Electromagnetic waves defined

Fig. 6.23. The direction of the electric-field vector of the electromagnetic wave defines the direction of polarization. In the upper diagram, the electric-field vector travels in the y-direction (y-polarized light), and in the lower diagram, in the x-direction (x-polarized light).

In the conventional solution of MEs as plane electromagnetic waves, the direction of propagation G is always perpendicular to the plane hence, it is time-independent. Let an external observer of the electromagnetic wave define the z-axis as parallel to G. Then, G = G(f)k, and (G) = (G)k. 

If measurements are made in thin oxide films (of thickness less than 5 nm), at highly polished Al, within a small acceptance angle (a < 5°), well-defined additional maxima and minima in excitation (PL) and emission (PL and EL) spectra appear.322 This structure has been explained as a result of interference between monochromatic electromagnetic waves passing directly through the oxide film and EM waves reflected from the Al surface. In a series of papers,318-320 this effect has been explored as a means for precise determination of anodic oxide film thickness (or growth rate), refractive index, porosity, mean range of electron avalanches, transport numbers, etc. 

The first cosine factor represents a wave like the originals with average wavelength and frequency and moving with velocity (uq + us2)/ k + k2). In the case of electromagnetic waves u = cAq and w2 = cfc2j so that v = c(ki + k2)/(ki + k2) = c, the original velocity. The composite wave however, has an amplitude that varies within a profile defined by the factor... 

The velocity of electromagnetic waves through any material other than the vacuum is (e ) 2 = v and the ratio n = c/v is called the index of refraction of that material. It follows that n = y /x/eoMo and, since the ratio n/fio 1, except for ferromagnetic materials, the index of refraction is commonly defined as the square root of the dielectric constant, e/e0- Since the frequency of the field is not affected by the medium, refraction can be described equally well as a change of the wavelength of light passing between different transparent media. 

This invariance defines the principle of (Galilean) relativity, once thought to be universally valid. However, the situation for electromagnetic waves is different and the form of equation (22) is destroyed3 under a transformation... 

The electromagnetic field defined above is a solution of Maxwell s equations, provided the new potentials . C are solutions of wave equations and satisfy the Lorenz gauge. 

The simplest example of the generation of energy from a pure gauge vacuum is to consider the case of an electromagnetic potential plane wave defined by... 

Let us consider the propagation of electromagnetic waves with both fields nonzero E O and B 0. As usual, propagation is parallel to the Poynting vector G, defined in Eq. (17). Evidently, by definition, vector G is perpendicular to both fields E and B. Hence, there cannot exist components of the magnetic field B parallel to the instantaneous direction of propagation G. 

The second (real) term accounts for the exponential decay of the electric field intensity in the direction normal to the interface. The reflected beam combines with the incident beam, forming a standing electromagnetic wave at the interface (Fig. 9.9). The electric field that penetrates to the optically rarer medium of refractive index n, the evanescent field, plays a critical role in many optical sensors based on the waveguiding principle. Its depth of penetration dv is defined as the distance at which the initial intensity Eq decays to 1/e of its value. Thus from (9.18), dv is... 

It is useful to consider the solution of Maxwell s Equations (5.1) for plane electromagnetic waves in the absence of boundary conditions, which can be written as exp[i(/ 2 — u>t) assuming propagation in z-direction of cartesian coordinates. The quantity / is the complex propagation constant of the medium with dominant real part for dielectrics and dominant imaginary part for metals. The impedance of the medium, Z, defined as ratio of electric to magnetic field is related to / by Z = ojp,0/f3 with /x0 = 1.256 x 10 6 Vs/Am. As it can be derived from Maxwell s equations, the impedance is related to the conductivity/dielectric function by the following expression ... 

When an electromagnetic wave, described by an electric field, E, impinges on a material, the absorption of the electromagnetic wave as a function of z behaves as E - exp /2, so the intensity falls off as / - exp . The immediate goal is to relate this classical absorption coefficient, a, which is the quantity of experimental interest, to the theory, wherein the quantum-mechanical mechanism responsible for absorbing a photon of a given frequency is found. To do this, a is defined as [18]... 

The lateral image resolution is defined by the ability of the imaging system to differentiate between two point objects separated by a small distance. The minimum distance at which the objects can be successfully differentiated is defined to be the resolution. The resolution for millimeter-wave imaging systems is limited by diffraction of the electromagnetic waves. Two objects can be resolved by an imaging system if the phase variation across the aperture differs by at least 2tt radians or one cycle [54], This definition leads to an angular resolution of... 

Problem 8.1.5) by using the electromagnetic wave equation and a frequency-dependent complex dielectric constant e(co) defined by... 

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