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Super-resolution fluorescence microscopy is of great interest in life science studies for visualizing subcellular structures at the nanometer scale. Among various kinds of super-resolution approaches, image scanning microscopy (ISM) offers a doubled resolution enhancement in a simple and straightforward manner, based on the commonly used confocal microscopes. ISM is also suitable to be integrated with multi-photon microscopy techniques, such as two-photon excitation and second-harmonic generation imaging, for deep tissue imaging, but it remains the twofold limited resolution enhancement and requires expensive femtosecond lasers. Here, we present and experimentally demonstrate the super-linear ISM (SL-ISM) to push the resolution enhancement beyond the factor of two, with a single low-power, continuous-wave, and near-infrared laser, by harnessing the emission nonlinearity within the multiphoton excitation process of lanthanide-doped upconversion nanoparticles (UCNPs). Based on a modified confocal microscope, we achieve a resolution of about 120 nm, 1/8th of the excitation wavelength. Furthermore, we demonstrate a parallel detection strategy of SL-ISM with the multifocal structured excitation pattern, to speed up the acquisition frame rate. This method suggests a new perspective for super-resolution imaging or sensing, multi-photon imaging, and deep-tissue imaging with simple, low-cost, and straightforward implementations., Comment: 9 pages, 4 figures

Miniaturized on-chip spectrometers with small footprints, lightweight, and low cost are in great demand for portable optical sensing, lab-on-chip systems, and so on. Such miniaturized spectrometers are usually based on engineered spectral response units and then reconstruct unknown spectra with algorithms. However, due to the limited footprints of computational on-chip spectrometers, the recovered spectral resolution is limited by the number of integrated spectral response units/filters. Thus, it is challenging to improve the spectral resolution without increasing the number of used filters. Here we present a computational on-chip spectrometer using electrochromic filters that can be electrochemically modulated to increase the efficient sampling number for higher spectral resolution. These filters are directly integrated on top of the photodetector pixels, and the spectral modulation of the filters results from redox reactions during the dual injection of ions and electrons into the electrochromic material. We experimentally demonstrate that the spectral resolution of the proposed spectrometer can be effectively improved as the number of applied voltages increases. The average difference of the peak wavelengths between the reconstructed and the reference spectra decreases from 14.48 nm to 2.57 nm. We also demonstrate the proposed spectrometer can be worked with only four or two filter units, assisted by electrochromic modulation. This strategy suggests a new way to enhance the performance of miniaturized spectrometers with tunable spectral filters for high resolution, low-cost, and portable spectral sensing, and would also inspire the exploration of other stimulus responses such as photochromic and force-chromic, etc, on computational spectrometers., Comment: 10 pages, 5 figures

A red-black (RB) tree is a data structure with red and black nodes coloration. The red and black color of nodes make up the principal component for balancing a RB tree. A balanced tree has an equal number of black nodes on any simple path. But when a black leaf node is deleted, a double-black (DB) node is formed, thus, causing a reduction in black heights and the tree becomes unbalanced. Rebalancing a RB tree with a DB node is a fairly complex process. Teaching and learning the removal of DB nodes is also challenging. This paper introduces a simplified novel method which is a symbolic-algebraic arithmetic procedure for the removal of DB nodes and the rebalancing of black heights in RB trees. This simplified approach has enhanced student learning of the DB node removal in RB trees. Feedback from students showed the learnability, workability and acceptance of the symbolic-algebraic method in balancing RB trees after a delete operation., Comment: 18 pages

Lensless imagers based on diffusers or encoding masks enable high-dimensional imaging from a single shot measurement and have been applied in various applications. However, to further extract image information such as edge detection, conventional post-processing filtering operations are needed after the reconstruction of the original object images in the diffuser imaging systems. Here, we present the concept of a temporal compressive edge detection method based on a lensless diffuser camera, which can directly recover a time sequence of edge images of a moving object from a single-shot measurement, without further post-processing steps. Our approach provides higher image quality during edge detection, compared with the conventional post-processing method. We demonstrate the effectiveness of this approach by both numerical simulation and experiments. The proof-of-concept approach can be further developed with other image post-process operations or versatile computer vision assignments toward task-oriented intelligent lensless imaging systems., Comment: 5 pages, 4 figures

Estimating properties of quantum states via randomized measurements has become a significant part of quantum information science. In this paper, we design an innovative approach leveraging metasurfaces to perform randomized measurements on photonic qubits, together with error mitigation techniques that suppress realistic metasurface measurement noise. Through fidelity and purity estimation, we confirm the capability of metasurfaces to implement randomized measurements and the unbiased nature of our error-mitigated estimator. Our findings show the potential of metasurface-based randomized measurement schemes in achieving robust and resource-efficient estimation of quantum state properties.

