arXiv subjects

Xing Fu

Publications and source records attributed to Xing Fu.

67 records · Page 4Linked to original sources

arXiv2020

High-dimensional classically entangled light from a laser

Vectorially structured light has emerged as an enabling tool in many diverse applications, from communication to imaging, exploiting quantum-like correlations courtesy of a non-separable spatially varying polarization structure. Creating these states at the source remains challenging and is presently limited to two-dimensional vectorial states by customized lasers. Here we invoke ray-wave duality in a simple laser cavity to produce polarization marked multi-path modes that are non-separable in three degrees of freedom and in eight dimensions. As a topical example, we use our laser to produce the complete set of Greenberger-Horne-Zeilinger (GHZ) basis states, mimicking high-dimensional multi-partite entanglement with classical light, which we confirm by a new projection approach. We offer a complete theoretical framework for our laser based on SU(2) symmetry groups, revealing a rich parameter space for further exploitation. Our approach requires only a conventional laser with no special optical elements, is easily scaleable to higher dimensions, and offers a simple but elegant solution for at-the-source creation of classically entangled states of structured light, opening new applications in simulating and enhancing high-dimensional quantum systems.

physics.optics↗

arXiv2020

A One-Shot Learning Framework for Assessment of Fibrillar Collagen from Second Harmonic Generation Images of an Infarcted Myocardium

Myocardial infarction (MI) is a scientific term that refers to heart attack. In this study, we infer highly relevant second harmonic generation (SHG) cues from collagen fibers exhibiting highly non-centrosymmetric assembly together with two-photon excited cellular autofluorescence in infarcted mouse heart to quantitatively probe fibrosis, especially targeted at an early stage after MI. We present a robust one-shot machine learning algorithm that enables determination of 2D assembly of collagen with high spatial resolution along with its structural arrangement in heart tissues post-MI with spectral specificity and sensitivity. Detection, evaluation, and precise quantification of fibrosis extent at early stage would guide one to develop treatment therapies that may prevent further progression and determine heart transplant needs for patient survival.

eess.IV↗

arXiv2018

Hybrid topological evolution of multi-singularity vortex beams: Generalized nature for helical-Ince-Gaussian and Hermite-Laguerre-Gaussian modes

A generalized family of scalar structured Gaussian modes including helical-Ince--Gaussian (HIG) and Hermite--Laguerre--Gaussian (HLG) beams is presented with physical insight upon a hybrid topological evolution nature of multi-singularity vortex beams carrying orbital angular momentum (OAM). Considering the physical origins of intrinsic coordinates aberration and the Gouy phase shift, a closed-form expression is derived to characterize the general modes in astigmatic optical systems. Moreover, a graphical representation, Singularities Hybrid Evolution Nature (SHEN) sphere, is proposed to visualize the topological evolution of the multi-singularity beams, accommodating HLG, HIG and other typical subfamilies as characteristic curves on the sphere surface. The salient properties of SHEN sphere for describing the precise singularities splitting phenomena, exotic structured light fields, and Gouy phase shift are illustrated with adequate experimental verifications.

physics.optics↗

arXiv2018

Truncated triangular diffraction lattices and orbital-angular-momentum detection of vortex SU(2) geometric modes

We for the first time report the truncated diffraction with a triangular aperture of the SU(2) geometric modes and propose a method to detect the complicated orbital angular momentum (OAM) of an SU(2) wave-packet, to the best of our knowledge. As a special vortex beam, a nonplanar SU(2) mode carrying special intensity and OAM distributions brings exotic patterns in truncated diffraction lattice. A meshy structure is unveiled therein by adjusting the illuminated aperture in vicinity of the partial OAM regions, which can be elaborately used to evaluate the partial topological charge and OAM of an SU(2) wave-packet by counting the dark holes in the mesh. Moreover, through controlling the size and position of the aperture at the center region, the truncated triangular lattice can be close to the classical spot-array lattice for measuring the center OAM. These effects being fully validated by theoretical simulations greatly extend the versatility of topological structures detection of special beams.

physics.optics↗

arXiv2018

Sub-MHz Self-Q-switching in Nd:LuAG Laser

A compact pulsed Nd:LuAG laser at 1064 nm based on the self-Q-switching technique is reported, having the output power as high as 6.61 W at the incident pump power of 21.32 W, corresponding to the optical conversion efficiency of ~31 %. The temporal width of the pulse was in the range from 532.2 ns to 652.6 ns, and the repetition rate varied between 488.6 kHz and 551.9 kHz. To the best of our knowledge, this is the first report on the self-Q-switching Nd:LuAG laser. Possible reasons for the self-Q-switching of Nd:LuAG were also provided, and the factor leading to the high repetition rate was analyzed. The compact cavity generating pulses with high output power and high repetition rate not only reveal that the self-Q-switching technique could be an efficient method for the generation of pulses with high output power and high repetition rate, but enrich the characteristics of Nd:LuAG crystal.

