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Plenty of exotic phenomena in moiré superlattices arise from the emergence of flatbands, but their significance could be diminished by structural disorders that will significantly alter flatbands. Thus, unveiling the effects of disorder on moiré flatbands is crucial. In this work, we explore the disorder effects on two sets of flatbands in silicon-based mismatched moiré superlattices, where the level of disorder is controlled by varying the magnitude of random perturbations of the locations of silicon strips. The results reveal that, after ensemble averaging, the average spectral positions of the four flatbands exhibit stability despite variations in the degree of disorder. However, the δ-like density of states (DOS) related to flatbands in the perfect superlattice evolves into a finite-width envelope of high DOS. By increasing the level of disorder, the width of the DOS envelope increases accordingly. Particularly, we observe a fascinating contrast: the width of bandgap flatbands saturates after initial growth, while the width of dispersive-band-crossed flatbands exhibits a linear increase versus the disorder. This unveils fundamental differences in how flatbands respond to structural imperfections, offering crucial insights into their perturbation characteristics within moiré superlattices. Our work offers new perspectives on flatbands in partially disordered moiré superlattices.

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.

Single-pixel imaging (SPI) is a novel lens-free imaging method quite different from the conventional spatially resolved imaging, yet it suffers the Rayleigh resolution limit imposed by the illumination aperture. Here we show that the Rayleigh resolution limit in SPI can be overcome by employing optical fluctuation. With Nth-order autocorrelation of the signal measured by the bucket detector in SPI, the imaging resolution can surpass the Rayleigh resolution limit by a factor of N. This result is important for optical microscopy based on SPI.

By using a dynamically phase-controlled screen proposed in [Opt. Express 25, 22789 (2017)], we demonstrated experimentally a correlation imaging scheme with its spatial resolution reaching the fundamental Heisenberg limit. In the experiments, the dynamically phase-controlled screen was realized through a commercial spatial light modulator by dynamically loading computer generated phase patterns, and the scanning-focused-beam illumination mode was employed to achieve the Heisenberg-resolution imaging with classical light such as laser and pseudo-thermal light.

We propose a N-photon imaging scheme with the resolution reaching the fundamental Heisenberg limit. The key imaging element is a phase-controlled screen which introduces synchronous-position N-photon interference, giving rise to enhanced resolution that exceeds the well-known Rayleigh resolution limit by a factor of N. In the standard wide-field illumination situation, our imaging scheme requires an entangled source to illuminate the object. Besides, we show that classical light is also applicable to realize this Heisenberg-resolution imaging if a scanning-focused-beam illumination is used. Our N-photon imaging scheme is practically realizable by using current well-developed technology.

By generalizing the phase structure of the random-phase grating we recently designed [Opt. Express21, 14056 (2013)OPEXFF1094-408710.1364/OE.21.014056], we show that non-HBT type (synchronous position) two-photon grating interference can be obtained, which physically relies on groups of multiple indistinguishable two-photon paths modulated by the spatial distributions of phase modes. By properly selecting the random-phase structures, synchronous position subwavelength interference can be obtained, the period of which, in the two-photon interference domain, is decreased by a factor N (=3,4,5,6,…), depending on the slit number and random-phase structure, and the visibility of N-fold subwavelength interference fringes could be improved by increasing the slit number of the grating. The results show that modulation on two-photon paths via spatial arrangements of the phase modes offers the possibility to actively control the optical high-order coherence in the same optical scheme.

Two-photon interference with independent classical sources, in which superposition of two indistinguishable two-photon paths plays a key role, is of limited visibility with a maximum value of 50%. By using a random-phase grating to modulate the wavefront of a coherent light, we introduce superposition of multiple indistinguishable two-photon paths, which enhances the two-photon interference effect with a signature of visibility exceeding 50%. The result shows the importance of phase control in the control of high-order coherence of classical light.