We theoretically investigate second-harmonic generation (SHG) from bilayer-graphene (BLG) embedded in photonic crystals (PCs) using the transfer-matrix method. Two kinds of cases are considered. One is a single BLG layer embedded in the defective PC; the other is a stack of BLG layers in the dielectric multilayer structure. It is found that the improved field localization within the defective PC enhances SHG by three orders of magnitude compared with the bare BLG. Although the SHG efficiency from the stack of BLG layers in the dielectric multilayer structure is lower than that from the defective PC due to the effect of absorption, there are some advantages in controlling the polarization dependence of the SHG for such a case. For example, various intensity ratios of -polarized and -polarized second-harmonic outputs can be realized by adjusting the azimuthal rotational angles of the BLG layers for the incident wave with a certain polarization. We believe that these phenomena are very beneficial for the design of optical devices.
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