Abstract
We study the transmission properties of light through the symmetric Fibonacci-class $[\mathrm{SFC}(n)]$ quasiperiodic dielectric multilayers, which possess a mirror symmetry. For a normal incidence of light, many perfect transmission peaks (the transmission coefficients are unity) are numerically obtained. The transmission coefficient exhibits a two-cycle feature in a family of the $\mathrm{SFC}(n)$ with an odd n, while a three-cycle feature in another family with an even n. The scaling factors $f(n),$ which give a description of the self-similar behaviors of transmission spectra, are analytical obtained. Let ${m}_{\mathrm{ij}}^{(n)}(k)$ $(i,j=1,2)$ be the elements of the total transfer matrix of the $k\mathrm{th}$ generation of $\mathrm{SFC}(n);$ it is proven that the positions (wavelength) of the perfect transmission peaks can be uniquely determined by ${m}_{12}^{(n)}{(k)+m}_{21}^{(n)}(k)=0.$ The analytical results are very well confirmed by the numerical calculations.
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