arXiv subjects

Quan Xu

Publications and source records attributed to Quan Xu.

13 recordsLinked to original sources

arXiv2026

Multiresonant Membrane Metasurfaces for Multifunctional Fingerprint Recognition and Real-time Biochemical Tracking

Label-free identification and real-time tracking of biochemical substances became critical for molecular diagnostics and chemical analysis, yet conventional resonant terahertz metasurface sensing relies on a single resonance, limiting spectral selectivity and dynamic capability. Here, we suggest multiresonant membrane metasurfaces and implement them for simultaneous static molecular fingerprint retrieval and dynamic reaction monitoring within a single pixel. We consider a membrane metasurface supporting multiple quasi-bound states in the continuum designed at target frequencies and enabling the tailoring of the field enhancement and frequency-selective interaction with target analytes. As a proof-of-concept, we achieve label-free detection of the dual fingerprint absorption features of pefloxacin at 0.78 THz and 0.99 THz, and real-time tracking of vitamin C oxidation and denaturation under ambient conditions. The kinetic profiles extracted from the THz amplitude evolution show excellent agreement with nonlinear reaction models, demonstrating quantitative biochemical tracking capabilities. Our results establish a versatile and scalable THz photonic platform that unifies static fingerprint identification and dynamic reaction monitoring, paving the way toward integrated on-chip biochemical analytics and multifunctional metasurface sensors.

physics.optics↗

arXiv2025

Electric-Magnetic-Switchable Free-Space Skyrmions in Toroidal Light Pulses via a Nonlinear Metasurface

Recent advances reveal that light propagation in free space supports many exotic topological textures, such as skyrmions. Their unique space-time topologies make them promising candidates as next-generation robust information carriers. Hence, the ability of switching different texture modes is highly demanded to serve as a manner of data transfer. However, previous studies focus on generation of one specific mode, lacking integrated devices with externally variable and stable mode generation capability. Here, we experimentally demonstrate the first realization of switchable skyrmions between electric and magnetic modes in toroidal light pulses using a nonlinear metasurface platform in terms of broadband terahertz generation driven by vectorial pulse. The spatial and temporal evolutions of them are also clearly observed. Our work establishes a new paradigm for manipulating and switching topologically structured light.

physics.optics↗

arXiv2024

Photonic Terahertz Phased Array

Phased arrays are crucial in various technologies, such as radar and wireless communications, due to their ability to precisely control and steer electromagnetic waves. This precise control improves signal processing and enhances imaging performance. However, extending phased arrays to the terahertz (THz) frequency range has proven challenging, especially for high-frequency operation, broadband performance, two-dimensional (2D) phase control with large antenna arrays, and strong phase modulation. Here, we introduce a photonic platform to realize a THz phased array that bypasses the above challenges. Our method employs 2D phase coding with 2-bit across a broad THz frequency range from 0.8 to 1.4 THz. The core of our design is a pixelated nonlinear Pancharatnam-Berry metasurface driven by a spatially modulated femtosecond laser, allowing precise phase control of THz signals. We showcase the effectiveness of our method through four proof-of-concept applications: single beamforming, dual beamforming, imaging and vortex beam generation. The realized photonic platform provides a promising pathway for developing broadband phased arrays in the THz regime.

physics.optics↗

arXiv2024

Time-varying Nonlinear Effects in Terahertz Generation

Time-varying effects have unveiled new possibilities for manipulating electromagnetic waves through the temporal dimension. In this study, we experimentally explore these effects in the nonlinear optical process of terahertz (THz) generation using optically pumped indium tin oxide (ITO) films. The ultrafast carrier dynamics in the ITO film endow the second-order nonlinear susceptibility (\c{hi}(2)) with sub-picosecond temporal evolution, establishing a temporal boundary for the generated THz waves. We observe significant amplitude and frequency modulations in the THz generation at various transients, attributed to the time-varying complex amplitude of the \c{hi}(2). Moreover, we also observed polarization modulations when further exploiting the tensor properties of \c{hi}(2). This work advances the exploration of time-varying effects into the nonlinear regime through frequency down-conversion, effectively transferring the strong time-varying material response from the near-infrared (NIR) band to the THz band. These findings open up new opportunities for realizing time-varying phenomena that specifically require single-cycle modulation.

physics.optics↗

arXiv2024

Multiple Bound States in the Continuum: Towards Intense Terahertz Matter Interaction

Bound states in the continuum (BICs) are an excellent platform enabling highly efficient light-matter interaction in applications for lasing, nonlinear generation, and sensing. However, the current focus in implementing BICs has primarily been on single sharp resonances, limiting the extent of electric field enhancement for multiple resonances. In this study, we conducted experimental demonstrations to showcase how metasurfaces can enable the control of symmetry-broken and Friedrich-Wintgen BICs by leveraging the asymmetry of split resonant rings. This approach allows for the existence of multiple free-control BIC resonances and tailored enhancement of controlling light-matter interactions. We have conducted further experiments to validate the effectiveness and performance of our approach for identification of the distinct fingerprint of {\alpha}-lactose with high sensitivity using only one single metasurface. These findings present a novel and efficient platform for the development of miniaturized and chip-scale photonics devices with intense light-matter interaction.

physics.optics↗

arXiv2022

A proof of the Generalized Jacobian conjecture

Based on the reduction of degree in polynomial mappings and some known results in algebraic geometry, by introducing the Brouwer degree, a tool from differential topology, algebraic topology and algebraic geometry, we completely prove the Generalized Jacobian conjecture in the field of real numbers, which implies the Generalized complex Jacobian conjecture. Also, for the strong real Jacobian conjecture, we present a newly sufficient and necessary condition.

math.AG↗

arXiv2020

Multiplexing-oriented plasmon-MoS2 hybrid metasurfaces driven by nonlinear quasi bound states in the continuum

