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We employed caustic theory to analyze the propagation dynamics of partially coherent self-accelerating beams such as self-healing of partially coherent Airy beams. Our findings revealed that as the spatial coherence decreases, the self-healing ability of beams increases. This result have been demonstrated both in simulation and experiment. This is an innovative application of the caustic theory to the field of partially coherent structured beams, and provides a comprehensive understanding of self-healing property. Our results have significant implications for practical applications of partially coherent beams in fields such as optical communication, encryption, and imaging., 9 pages, 4 figures

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

Photonic analogs of the moir\'e 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 moir\'e 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 moir\'e flatbands, providing new opportunities to utilize photonic moir\'e superlattices for advanced light-matter interaction including lasing and nonlinear harmonic generation., Comment: 5 pages, 5 figures

To date, second-harmonic generation (SHG) at nanoscale has been concentrated on employing high-refractive-index nanostructures, owing to the strong field confinement at deep subwavelength scales based on optically resonant effects. However, low-index nanostructures generally exhibit weaker resonant effects and lower field confinement. To address this issue, by harnessing the large nonlinearity of LiNbO$\mathrm{_3}$, we propose a novel approach to employ guided resonances and bound states in the continuum (BICs) with a LiNbO$\mathrm{_3}$ metasurface consisting of a LiNbO$\mathrm{_3}$ disk array sitting on a LiNbO3 thin film. Such a system can transform the guided modes supported by LiNbO$\mathrm{_3}$ thin film into high-quality guided resonances which can be excited directly under plane-wave illumination. Importantly, we further demonstrate strong field confinement inside LiNbO3 thin film with tailorable Q-factor by realising a Friedrich-Wintgen BIC. Such a unique mode engineering enables a record-high SHG efficiency of 5\% under a pump intensity as low as 0.4 $\mathrm{MW/cm^{2}}$. Moreover, we reveal the influence of nonlinear resonances and cross-coupling on the SHG by showing the anomalous SHG and efficiency tuning with the rotation of the crystal axis. Our work offers a new route to constructing enhanced SHG based on high-Q guided resonances and BICs, including low-index and high-index nonlinear materials., 11 pages, 7 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

While a three-dimensional (3D) scattering medium is from the outset opaque, such a medium sustains intriguing transport channels with near-unity transmission that are pursued for fundamental reasons and for applications in solid-state lighting, random lasers, solar cells, and biomedical optics. Here, we study the 3D spatially resolved distribution of the energy density of light in a 3D scattering medium upon the excitation of highly transmitting channels. The coupling into these channels is excited by spatially shaping the incident optical wavefronts to a focus on the back surface. To probe the local energy density, we excite isolated fluorescent nanospheres distributed inside the medium. From the spatial fluorescent intensity pattern we obtain the position of each nanosphere, while the total fluorescent intensity gauges the energy density. Our 3D spatially resolved measurements reveal that the differential fluorescent enhancement changes with depth, up to 26× at the back surface of the medium, and the enhancement reveals a strong peak versus transverse position. We successfully interpret our results with a newly developed 3D model without adjustable parameters that considers the time-reversed diffusion starting from a point source at the back surface.

We study the three-dimensional (3D) spatially-resolved distribution of the energy density of light in a 3D scattering medium upon the excitation of open transmission channels. The open transmission channels are excited by spatially shaping the incident optical wavefronts. To probe the local energy density, we excite isolated fluorescent nanospheres distributed inside the medium. From the spatial fluorescent intensity pattern we obtain the position of each nanosphere, while the total fluorescent intensity gauges the energy density. Our 3D spatially-resolved measurements reveal that the local energy density versus depth (z) is enhanced up to 26X at the back surface of the medium, while it strongly depends on the transverse (x; y) position. We successfully interpret our results with a newly developed 3D model that considers the time-reversed diffusion starting from a point source at the back surface. Our results are relevant for white LEDs, random lasers, solar cells, and biomedical optics.

Random scattering is usually viewed as a serious nuisance in optical imaging, and needs to be prevented in the conventional imaging scheme based on single-photon interference. Here we proposed a two-photon imaging scheme with the widely used lens replaced by a dynamic random medium. In contrast to destroying imaging process, the dynamic random medium in our scheme works as a crucial imaging element to bring constructive interference, and allows us to image an object from light field scattered by this dynamic random medium. On the one hand, our imaging scheme with incoherent two-photon illumination enables us to achieve super-resolution imaging with the resolution reaching Heisenberg limit. On the other hand, with coherent two-photon illumination, the image of a pure-phase object can be obtained in our imaging scheme. These results show new possibilities to overcome bottleneck of widely used single-photon imaging by developing imaging method based on multi-photon interference.

High-order coherence effects between two first-order incoherent sources with fully independent phases have been well studied in the literature, which shows interference fringes with respect to the position separations among different space points. Here we show that this is not the whole story, and find that the high-order coherence effects depend on the mode of the phase random walk of the first-order incoherent sources, which can be controlled artificially and represented geometrically by vectorial polygons. Interestingly, by scanning the detectors along the same direction with the position separations between them kept constant, a set of high-order coherence fringes, which fingerprint the phase random walk of the first-order incoherent sources, can be observed. Our results show that it is possible to control the high-order coherence of two first-order incoherent sources, which could have important practical applications such as superhigh resolution optical lithography., 6 pages, 5 figures