Nonlinear 2D layered crystals provide ideal platforms for applications and fundamental studies in ultrathin nonlinear optical (NLO) devices. However, the NLO frequency conversion efficiency constrained by lattice symmetry is still limited by layer numbers of 2D crystals. In this work, 3R MoS with broken inversion symmetry structure are grown and proved to be excellent NLO 2D crystals from monolayer (0.65 nm) toward bulk-like (300 nm) dimension. Thickness and wavelength-dependent second harmonic generation spectra offer the selection rules of appropriate working conditions. A model comprising of bulk nonlinear contribution and interface interaction is proposed to interpret the observed nonlinear behavior. Polarization enhancement with two petals along staggered stacking direction appears in 3R MoS is first observed and the robust polarization of 3R MoS crystal is caused by the retained broken inversion symmetry. The results provide a new arena for realizing ultrathin NLO devices for 2D layered materials.

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The reproducing kernel particle method (RKPM) for the elastic mechanical problems of the functionally graded materials (FGM) is proposed in this paper. The corresponding formulae of the RKPM for the FGM are derived. Furthermore, the control parameter of influence domain radius, penalty factor and different node distribution on the calculation accuracy are discussed. The different functional gradient exponents of the FGM are analyzed. The numerical results illustrate that the RKPM is correct and effective to solve the elastic mechanical problems of the FGM.

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