In addition, we have a new velocity field V, which has the role of indicating the direction and speed of development of the energy flow (a sort of generalization of the
Poynting vector).
The on-surface longitudinal
Poynting vector of a 10-wavelength, center-fed dipole consequently also decays with distance as shown in Figure 3 [17].
Figure 7 demonstrates magnetic field [H.sub.z] (Figure 7(a)) and
Poynting vector [P.sub.y] (Figure 7(b)) pattern as a function on [k.sub.x] and y.
It has been obtained that a real part of the
Poynting vector normal component of a wave propagating in an anisotropic medium is not equal to zero when an incident wave propagates tangentially to an interface between the media.
Using the computed electromagnetic field values, the spatial distribution of the surface current density excited on the reflector and on the dipole arms, as well as the real part of the
Poynting vector, and the radiation patterns (see Figure 9) have been evaluated at the working frequencies of 5 GHz, 6 GHz, and 7 GHz, both for the antenna with and without metal reflector.
The linear momentum density is given by the
Poynting vector E x B and the angular momentum is the cross product of the
Poynting vector with the position vector.
This use of the right hand rule is called the
Poynting vector.
This choice can be expressed by means of the
Poynting vector of (E, H) evaluated at [c.sub.n] as
[r.sub.k] = [[[u.sub.k], [v.sub.k], [w.sub.k]].sup.T] = [[sin [[theta].sub.k] cos [[phi].sub.k], sin [[theta].sub.k] sin [[phi].sub.k], cos [[theta].sub.k]].sup.T] denotes the normalized
Poynting vector. [(x).sup.T] denotes the transpose.
To this end, let us consider the EM field distribution in the periodic structure and the imaginary part of the
Poynting vector. It is generally known, that the Poynting energy flux vector S is a complex quantity [39, 40]