The low-frequency magneto-optical properties of bilayer Bernal graphene are studied by the tight-binding model with the four most important interlayer interactions taken into account. Since the main features of the wave functions are well-depicted, the Landau levels can be divided into two groups based on the characteristics of the wave functions. These Landau levels lead to four categories of absorption peaks in the optical absorption spectra. Such absorption peaks own complex optical selection rules, and these rules can be reasonably explained by the characteristics of the wave functions. In addition, twin-peak structures, regular frequency-dependent absorption rates, and complex field-dependent frequencies are also obtained in this work. The main features of the absorption peaks are very different from those in monolayer graphene and have their origin in the interlayer interactions.

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The low-frequency optical excitations of AA-stacked bilayer graphene are investigated by the tight-binding model. Two groups of asymmetric LLs lead to two kinds of absorption peaks resulting from only intragroup excitations. Each absorption peak obeys a single selection rule similar to that of monolayer graphene. The excitation channel of each peak is changed as the field strength approaches a critical strength. This alteration of the excitation channel is strongly related to the setting of the Fermi level. The peculiar optical properties can be attributed to the characteristics of the LL wave functions of the two LL groups. A detailed comparison of optical properties between AA-stacked and AB-stacked bilayer graphenes is also offered. The compared results demonstrate that the optical properties are strongly dominated by the stacking symmetry. Furthermore, the presented results may be used to discriminate AABG from MG, which can be hardly done by STM