We present a systematic overview on laser transverse modes with ray-wave duality. We start from the spectrum of eigenfrequencies in ideal spherical cavities to display the critical role of degeneracy for unifying the Hermite–Gaussian eigenmodes and planar geometric modes. We subsequently review the wave representation for the elliptical modes that generally carry the orbital angular momentum. Next, we manifest the fine structures of eigenfrequencies in a spherical cavity with astigmatism to derive the wave-packet representation for Lissajous geometric modes. Finally, the damping effect on the formation of transverse modes is generally reviewed. The present overview is believed to provide important insights into the ray-wave correspondence in mesoscopic optics and laser physics.

The interchangeable operation of alkaline oxygen evolution and reduction using bifunctional electrocatalysts in devices consolidates the commercialization milestone of energy storage in hydrogen, and yet, it is usually limited by issues of carbon corrosion in electrocatalysts and inhomogeneous electrode fabrication. Here, we demonstrate a synthetic route toward carbon-free ternary rock salt oxide (i.e., NiO/CoO/FeO) hollow spheres with silver decoration on the surface for durable operation in bifunctional cells. These Ag-decorated ternary oxides exhibit an overall bifunctional potential gap (ΔE = E j10, OER – E jhalf, ORR) of 0.89 V. Operando Raman studies show that the rock salt structure shows the phenomenon of a highly reversible local environment during the charge–discharge OER cycles, a key characteristic for high durability in bifunctional devices. At equivalent content between Ni and Co, NiOOH is the main OER-active species with CoOOH and/or CoO2 as the cocatalyst, where the presence of the FeO dopant facilitates structural activation and reversibility. With the proof-of-concept performance in anion-exchange membrane (AEM) devices, the catalysts achieve a durable cyclic operation with a high current density (1000 mA cm–2) at smaller potentials (2.03 V) than RuO2 (2.16 V) under the electrolyzer mode, while it can yield two times greater power density (96.98 mW cm–2) than Pt/C (53.58 mW cm–2) in the fuel cell mode.

The quantum and classical dynamics of the SU(2) coupled oscillator model are systematically reviewed to provide the quantum eigenstates and stationary coherent states for characterizing laser transverse modes from the analogy with the quantum-classical connection. The integral formula for the representation of the stationary coherent states derived from the evolution of the time-dependent wave packet state is completely reviewed. Several calculated results for the stationary coherent states are illustratively presented to display the spatial distributions for the quantum-classical transition and the plentiful variations of phase singularities. The overall review is believed to provide a comprehensive insight into laser transverse modes characterized by the stationary coherent states of the SU(2) coupled oscillator model.

The thermal stability of (Mg0.95Ni0.05)2TiO4 dielectric ceramics has been improved by mixing with CaTiO3 phases owing to higher positive temperature coefficients. The pure (Mg0.95Ni0.05)2TiO4 and the mixture phase systems of CaTiO3-modified (Mg0.95Ni0.05)2TiO4 were verified by XRD diffraction patterns to ensure the crystallite of different phases. The microstructures of the CaTiO3-modified (Mg0.95Ni0.05)2TiO4 were observed by SEM and EDS to investigate the relation between element ratios and grains. As a result, it can be seen that the thermal stability of the CaTiO3-modified (Mg0.95Ni0.05)2TiO4 can be effectively enhanced, compared with the pure (Mg0.95Ni0.05)2TiO4. Moreover, the radio frequency dielectric performances of CaTiO3-modified (Mg0.95Ni0.05)2TiO4 dielectric ceramics are strongly dependent upon the density and the morphology of the specimens. The champion sample with the ratio of (Mg0.95Ni0.05)2TiO4 and CaTiO3 of 0.92:0.08 showed an εr value of 19.2, an Qf value of 108,200 GHz, and a τf value of −4.8 ppm/°C, which may encourage (Mg0.95Ni0.05)2TiO4 ceramics to broaden the range of novel applications and match the requirements of 5G or next-generation communication systems.

No abstract