•Silica/gold core–shell (SiO2@Au) spheres are synthesized.•Different amounts of SiO2@Au spheres are incorporated into TiO2 films.•The power conversion efficiency of DSSCs increases from 3.95% to 5.29%.•Enhancement of Voc is attributed to a more negative quasi-Fermi level.•Enhancement of Jsc is resulted from increase of light harvesting efficiency.This paper describes a series of dye-sensitized solar cells (DSSCs) including TiO2 photoanodes with different amounts of silica/gold core–shell (SiO2@Au) spheres. The results show that the DSSC containing TiO2 photoanode with a certain amount of SiO2@Au spheres can attain its relatively better power conversion efficiency of 5.29%. Compared with a reference DSSC containing a pure TiO2 photoanode, the power conversion efficiency of the DSSC has been remarkably enhanced by 33.9%.The performance of DSSCs containing the TiO2 photoanodes with SiO2@Au spheres has been improved with comparison to a reference DSSC containing a pure TiO2 photoanode, and the best performance of the DSSCs is achieved with the open-circuit voltage of 0.68 V, the short-circuit current density of 11.45 mA cm−2, and the power conversion efficiency of 5.29%.

In this study, optical stop band of three-dimensional silica shell photonic crystals is tuned by adjusting inner diameter and shell thickness of hollow silica spheres. The silica shell photonic crystals are fabricated by sintering crystalline arrays, which are assembled from polystyrene/silica core–shell spheres by an improved vertical deposition method. The inner diameter and the shell thickness are controlled by diameter of polystyrene spheres and concentration of tetraethoxysilane. The results of transmission spectra show that there is an evident red shift of optical stop band as the inner diameter and the shell thickness increase. The red shift of optical stop band is due to variations in the inter-planar spacing and the effective refractive index of silica shell photonic crystals, which result from the variations of the inner diameter and the shell thickness of hollow silica spheres.

The relationship between silica shell thickness and optical properties of three-dimensional photonic crystals (3D PCs) is studied in this work. Core-shell spheres are synthesized by the modified Stöber method and self-assembled into 3D PCs through a simple improved vertical deposition method. Silica shell PCs are fabricated by sintering the PCs composed of the core-shell spheres. The morphologies and microstructures of PCs are identified by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The transmission spectra of PCs are measured by UV–vis spectrum measurements (UV). The results show that the positions of Bragg diffraction peaks are shifted to a longer wavelength with the increase of silica shell thickness. The shift range of peak positions for silica shell PCs is wider than that for PCs of core-shell spheres. The main reason for this is because the variation range of effective refractive indices for silica shell PCs becomes larger than that for PCs of core-shell spheres.Graphical abstractThe silica shell photonic crystals are fabricated by sintering the photonic crystals composed of polystyrene-core silica-shell spheres, and the optical properties of photonic crystals have been investigated by tuning silica shell thickness.Highlights► Polystyrene-core silica-shell spheres are self-assembled into photonic crystals. ► The silica shell photonic crystals are fabricated by sintering process. ► The optical properties of photonic crystals of core-shell spheres are investigated. ► The optical properties of silica shell photonic crystals are investigated.

Bessel solitary wave solutions to a two-dimensional strongly nonlocal nonlinear Schrödinger equation with distributed coefficients are obtained. Bessel solitary wave solutions have unique characteristics compared with Gaussian solitary wave solutions, Laguerre–Gaussian solitary wave solutions, and Hermite–Gaussian solitary wave solutions. The generalized two-dimensional nonlocal nonlinear Schrödinger equation with distributed coefficients is investigated for the first time to our knowledge.

An analytical solution of self-similar waves, Hermite–Gaussian solitons, emerging in a strongly nonlocal thermal nonlinear medium with the rectangular boundaries was found. The theoretical analysis and numerical simulation showed that the Hermite–Gaussian solitons are elliptic and form a rectangular matrix cluster. Moreover, the symmetries of the soliton and matrix cluster depend not only on the boundary conditions, but also on the symmetry and power of the input beam as well as the propagation distance. The particular interest lies in that the intensities of the solitons in the edges of the rectangular cluster are bigger than those on the center, the most intense solitons occurring at four angles.