摘要

In this paper we Study under the small-signal approximation the properties of the Output electric field of second harmonic generation (SHG) for vertical transmission in Family A of the generalized Fibonacci (GF(m, 1)) quasiperiodic ferroelectric domain system. It is found that under perfect quasi-phase-matched (PQPM) conditions there exists self-similarity for the intense peaks of SHG (IPSHG) in real space and the two integers q and p indexing IPSHG make an interesting zero-odd set when in is large enough. On the other hand, self-similarity for IPSHG is broken under imperfect quasi-phase-matched (IQPM) conditions and the SHG spectra comprise a group of intense peaks and another group of satellite weak lines when in is very large. The corresponding integers q and p make an interesting odd-odd set and a successive integer set, respectively. Two kinds of effects of vacancies on SHG have also been found. The analytical results are confirmed by numerical simulations.