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The self-accelerating beams such as the Airy beam show great potentials in many applications including optical manipulation, imaging and communication. However, their superior features during linear propagation could be easily corrupted by optical nonlinearity or spatial incoherence individually. Here we investigate how the interaction of spatial incoherence and nonlinear propagation affect the beam quality of Airy beam, and find that the two destroying factors can in fact balance each other. Our results show that the influence of coherence and nonlinearity on the propagation of partially incoherent Airy beams (PIABs) can be formulated as two exponential functions that have factors of opposite signs. With appropriate spatial coherence length, the PIABs not only resist the corruption of beam profile caused by self-focusing nonlinearity, but also exhibits less anomalous diffraction caused by the self-defocusing nonlinearity. Our work provides deep insight into how to maintain the beam quality of self-accelerating Airy beams by exploiting the interaction between partially incoherence and optical nonlinearity. Our results may bring about new possibilities for optimizing partially incoherent structured field and developing related applications such as optical communication, incoherent imaging and optical manipulations., Comment: 12pages,6 figures

Supplementary document

Photonic analogs of the moiré superlattices mediated by interlayer electromagnetic coupling are expected to give rise to rich phenomena such as nontrivial flatband topology. Here we propose and demonstrate a scheme to tune the flatbands in a bilayer moiré superlattice by employing the band-offset. The band-offset is changed by fixing the bands of one slab but shifting that of the other slab, which is realized by changing the thickness of latter slab. Our results show that the band-offset tuning not only makes a few flatbands emerge and disappear, but also leads to two sets of robustly formed flatbands. These robust flatbands form either at the AA-stack site or at the AB-stack site, enabling the construction of a tunable, high-quality, and doubly-resonant single-cell superlattice. Moreover, we develop a diagrammatic model to give an intuitive insight into the formation of the robust flatbands. Our work demonstrates a simple yet efficient way to design and control complex moiré flatbands, providing new opportunities to utilize photonic moiré superlattices for advanced light-matter interaction including lasing and nonlinear harmonic generation., 5 pages, 5 figures