Studies On Optical And Electronic Properties For Fibonacci-class & Generalized Fibonacci Superlattices

In this thesis, we mainly investigated the spectral properties of two-dimensional Fibonacci-class quasilattices and the transmission properties of light through Generalized Fibonacci multilayers.On the basis of our former work and by means of the decomposition-decimation method, we firstly study the splitting rules for the second hierarchy of the electronic energy spectra for two-dimensional Fibonacci-class quasicrystals with one kind of atom and two bond lengths. It is found that every line of the sub-spectra for n×n and (n + 1)×(n +1)clusters of FC(n) (n>2) splits as type Y(n-1)-2-1 and Yn-2-1, respectively. The one for n×(n + 1) clusters of FC(n) consists of three sub-subbands when n≤2, and fivesub-subbranches when n > 3 . The general formulae of the number of energy levels for the spectra of the second hierarchy are obtained. The analytical results are confirmed by numerical simulations.Secondely, by means of a decomposition-decimation method we study the splitting rules of energy spectra for two-dimensional Fibonacci-class quasilattices with three kinds of atoms (A, B, and C) and one bond length, and find that the sublattices of B atoms and C atoms are different from those of normal two-dimensional FC(n) and the corresponding splitting manners are new and interesting. B atom forms a kind of two-dimensional so-called FC(n)', which structure is some different from that of normal FC(n-1)(n > 2), but the spectra lines are as the same as that of the latter. C atom forms two kinds of interesting one-dimensional periodic chains: n-atom chain and (n-1)-atom chain, which spectra will both tend to become continuous, respectively. The analytical results are also confirmed by numerical simulations.Thirdly, the transmission properties of light through Generalized Fibonacci systems,which follows by the substitution rules: B→A, A→AmBn are studied. The expressions for propagation matrices and transmission coefficients are obtained. First of all, when lighttransmits normally the multilayers followed by Generalized Fibonacci sequences, we find that when parameters m and n are variable, there exist four kinds of cases for propagation matrices and corresponding transmission coefficients: (1) when m and n are both even, the former are four different matrices for the first-four generations and all aidentity matrix for gth-generation (q ≥ 5), the latter are all equal to a constant of B2 =1for all generations except for the 2nd generation; (2) for odd m andeven n, for 1 st-generation the latter is equal to B2; from 2nd-generation on the former aretwo-cycle and the latter are a constant of B1; (3) for even m and odd n, the former arefour-cycle and the latter are two-cycle; (4)when m and n are both odd, the former and the latter are pseudo-six-cycle when n = 1; when n ≥ 3, the latter are two constants for the first-three generations; from 4th-generation on, the latter are pseudo-three-cycle when m = n and decay to zero in three different cases when m≠n. The analytic results are confirmed by numerical simulations.