In this article, the increase of the efficiency of second-harmonic generation (SHG) from MoS2 monolayers embedded in different one-dimensional Fibonacci photonic crystal structures is investigated. The systems contain ZnS, SiO2, and MoS2 layers with the same thickness of ZnS and SiO2 films, which are arranged on the basis of different Fibonacci sequences. The transfer matrix method is used to calculate the forward and backward SHG efficiencies in the undepleted pump approximation. The thicknesses of the ZnS and SiO2 films are changed to obtain the maximum frequency conversion in different structures. Tuning the thicknesses causes the second-harmonic waves generated in each MoS2 monolayer to interfere constructively. Also, the fundamental and second-harmonic wavelengths are both located at the photonic band gap edges, where the density of electromagnetic modes and the nonlinear interaction time are enhanced. Our results show that the SHG efficiencies were increased in quasiperiodic photonic crystals with respect to the periodic structure with the same number of MoS2 layers. In Fibonacci photonic crystal structures there are more geometrical parameters that can be tuned to obtain the highest efficiencies. Furthermore, we used a Bragg mirror at one side of each structure to control the propagation direction of the generated second-harmonic waves and to decrease the backward waves, which led to enhancement of the forward waves.

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