The main aim of the present paper is to survey different inequalities for convex functions of selfadjoint operators in Hilbert spaces which have appeared recently in the literature. Applications for ...some particular convex functions of interest are also given.
Some Hermite–Hadamard’s type inequalities for operator convex functions of selfadjoint operators in Hilbert spaces are given. Applications for particular cases of interest are also provided.
Optical metasurfaces have developed as a breakthrough concept for advanced wave‐front engineering enabled by subwavelength resonant nanostructures. However, reflection and/or absorption losses as ...well as low polarization‐conversion efficiencies pose a fundamental obstacle for achieving high transmission efficiencies that are required for practical applications. Here, for the first time to our knowledge, highly efficient all‐dielectric metasurfaces are demonstrated for NIR frequencies using arrays of silicon nanodisks as metaatoms. The main features of Huygens' sources are employed, namely, spectrally overlapping crossed electric and magnetic dipole resonances of equal strength, to demonstrate Huygens' surfaces with full transmission‐phase coverage of 360° and near‐unity transmission. Full‐phase coverage combined with high efficiency in transmission are experimentally confirmed. Based on these key properties, all‐dielectric Huygens' metasurfaces can become a new paradigm for flat optical devices, including beam‐steering, beam‐shaping, and focusing, as well as holography and dispersion control.
All‐dielectric Huygens' metasurfaces are experimentally demonstrated providing transmission‐phase coverage from 0 to 2π with record resonant transmission efficiencies of more than 55% at NIR wavelengths. Transmission efficiencies very close to 100% can be achieved for an appropriate choice of the embedding medium, and possible applications of this new concept are explored.
All‐dielectric metasurfaces provide a powerful platform for a new generation of flat optical devices, in particular, for applications in telecommunication systems, due to their low losses and high ...transparency in the infrared. However, active and reversible tuning of such metasurfaces remains a challenge. This study experimentally demonstrates and theoretically justifies a novel scenario of the dynamical reversible tuning of all‐dielectric metasurfaces based on the temperature‐dependent change of the refractive index of silicon. How to design an all‐dielectric metasurface with sharp resonances by achieving interference between magnetic dipole and electric quadrupole modes of constituted nanoparticles arranged in a 2D lattice is shown. Thermal tuning of these resonances can cause drastic but reciprocal changes in the directional scattering of the metasurface in a spectral window of 75 nm. This change can result in a 50‐fold enhancement of the radiation directionality. This type of reversible tuning can play a significant role in novel flat optical devices including the metalenses and metaholograms.
Via controlling the temperature and employing the right combination of the electric and magnetic resonant responses of the metasurfaces, drastic and reciprocal interchanges in directional scattering are demonstrated experimentally and theoretically. At 1425 nm forward to backward ratio variation from 1 to >50 can be obtained. The results provide an important step toward tunable nanophotonic components and all‐optical circuitry on a chip.
Metasurfaces provide opportunities for wavefront control, flat optics, and subwavelength light focusing. We developed an imaging-based nanophotonic method for detecting mid-infrared molecular ...fingerprints and implemented it for the chemical identification and compositional analysis of surface-bound analytes. Our technique features a two-dimensional pixelated dielectric metasurface with a range of ultrasharp resonances, each tuned to a discrete frequency; this enables molecular absorption signatures to be read out at multiple spectral points, and the resulting information is then translated into a barcode-like spatial absorption map for imaging. The signatures of biological, polymer, and pesticide molecules can be detected with high sensitivity, covering applications such as biosensing and environmental monitoring. Our chemically specific technique can resolve absorption fingerprints without the need for spectrometry, frequency scanning, or moving mechanical parts, thereby paving the way toward sensitive and versatile miniaturized mid-infrared spectroscopy devices.
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