Because of this decoupling (mutual independence) it appears that the reciprocal relations between phases and moduli derived in Section III hold to a good approximation for each spinor component separately, too. For velocities and electromagnetic field strengths that ate nomrally below the relativistic scale, the Berry phase obtained from the Schrddinger equation (for scalar fields) will not be altered by consideration of the Dirac equation. 

As a result, several schemes including cavity-enhanced Raman [6], photonic crystal-enhanced Raman [7], surface-enhanced Raman [8], etc., have been put forward in an attempt to increase the electromagnetic field strength for excitation. Among them, surface-enhanced Raman scattering (SERS), by far, is one of... 

The last expression gives the potential matrix in the standard representation. The transformation law (89) gives precisely the Poincare transformation of the electromagnetic field strengths E and B, which can be combined into a tensor field on Minkowski space. 

The transformation law of electromagnetic fields under Poincare transformations (as it follows from Maxwell s equations) is almost compatible with the potential transformation law (89). There is a slight mismatch concerning the behavior under the parity transformation. The matrix structure of (91) would require that the fields E and B change their sign under a space reflection, but the electromagnetic field strengths don t. Therefore, the Dirac equation with this potential matrix is not covariant with respect to a parity transformation. 

Figure 7.2 Schematic illustration of the electromagnetic field distribution around Au Pt coreshell NPs under laser irradiation (left, with 633 nm excitation). The dependence of the electromagnetic field strength (normalized with the strength on the Pt surface) on the distance from the Pt shell is shown in the right-hand plot, indicating that a substantially strong field enhancement can still be obtained on the surface. Reprinted from Ref [49] with permission from Royal Society of Chemistry.

As we have already stated, by dropping the point molecule supposition and thereby allowing for the fact that different parts of the molecule will see different electromagnetic field strengths at the same instant of time, Rosenfeld found to the next higher order of approximation that... 

As a model consider two solids, as shown in Fig. 2-1. The solids are separated from each other by a gap of width Zq. The internal electromagnetic fluctuation fields in solids set up an electromagnetic field F3, in the gap. The resultant electromagnetic field strengths 3 and 7/3 of the gap are used to determine the Maxwell electromagnetic stress tensor T. The force component parallel to the Z axis is... 

Before speaking about experimental results on controlling the reaction, we explain what is implied for phase characteristics of the light pulse. The electromagnetic field strength can be written in the form... 

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