Rapid progress in nonlinear plasmonic metasurfaces enabled many novel optical characteristics for metasurfaces, with potential applications in frequency metrology, timing characterization and quantum information. However, the spectrum of nonlinear optical response was typically based upon the linear optical resonance. In this work, a wavelength-multiplexed nonlinear plasmon-MoS2 hybrid metasurface with suppression phenomenon was proposed, where multiple nonlinear signals could to be simultaneously processed and optionally tuned. A clear physical picture to depict the nonlinear plasmonic bound states in the continuum (BICs) was presented, from the perspective of both classical and quantum approaches. Particularly, beyond the ordinary plasmon-polariton effect, we numerically demonstrated a giant BIC-inspired second-order nonlinear susceptibility $10^{-5}$~$m/V$ of MoS2 in the infrared band. The novelty in our study lies in the presence of a quantum oscillator that can be adopted to both suppress and enhance the nonlinear quasi BICs. This selectable nonlinear BIC-based suppression and enhancement effect can optionally block undesired modes, resulting in narrower linewidth as well as smaller quantum decay rates, which is also promising in slow-light-associated technologies.

physics.optics↗

arXiv2020

The intrinsic topology of linear maps

Based on many experts' former work in the Jacobian conjecture and an essential analysis of intrinsic topology of linear maps, I completely prove the Jacobian conjecture by demonstrating the injectivity of real Keller map of any $n$-dimensions.

math.AG↗

arXiv2019

Machine learning-guided synthesis of advanced inorganic materials

Synthesis of advanced inorganic materials with minimum number of trials is of paramount importance towards the acceleration of inorganic materials development. The enormous complexity involved in existing multi-variable synthesis methods leads to high uncertainty, numerous trials and exorbitant cost. Recently, machine learning (ML) has demonstrated tremendous potential for material research. Here, we report the application of ML to optimize and accelerate material synthesis process in two representative multi-variable systems. A classification ML model on chemical vapor deposition-grown MoS2 is established, capable of optimizing the synthesis conditions to achieve higher success rate. While a regression model is constructed on the hydrothermal-synthesized carbon quantum dots, to enhance the process-related properties such as the photoluminescence quantum yield. Progressive adaptive model is further developed, aiming to involve ML at the beginning stage of new material synthesis. Optimization of the experimental outcome with minimized number of trials can be achieved with the effective feedback loops. This work serves as proof of concept revealing the feasibility and remarkable capability of ML to facilitate the synthesis of inorganic materials, and opens up a new window for accelerating material development.

cond-mat.mtrl-sci↗

arXiv2019

A minimax principle to the injectivity of the Jacobian conjecture

The main result of this paper is to prove some type of Real Jacobian Conjecture. It is proved by the Minimax Principle and asserts if the eigenvalues of $F'(x)$ are bounded from zero and all the eigenvalues of $F'(x)+F'(x)^T$ are strictly same sign, where $ F $ is $ C^1 $ mapping from $ \mathbb{R}^n $ to $ \mathbb{R}^n $, then $ F $ is injective. Moreover $F$ has a $ C^1 $ mapping inverse.

math.AG↗

arXiv2018

The Deligne pairing and a functorial Riemann Roch theorem in positive characteristic

In this paper, we prove the functorial Riemann-Roch theorem in positive characteristic for a smooth and projective morphism with any relative dimension. In the case of relative dimension $1$, we have given an analogue with Deligne's functorial Riemann Roch theorem in previous author's paper. For any relative dimension, our result can deduce an analogue to the Knudsen-Mumford extension. The present result is a generalization, which mainly originated from the extended Deligne pairing by S. Zhang and the Adams Riemann Roch theorem in positive characteristic by R. Pink and D. Rössler.

math.AG↗

arXiv2015

Polarization-controlled anisotropic coding metamaterials at terahertz frequencies

Metamaterials based on effective media have achieved a lot of unusual physics (e.g. negative refraction and invisibility cloaking) owing to their abilities to tailor the effective medium parameters that do not exist in nature. Recently, coding metamaterials have been suggested to control electromagnetic waves by designing the coding sequences of digital elements '0' and '1', which possess opposite phase responses. Here, we propose the concept of anisotropic coding metamaterial at terahertz frequencies, in which coding behaviors in different directions are dependent on the polarization status of terahertz waves. We experimentally demonstrate an ultrathin and flexible polarization-controlled anisotropic coding metasurface functioning in the terahertz regime using specially- designed coding elements. By encoding the elements with elaborately-designed digital sequences (in both 1 bit and 2 bits), the x- and y-polarized reflected waves can be deflected or diffused independently in three dimensions. The simulated far-field scattering patterns as well as near-electric-field distributions are given to illustrate the bifunctional performance of the encoded metasurface, which show good agreement to the measurement results. We further demonstrate the abilities of anisotropic coding metasurface to generate beam splitter and realize anomalous reflection and polarization conversion simultaneously, providing powerful controls of differently-polarized terahertz waves. The proposed method enables versatile beam behaviors under orthogonal polarizations using a single metasurface, and hence will promise interesting terahertz devices.

physics.optics↗

arXiv2014

On Deligne's functorial Riemann-Roch theorem in positive characteristic

In this note, we give a proof for a variant of the functorial Deligne-Riemann-Roch theorem in positive characteristic based on ideas appearing in Pink and Rössler's proof of the Adams-Riemann-Roch theorem in positive characteristic (see \cite{Pi}). The method of their proof appearing in \cite{Pi}, which is valid for any positive characteristic and which is completely different from the classical proof, will allow us to prove the functorial Deligne-Riemann-Roch theorem in a much easier and more direct way. Our proof is also partially compatible with Mumford's isomorphism.

math.AG↗