J. ZAGHDOUDI ET AL.
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width of the PBG is larger and the peak number increases.
We can notice that the effect of the Thue-Morse structure
of the system considered is obtained only from m = 4. In
the case where m = 2, it is clear that just the effect of
symmetry that appears (the appearance of a central peak at
the PBG of the system). It follows that when m increases
we have the following results:
The peak positions are symmetricaly about the central
peak.
The width of the complete PBG increases. Indeed, the
width of the band gap of the resulting system Br8/Tm/BR8
is the sum of the bandgaps of periodic systems and quasi-
periodic system (Thue-Morse). We note that the PBG of
the periodic system covers the spectral range between the
two PBGs of the Thue-Morse system. This result is very
important because it is possible to calculate the widh of
the PBG of the considered hybrid system from the spectra
of individual systems (Bragg and Thue-Morse) without
representing the spectrum of the entire structure.
4. Conclusions
The effect of symmetry applied to symmetric multilayer
systems results in the appearance of optical windows at
the PBG of the system which are symmetrical about the
value λ0/λ = 1.
The use of hybrid symmetric systems kinds PS/QPS/
PS and QPS/PS/QPS, at normal incidence in the visible
range show that:
The complete photonic bandage is the sum of individ-
ual bands from systems.
The width of the PBG and the optical windows, which
appear at this band, depend on the parameters and the
nature of the system built.
Also, the numbers of PBGs and transmission peaks are
controlled by the variations of the parameters n and m of
the symmetric Fibonacci and Thue-Morse structures. There-
fore, against the conventional quasi-periodic structures,
the hybrid systems offer the possibility of obtaining poly-
chromatic filters and of controlling the properties of these
filters.
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