In the water splitting process for sustainable hydrogen production, the oxygen evolution reaction (OER) stands as one of the pivotal half-reactions. Nevertheless, the sluggish four-electron transfer process inherent to OER has emerged as a kinetic bottleneck that impedes water electrolysis. To address this challenge, researchers have been devoting substantial efforts to developing high-performance OER electrocatalysts. Currently, iridium (Ir)-based or ruthenium (Ru)-based oxides are widely acknowledged as benchmark catalysts for OER. However, their scarcity and exorbitant cost render large-scale applications impractical. In recent years, transition metal carbides have garnered extensive attention in the realm of OER electrocatalysts, exhibiting tremendous application prospects owing to their advantages of low cost, high catalytic activity, and excellent stability. This review briefly introduces the fundamental characteristics and synthesis methodologies of transition metal carbides, summarizes the recent research advances in their application as OER catalysts, elaborates on the modification strategies and catalytic mechanisms of transition metal carbide nanomaterials, and finally discusses the challenges confronted by these metal carbides as well as the future research directions.

A partially coherent off-axis double vortex beam (PCOADVB) composed of two off-axis vortices is theoretically presented. The analytical equations of a PCOADVB in oceanic turbulence are presented, and the intensity profiles and the number of coherence vortices of the PCOADVBs are investigated based on the derived expressions. The numerical results show that the intensity profiles of PCOADVBs are determined by the initial topological charges $M_1$ and $M_2$ and the positions of the off-axis vortices $\left(x_{1d},y_{1d}\right)$ and $\left(x_{2d},y_{2d}\right)$. The intensity profiles of PCOADVBs will lose the off-axis ring intensity profile and acquire a Gaussian-like profile as $z$ increases, and stronger oceanic turbulence and a smaller $\sigma$ can help the PCOADVB evolve into a spot with a Gaussian-like profile faster on propagation. The number of coherence vortices of a PCOADVB in oceanic turbulence will increase on propagation. The PCOADVB may have potential applications in underwater laser sensing and wireless communications.

In this work, a new beam named the Hermite–Gaussian correlated vortex beam (HGCVB) is introduced. The intensity and coherence of this HGCVB in oceanic turbulence are analyzed. The results show that the HGCVB displays a splitting property during propagation, and the HGCVB can evolve into the array profile with hollow center beamlets. The results display that the evolution of the intensity of the HGCVB is manipulated by the coherence length δ₀ and topological charge M. Meanwhile, the array distribution of coherence of the HGCVB in oceanic turbulence can evolve into a one-spot pattern on propagation. The results show that this HGCVB evolves from a Gaussian beam into a beam array composed of beamlets with hollow centers and may have a potential application in oceanic turbulence.

The descriptions of a radially phased-locked Hermite–Gaussian correlated beam array are introduced, the equation of this beam array in oceanic turbulence is derived, and the intensity profiles of this beam array are shown and analyzed. The results imply that the evolutions of the sub-beam of this beam array in free space are the same as the Hermite–Gaussian correlated beam, while the intensity of this beam array can be adjusted by controlling the initial beam radius $R$ and the coherence length. The intensity profiles of this beam array in free space have multiple spots during propagation, while the same beam array in oceanic turbulence can become a beam spot due to the influences of $R$ and oceanic turbulence. The beam array with smaller coherence length in oceanic turbulence retains the splitting properties better during propagation.

In this paper, based on a theory given by Gori, we have introduced a flat-topped lattice named a multi-cosine-multi-Gaussian correlated beam (McMGCB); the coherence function of the McMGCB consists of a multi-cosine component and a multi-Gaussian component, and the array composed of flat-topped beamlets can be realized by this McMGCB. Based on the extended Huygens-Fresnel integral, the propagation equation of such McMGCB is derived. The McMGCB with smaller $\delta$ will split into a beam array faster. And the number of beamlets is determined by $N_x$ and $N_y$. The flatness of the beamlets is controlled by $F$. Moreover, the beamlets of such a McMGCB in stronger oceanic turbulence can overlap and merge into one spot. The characterizations of this flat-topped lattice with its adjustable parameters provide a method to generate a rectangular flat-topped beam array, which may have applications that demand a flat-topped array.