Generating photogalvanic effects in centrosymmetric materials can provide new opportunities for developing passive photodetectors and energy harvesting devices. In this work, we investigate the photogalvanic effects in centrosymmetric two-dimensional materials, AA- and AB-stacked bilayer graphene, by applying an external gate voltage to break the symmetry. Using a tight-binding model to describe the electronic states, the injection coefficients for circular photogalvanic effects and shift conductivities for linear photogalvanic effects are calculated for both materials with light wavelengths ranging from THz to visible. We find that gate voltage induced photogalvanic effects can be very significant for AB-stacked bilayer graphene, with generating a maximal dc current in the order of mA for a 1 $\mu$m wide sample illuminated by a light intensity of 0.1 GW/cm$^2$, which is determined by the optical transition around the band gap and van Hove singularity points. Although such effects in AA-stacked bilayer graphene are about two orders of magnitude smaller than those in AB-stacked bilayer graphene, the spectrum is interestingly limited in a very narrow photon energy window, which is associated with the interlayer coupling strength. A detailed analysis of the light polarization dependence is also performed. The gate voltage and chemical potential can be used to effectively control the photogalvanic effects.

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., Comment: 11 pages, 7 figures

Disclinations are ubiquitous lattice defects existing in almost all crystalline materials. In two-dimensional nanomaterials, disclinations lead to the warping and deformation of the hosting material, yielding non-Euclidean geometries. However, such geometries have never been investigated experimentally in the context of topological phenomena. Here, by creating the physical realization of disclinations in conical and saddle-shaped acoustic systems, we demonstrate that disclinations can lead to topologically protected bound modes in non-Euclidean surfaces. In the designed honeycomb sonic crystal for p-orbital acoustic waves, non-Euclidean geometry interplay with the p-orbital physics and the band topology, showing intriguing emergent features as confirmed by consistent experiments and simulations. Our study opens a pathway towards topological phenomena in non-Euclidean geometries that may inspire future studies on, e.g., electrons and phonons in nanomaterials with curved surfaces., Comment: 19 pages, 4 figures

We theoretically investigate optical injection processes, including one- and two-photon carrier injection and two-color coherent current injection, in twisted bilayer graphene with moderate angles. The electronic states are described by a continuum model, and the spectra of injection coefficients are numerically calculated for different chemical potentials and twist angles, where the transitions between different bands are understood by the electron energy resolved injection coefficients. The comparison with the injection in monolayer graphene shows the significance of the interlayer coupling in the injection processes. For undoped twisted bilayer graphene, all spectra of injection coefficients can be divided into three energy regimes, which vary with the twist angle. For very low photon energies in the linear dispersion regime, the injection is similar to graphene with a renormalized Fermi velocity determined by the twist angle; for very high photon energies where the interlayer coupling is negligible, the injection is the same as that of graphene; and in the middle regime around the transition energy of the Van Hove singularity, the injection shows fruitful fine structures. Furthermore, the two-photon carrier injection diverges for the photon energy in the middle regime due to the existence of double resonant transitions.

Optically resonant dielectric metasurfaces offer unique capability to fully control the wavefront, polarisation, intensity or spectral content of light based on the excitation and interference of different electric and magnetic Mie multipolar resonances. Recent advances of the wide accessibility in the nanofabrication and nanotechnologies have led to a surge in the research field of high-quality functional optical metasurfaces which can potentially replace or even outperform conventional optical components with ultra-thin feature. Replacing conventional optical filtering components with metasurface technology offers remarkable advantages including lower integration cost, ultra-thin compact configuration, easy combination with multiple functions and less restriction on materials. Here we propose and experimentally demonstrate a planar narrow-band-pass filter based on the optical dielectric metasurface composed of Si nanoresonators in array. A broadband transmission spectral valley (around 200~nm) has been realised by combining electric and magnetic dipole resonances adjacent to each other. Meanwhile, we obtain a narrow-band transmission peak by exciting a high-quality leaky mode which is formed by partially breaking a bound state in the continuum generated by the collective longitudinal magnetic dipole resonances in the metasurface. Our proposed metasurface-based filter shows a stable performance for oblique light incidence with small angles (within 10 deg). Our work imply many potential applications of nanoscale photonics devices such as displays, spectroscopy, etc., Comment: 6