Applications of Chaos and Fractal Theories in the Field of Electromagnetic Scattering - Intelligent Computing for Sustainable Energy and Environment - page 61

quasi-random antenna arrays which had fractal inherent by combining virtrues
of the periodic subarray generators with those of random initiators. The cur-
rent response of the fractal antenna arrays was studied and a modified fractal
dimension was introduced in order to characterize the energy distribution in
the radiation pattern. The research showed that the radiation pattern of the
subarray became the envelope of the overall radiation pattern which forced the
sidelobe pattern to be well controlled[16].
In recent researches, based on FBM, Giuseppe Ruello et al presented an inno-
vative procedure for manufacturing fractal surfaces using Weierstrass function. A
cardboard-aluminum fractal surface was built as a representation of WM fractal
process. The comparison between the obtained calibrated data and the theoret-
ical results deriving from the FBM using the KA and SPM (small perturbation
method) showed matching and discrepancies between theoretical prediction and
experimental results. They concluded that fractal synthesis was closer to exper-
imental date and that the surface was eciently described in terms of only two
intrinsic parameters, the standard deviation and the correlation length[17].
It's well known that fractals can eciently reflect(and conduct) EM waves
with wavelengths much larger than fractal dimensions. In the year of 1993, Sha-
laev predicted that strong localization of dipole radiation in fractals results in
very high local fields[18]. In order to gain a deeper understanding of the pro-
cesses responsible for EM wave localization in 3-D fractals, Semouchkina and
Miyamoto et al produced a second stage 3 D Menger sponge of 81 81 mm 3

the same way that the Cantor bar formed. In the experiment, the Menger sponge
was illuminated by EM waves whose frequency range was 6 20GHz. The exper-
iment confirmed deep attenuation of reflection and transmission characteristics
of Menger sponge and an increase in 90 o scattering at a previously found local-
ization frequency. Simulations of FDTD(finite-difference time-domain) demon-
strated a formation of the full wavelength resonance in the central cavity and a
bandgap which could be considered as a signature of the bandgap formation of
the front side. EM energy inside the fractal structure in the narrow frequency
band. When it was blocked by the resonances in the front part of the sponge,
equalizing and symmetrization of the EM response showed up from different
parts of the structure[19].

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3.4 The Application of Chaos and Fractal in Scatter Communication

In the field of scatter communication, EM waves can be scattered by troposphere,
Ionosphere, meteor trail, manmade scatters and so on. EM waves could be scat-
tered into any direction, only the ones scattered the way nearly front can reach far
away. The energy dissipation in scatter communication is so much that EM waves
received are usually very feeble. To solve this problem, transmitter of high-power,
termination of high level sensitivity and antenna of great gain and narrow wave
band are adapted traditionally[20]. Theories of chaos and fractal bring new ways
to make this problem resolved. Chaos system is very propitious to detect weak
signal as it is sensitive to even a small change of the initial value. Nie Chun-yan