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We prove the absolute winning property of weighted simultaneous inhomogeneous badly approximable vectors on non-degenerate analytic curves. This answers a question by Beresnevich, Nesharim, and Yang. In particular, our result is an inhomogeneous version of the main result in \cite{BNY22} by Beresnevich, Nesharim, and Yang. Also, the generality of the inhomogeneous part that we considered extends the previous result in \cite{ABV}. Moreover, our results even contribute to classical results, namely establishing the inhomogeneous Schmidt's conjecture in arbitrary dimensions.

Distributed acoustic sensing (DAS) is a novel enabling technology that can turn existing fibre optic networks to distributed acoustic sensors. However, it faces the challenges of transmitting, storing, and processing massive streams of data which are orders of magnitude larger than that collected from point sensors. The gap between intensive data generated by DAS and modern computing system with limited reading/writing speed and storage capacity imposes restrictions on many applications. Compressive sensing (CS) is a revolutionary signal acquisition method that allows a signal to be acquired and reconstructed with significantly fewer samples than that required by Nyquist-Shannon theorem. Though the data size is greatly reduced in the sampling stage, the reconstruction of the compressed data is however time and computation consuming. To address this challenge, we propose to map the feature extractor from Nyquist-domain to compressed-domain and therefore vibration detection and classification can be directly implemented in compressed-domain. The measured results show that our framework can be used to reduce the transmitted data size by 70% while achieves 99.4% true positive rate (TPR) and 0.04% false positive rate (TPR) along 5 km sensing fibre and 95.05% classification accuracy on a 5-class classification task.

The photonic hook, a beam that can propagate along a curved path, has attracted wide attention since its inception and experimental confirmation. In this paper, we propose a new type of structure, which was made by a hollow microcylinder and a Janus-shaped liquid column of two insoluble filling liquids, for producing photonic hook of easily tunable properties and long length. The E^2 field intensity distribution characteristics and formation mechanism of the photonic hook are studied by analyzing the energy flow using the finite element method. The profile and properties of the photonic hook can be effectively tuned by rotating the hollow microcylinder or changing the light incident angle. A long photonic hook with a decay length of ~18{\lambda} and a photonic hook with a large focal distance ~8{\lambda} are obtained by this model.

Recently, two special photonic jets, photonic hooks and twin photonic jets, have been proposed to deal with complex conditions in nanoscale manipulation. Photonic hooks are generated by a single light plane wave and an asymmetric microparticle, while the twin photonic jets are produced by two incident light beams. In this letter, we presented and demonstrate a method to combine photonic hooks and twin photonic jets. A single light plane wave and a symmetric microparticle, twin-ellipse microcylinder, are used in this research. The curvature degree, length and maximum E2 filed enhancement of twin photonic hooks are varied significantly, with the change of refractive indices and shape of twin-ellipse microcylinder. And a liquid-immersed core-shell is built to achieve a flexible tunability.

Recently, a type of curved light beams, photonic hooks (PHs), was theoretically predicted and experimentally observed. The production of photonic hook (PH) is due to the breaking of structural symmetry of a plane-wave illuminated microparticle. Herein, we presented and implemented a new approach, of utilizing the symmetry-broken of the microparticles in material composition, for the generation of PHs from Janus microcylinders. Finite element method based numerical simulation and energy flow diagram represented theoretical analysis were used to investigate the field distribution characteristics and formation mechanism of the PHs. The full width at half-maximum (FWHM) of the PH (~0.29$\lambda$) is smaller than the FWHM of the photonic nanojet (~0.35$\lambda$) formed from a circular microcylinder with the same geometric radius. By changing the refractive index contrasts between upper and lower half-cylinders, or rotating the Janus microcylinder relative to the central axis, the shape profiles of the PHs can be efficiently modulated. The tunability of the PHs through simple stretching or compression operations, for the Janus microcylinder constituted by one solid inorganic half-cylinder and the other flexible polymer half-cylinder, was studied and discussed as well.

Today, wide-open, high-resolution Doppler frequency shift (DFS) estimation is essential for radar, microwave/millimeter-wave, and communication systems. Using photonics technology, an effective approach is proposed and experimentally demonstrated, providing a high-resolution and frequency-independent solution. In the approach consisting of two cascaded opto-electronic modulators, DFS between the transmitted microwave/ millimeter-wave signal and the received echo signal is mapped into a doubled spacing between two target optical sidebands. Subsequently, the DFS is then estimated through the spectrum analysis of a generated low-frequency electrical signal, with an improved resolution by a factor of 2. In experiments, DFSs from -90 to 90 KHz are successfully estimated for microwave/millimeter-wave signals at 10, 15, and 30 GHz, where estimation errors keep lower than +/- 5e-10 Hz. For radial velocity measurement, these results reveal a range from 0 to 900 m/s (0 to 450 m/s) and a resolution of 1e-11 m/s (5e-12 m/s) at 15-GHz (30-GHz) frequency band., Comment: 8 pages, 10 figures