Coupling electron beams carrying information into electronic units is fundamental in microelectronics. This requires precision manipulation of electron beams through a coupler with a good focusing ability. In graphene, the focusing of wide electron beams has been successfully demonstrated by a circular p-n junction. However, it is not favorable for information coupling since the focal length is so small that the focal spot locates inside the circular gated region, rather than in the background region. Here, we demonstrate that an array of gate-defined quantum dots, which has gradually changing lattice spacing in the direction transverse to propagation, can focus electrons outside itself, providing a possibility to make a coupler in graphene. The focusing effect can be understood as due to the gradient change of effective refractive indices, which are defined by the local energy band in a periodic potential. The strong focusing can be achieved by suitably choosing the lattice gradient and the layer number in the incident direction, offering an effective solution to precision manipulation of electron beams with wide electron energy range and high angular tolerance.

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By using single-layer metasurfaces, we realized ultrawide-angle high-transmission in the millimeter-wave band, which allowed more than 98% transmission of dual-polarized electromagnetic waves for almost all incident angles. The multipolar expansion method was used to analyze and verify the condition of the generalized Kerker effect at the corresponding reflected angles. Using quartz glass substrates with the same metallic periodic structures, electromagnetic windows are proposed that can improve any-directed 5G millimeter-wave communication signals from outdoor to indoor environments. The proposed interpretations can connect the Kerker effect with actual applications and enable the design of easy-to-integrate all-angle Kerker effect metasurface devices.

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Achieving Goos–Hänchen shift enhancement with high transmittance or reflectance based on the resonance effect is challenging due to the drop in the resonance region. This Letter demonstrates the realization of large transmitted Goos–Hänchen shifts with high (near 100%) transmittance based on a coupled double-layer grating system. The double-layer grating is composed of two parallel and misaligned subwavelength dielectric gratings. By changing the distance and the relative dislocation between the two dielectric gratings, the coupling of the double-layer grating can be flexibly tuned. The transmittance of the double-layer grating can be close to 1 in the entire resonance angle region, and the gradient of the transmissive phase is also preserved. The Goos–Hänchen shift of the double-layer grating reaches ∼30 times the wavelength, approaching 1.3 times the radius of the beam waist, which can be observed directly.

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