Studies On Optical And Electronic Properties For SML & Generalized Thue-Morse Quasiperiodic Superlattices

In this thesis, we mainly investigated the spectral properties of two-dimensional SML quasilattices, and the transmission properties of light through both SML quasiperiodic multilayers and Generalized Thue-Morse ones.First of all, after establishing the method of constructing a class of two-dimensional SML quasilattices, in the framework of single-electronic tight-binding nearest-interaction transfer model, we have studied the spectral properties of two-dimensional SML quasilattices by means of a decomposition-decimation method based the renormalization-group technique. It is found that the spectra have a variety of multifurcating structures, the total spectra are symmetrical, and every spectral line splits into odd sub-bands in the higher hierarchy. The analytic results show that under the first approximation, there exist only six kinds of clusters and the bare energy splits into thirteen subbands, and under the second approximation, several kinds of new spitting manners occur, e.g., 1:33, 1:19. The analytical results are confirmed by numerical simulations.Secondly, we introduce the substitution rules of SML model, study the transmission properties of light through SML quasiperiodic multilayers by means of the electromagnetic wave theory and matrix one. The trace map of propagation matrices, invariant of motion, and the expression for transmission coefficient are obtained. We find that the half of the propagation matrices' traces posses interesting symmetric and antisymmetric properties to the point of θ = π /2 . When light transmits normally the multilayers, the propagation matrices exhibit apseudo-seven-cycle feature and transmission coefficients posses quasi-seven-cycle properties (...→ C1 → Tj7 → Tj1 → Tj2 → C2 → Tj4 → C1...). These analyticresults are confirmed by numerical simulations.Finally, we study the transmission properties of light through GeneralizedThue-Morse systems followed by the substitution rules: B - Bm A", A ? A"Bm. Theexpressions for propagation matrices and transmission coefficients are obtained. First of all, we discuss two kinds of special cases: (1) m = l and n is natural number; (2) n = 1 and m is natural number, when light transmits normally the multilayers followed by Generalized Thue-Morse sequences, obtain the propagation matrices and corresponding transmission coefficients. Then we find when both parameter m and n are natural numbers, there exist four kinds of cases for propagation matrices andcorresponding transmission coefficients: (l)When m = 2i, n-2jthe former exhibit a unite matrix feature and the later are constant C1 ; (2)When m=2i, n=2j+l, the former are two-cycled, and the later are constant C2; (3)When m = 2i +1, n = 2j the former are two-cycled, and the later are a constant of Cx; (4)When m = 2i + 1, n = 2j+1 the former are diagonal except 1 st-generation system, and the two non-zeroelements are count-downs for each other, and the later will rapidly decrease to zero with the increase of both the generation and the parameter m, n. These analytic results are confirmed by numerical simulations.