Page 56 - Integrated Wireless Propagation Models

34 C h a p t e r O n e

1.9.2 Diffraction

1.9. . 1 Fresnel Zones and Huygens' Principle
2
From the propagation of electromagnetic wave, if the wave impacts on an obstacle that
is "large" compared to the wavelength in dimension, reflection usually occurs, while if
it impacts on an obstacle that is more or less the same wavelength in dimension, diffrac­
tion usually occurs. Diffraction is a physical phenomenon that an electromagnetic
wave can pass around an obstacle. Huygens' principle provides some insight into
diffraction.33 The Principle states that every point of the wave front can act as a source
to generate a secondary wavelet when the wave front encounters a obstacle.
Let's assume that the wave front is infinite. Then if an obstacle blocks some part of
the wave front, the wave front will produce some wavelets, and these wavelets that
occurs around the obstacle are disturbed. The directions of these wavelet propagations
may be different from the original wave front. This phenomenon is called diffraction.
Let's consider a scenario shown in Fig. . 9.2 1 . 1 that a plane wave front moves
1
.
'
toward the plane obstacle AA with several holes, and these holes are relatively not
large to the wavelength so that diffraction can occur. From the observation, we notice
'
that the diffracted wavelet beyond AA points to different directions, and in each direc­
tion the amplitude of the wavelet is different, proportional to (1 + cosa ), and will be
shown in Eq. (1.9.2.1.3) later. When the wavelet has the same direction as the original
wave front (a = 0), the amplitude reaches the maximum value 2, while when the wave­
let has the opposite direction as the original wave front (a = ) , the amplitude reaches
n
the minimum value 0. Therefore, the amplitude of the wavelet varies from 0 to 2,
2
depending on the angle a from 0° to 180°, as shown in the equation ::; 1 + cosa ::; .
0
Several facts are observed:
Diffraction still happens regardless of whether the obstacle is conductive or non­
conductive.
The fields of the shadow area are not strictly zeroes because the directions of the
wavelets could be different from the propagation of the original wave front, and the
propagation energy could reach the shadow area via diffraction.
We can calculate the fields of the shadow area based on Huygens' principle. The
amplitude of the wavelet is proportional to the angle between the directions of the
original wave front and wavelets.

Wavelet
FIGURE 1.9.2.1.1 Diffraction illustrated.