Quasi-Phase-Matched Second Harmonic Generation In GF(m, N) Optical Superlattices

In this thesis, we mainly investigated the properties of quasi-phase-matched (QPM)second-harmonic generation (SHG) in generalized Fibonacci (GF(m, n)) optical super-lattices. Generally, in terms of the symmetry of sequence, the GF(m, n) sequences canbe devided into Family A and Family B. By use of two different methods, In this thesisthe distribution of SHG spectra in these two kinds of optical superlattices were studiedtheoretically, respectively.On the one hand, under the small-singal and plane wave approximation we have stud-ied the properties of SHG in one-dismensinal (1D) GF(m, 1) ferroelectric superlattices, byuse of the projection and Fourier transform method. The analytic formula of the outputelectric field of SHG and the corresponding spectra for different models were obtained.(1) It was found that in the case of perfect QPM (PQPM), when m changes from smallto large, the structure, the relative intensity, and the position of SHG peaks all tend tobe stable. If m is big enough, the two integers q and p indexing the intense peaks of SHGcompose an interesting zero-odd set. (2) In the case of imperfect QPM (IQPM), SHGspectra are made up of a group of intense peaks and another group of satellite weak lineswhen m is large enough. The two integers q and p indexing these two kinds of SHG linescompose corresponding odd-odd set and successive integers one. (3) The self-similarityof intense peaks of SHG was studied and it only exists in real space when the PQPMcondtion is satisfied. In other situations, the self-similarity would be borken. (4) Fordifferent phase-matched conditions, two different kinds of effects of vacancies of SHG havealso been found. In conclusion, GF(m, 1) are not perfect quasiperiodic sequences andthe substitution method for generating GF(m, 1) is not accordant with the correspond-ing projection one completely. So the sequences have two important irrationals,δ_m andτ_m. This is quite different from that of FC(n) sequences which are perfect quasiperiodicones, where only one characteristic parameterψ_n exsits in their sequences. It makes thestructures of GF(m,1)'s fitting PQPM condition should be dependent on both of the twoirrationals,δ_m andτ_m. The analytic results were confirmed by the numerical simulations.On the other hand, we investigated the properties of distribution of SHG spectrain GF(1, n) optical superlattice by use of numerical calculation. For a Fibonacci (i.e. n=1 for GF(1, n)) quasiperiodic optical superlattice, the dependence of the relativeintensity of SHG I(2ω) on the the ratio of l_A to l_B andλof fundamental beam has beenstudied. It was found that the thicknesses of polarized domains of the Fibonacci opticalsuperlattices only influence the intensity but not the position of SHG peaks and the SHGwith certain wavelength can be generated by a superlattice system only depends on thestructure (sequence, symmetry) of the system but not the thicknesses of domains. In thecase of l_A/IB=τ= (1+5^1/2)/2, our numerical results were accordant with the previoustheoretical analysis. Additionally, we have found that the distribution of SHG spectrain GF(1, n) (n＞2) aperiodic optical superlattices and Fibonacci quasiperiodic one arequite different, the latter is composed of a series of isolatedδpeaks while the formersare made up of compound peaks which comprise someδpeaks mixing with some quasi-consecutive "mountains". The more reciprocal vectors the superlattice system provides,the more plentiful spectral structures of SHG it will obtain. The numerical calculationmethod used here can be carried over to the other types of aperiodic and disordered opticalsuperlattices.