Abstract
In recent years, twisted bilayer graphene has become a hot topic and inspired the upsurge of research on the photonic moir\'e lattice. Here, we design a photonic moir\'e superlattice with two synthetic twist angles and construct a synthetic moir\'e sphere based on these two angles. Thus, we have more degrees of freedom to design the band structure flexibly. A type of transition photonic band (TPB) is obtained in such a moir\'e superlattice. We investigate the influence of two twist angles on TPBs and find a series of magic angle pairs with optimal band compression of the TPB. Interesting optical properties of TPBs are experimentally demonstrated, including pulse delay, nonlinear optical enhancement, and pulse-width compression. Our work introduces an alternative path to explore multitwist-angle moir\'e superlattices and reveals that the designed photonic moir\'e superlattice based on moir\'e spheres has broad application prospects, including optical signal processing, nonlinear optic processes, and other light-matter interactions.
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