Poynting s vector

Hence, the microwave wavelength varies between 1 m and 1 mm as the frequency increases. Each frequency range is referred to by its band designation as listed in Table 1. The microwave power (P) transmitted per unit area is given by Poynting s Vector as... 

Since is not ir/2, Poynting s vector for the extraordinary wave is not collinear with k the wave-vector (D is not parallel to E) and so the fundamental beam gradually walks away from the UV it has generated. This leads to an astigmatic UV beam. The extent of the walk-off Is given by the angle p which can be evaluated from the equation... 

Poynting s vector theorem can be derived from Maxwell s equations as a consequence of power conservation. It shows that the time-averaged power produced by a distribution of currents with density J within volume is given by[l]... 

Poynting s theorem for the energy flow of plane waves in vacuo thus applies to the EM and EMS modes, but not to the S mode. Vector multiplication of Eqs. (52) and (53) by k, and combination with Eq. (49) and the result E C = 0, is easily shown [16,20] to result in a Poynting vector that is parallel with the group velocity C of Eq. (56). Later in Section VII.C.3 we shall return to Poynting s theorem in the case of axisymmetric photon wavepackets. 

Thus we see that four of the conservation equations in (24) correspond to all four conservation equations of the standard theory one is the conservation of energy (25a) (Poynting s equation), and the other three are the conservation of the three components of momentum (25b) of the standard form of electromagnetic field theory. But since (24) are eight real-number valued equations rather than four, the spinor formalism predicts more facts than the standard vector Maxwell formalism—it is a true generalization. 

It was shown in Section 2.8.3 that the energy transferred by an electromagnetic wave is proportional to the square of the wave amplitude E. Without proof, we state that the energy density carried by a wave is defined by the vector product [E B] = S vector S being referred to as the Poynting vector. 

The average energy flux in the evanescent wave is given by the real part of the Poynting vector S = (c/47t)ExH. However, the probability of absorption of energy per unit time from the evanescent wave by an electric dipole-allowed transition of moment pa in a fluorophore is proportional to lnfl - El2. Note that Re S and pa E 2 are not proportional to each other they have a different dependence on 0. 

Consider an electromagnetic field (E, H), which is not necessarily time harmonic. The Poynting vector S = E X H specifies the magnitude and direction of the rate of transfer of electromagnetic energy at all points of space it is... 

The instantaneous Poynting vector (2.38) is a rapidly varying function of time for frequencies that are usually of interest. Most instruments are not capable of following the rapid oscillations of the instantaneous Poynting vector, but respond to some time average (S) ... 

When it is clear from the context that it is the time-averaged Poynting vector with which we are dealing, the brackets enclosing S will be omitted. 

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 ... 

S, the Poynting vector associated with the incident wave, is independent of position if the medium is nonabsorbing Ss is the Poynting vector of the scattered field and we may interpret Sext as the term that arises because of interaction between the incident and scattered waves. 

We showed in Section 3.3 that the total Poynting vector S in the region surrounding an arbitrary particle can be written as the sum of three terms ... 

Because of the symmetry conditions integration of the local forces (160) results in vanishing electric and magnetic volume forces Fe and Fm as given by Eqs. (13). Of the Poynting vector S and the electromagnetic momentum vector g... 

An absorption cross section, qabs = —E/S, is obtained from Eq. 2.83 by dividing by the magnitude of the Poynting vector, S, averaged over one period,... 

An electromagnetic wave transports energy. The energy flow per second per unit area (i.e., the intensity) is given by the Poynting vector S for an electromagnetic wave moving in vacuum,... 

Here, S(vac) is the Poynting vector of the U(l) configured vacuum, representing electromagnetic energy flow, and is defined by... 

In physical terms, this can be understood in the following way. Take an electromagnetic field with Poynting vector S = E x B. By a suitable Lorentz transformation [with direction unit vector n and velocity parameter q given by ntanh2ri = 2S/(E2 +B2)], we can change to a frame in which S = 0 at any... 

To see this, let us introduce some definitions first. The Poynting vector G represents energy flux density (units esu2cm-3 s-1 = ergcm2s 1). It is a capability of the electromagnetic field to perform work defined as... 

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