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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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