physics.optics↗

arXiv2018

Polygonal vortex beams in quasi-frequency-degenerate states

We originally demonstrate the vortex beams with patterns of closed polygons [namely polygonal vortex beams (PVBs)] generated by a quasi-frequency-degenerate (QFD) Yb:CALGO laser resonator with astigmatic transformation. The PVBs with peculiar patterns of triangular, square, and parallelogram shapes carrying large orbital angular momentums (OAMs) are theoretically investigated and experimentally obtained in the vicinity of the SU(2) degenerate states of laser resonator. The PVBs in QFD states are compared with the vortex beams with patterns of isolated spots arrays located on the triangle-, square-, and parallelogram-shaped routes [namely polygonalspots-array vortex beams (PSA-VBs)] under normal SU(2) degenerate states. Beam profile shape of PVB or PSA-VB and OAM can be controlled by adjusting the cavity length and the position of pump spot. The simulated and experimental results validate the performance of our method to generate PVB, which is of great potential for promoting novel technologies in particle trapping and beam shaping.

physics.optics↗

arXiv2018

Dual-wavelength vortex beam with high stability in diode-pumped Yb:CaGdAlO4 Laser

We present a stable dual-wavelength vortex beam carrying orbital angular momentum (OAM) with two spectral peaks separated by a few terahertz in diode-pumped Yb:CaGdAlO4 (CALGO) laser. The dual-wavelength spectrum is controlled by the pump power and off-axis loss in laser resonator, arising from the broad emission bandwidth of Yb:CALGO. The OAM beam is obtained by a pair of cylindrical lens that serves as an π/2 convertor for the high-order Hermite-Gaussian modes. The stability is verifed that the 1 h OAM beam with two spectral peaks at 1046.1 nm and 1057.2 nm (3.01 THz interval) can steadily operate for more than three hours. It has great potential for scaling the application for OAM beams in Terahertz spectroscopy, high-resolution interferometry, and so on.

physics.optics↗

arXiv2016

Riesz Transform Characterization and Fefferman-Stein Decomposition of Triebel-Lizorkin Spaces

Let $D\in\mathbb{N}$, $q\in[2,\infty)$ and $(\mathbb{R}^D,|\cdot|,dx)$ be the Euclidean space equipped with the $D$-dimensional Lebesgue measure. In this article, via an auxiliary function space $\mathrm{WE}^{1,\,q}(\mathbb R^D)$ defined via wavelet expansions, the authors establish the Riesz transform characterization of Triebel-Lizorkin spaces $\dot{F}^0_{1,\,q}(\mathbb{R}^D)$. As a consequence, the authors obtain the Fefferman-Stein decomposition of Triebel-Lizorkin spaces $\dot{F}^0_{\infty,\,q'}(\mathbb{R}^D)$. Finally, the authors give an explicit example to show that $\dot{F}^0_{1,\,q}(\mathbb{R}^D)$ is strictly contained in $\mathrm{WE}^{1,\,q}(\mathbb{R}^D)$ and, by duality, $\mathrm{WE}^{\infty,\,q'}(\mathbb{R}^D)$ is strictly contained in $\dot{F}^0_{\infty,\,q'}(\mathbb{R}^D)$. Although all results when $D=1$ were obtained by C.-C. Lin et al. [Michigan Math. J. 62 (2013), 691-703], as was pointed out by C.-C. Lin et al., the approach used in the case $D=1$ can not be applied to the case $D\ge2$, which needs some new skills.

math.CA↗

arXiv2015

Products of Functions in ${\mathop\mathrm{BMO}}({\mathcal X})$ and $H^1_{\rm at}({\mathcal X})$ via Wavelets over Spaces of Homogeneous Type

Let $({\mathcal X},d,μ)$ be a metric measure space of homogeneous type in the sense of R. R. Coifman and G. Weiss and $H^1_{\rm at}({\mathcal X})$ be the atomic Hardy space. Via orthonormal bases of regular wavelets and spline functions recently constructed by P. Auscher and T. Hytönen, the authors prove that the product $f\times g$ of $f\in H^1_{\rm at}({\mathcal X})$ and $g\in\mathop\mathrm{BMO}({\mathcal X})$, viewed as a distribution, can be written into a sum of two bounded bilinear operators, respectively, from $H^1_{\rm at}({\mathcal X})\times\mathop\mathrm{BMO}({\mathcal X})$ into $L^1({\mathcal X})$ and from $H^1_{\rm at}({\mathcal X})\times\mathop\mathrm{BMO}({\mathcal X})$ into $H^{\log}({\mathcal X})$, which affirmatively confirms the conjecture suggested by A. Bonami and F. Bernicot (This conjecture was presented by L. D. Ky in [J. Math. Anal. Appl. 425 (2015), 807-817]).

math.CA↗

arXiv2015

Wavelet Characterizations of the Atomic Hardy Space $H^1$ on Spaces of Homogeneous Type

math.CA↗

arXiv2015

Multi-Resolution Dynamic Mode Decomposition

We demonstrate that the integration of the recently developed dynamic mode decomposition (DMD) with a multi-resolution analysis allows for a decomposition method capable of robustly separating complex systems into a hierarchy of multi-resolution time-scale components. A one-level separation allows for background (low-rank) and foreground (sparse) separation of dynamical data, or robust principal component analysis. The multi-resolution dynamic mode decomposition is capable of characterizing nonlinear dynamical systems in an equation-free manner by recursively decomposing the state of the system into low-rank terms whose temporal coefficients in time are known. DMD modes with temporal frequencies near the origin (zero-modes) are interpreted as background (low-rank) portions of the given dynamics, and the terms with temporal frequencies bounded away from the origin are their sparse counterparts. The multi-resolution dynamic mode decomposition (mrDMD) method is demonstrated on several examples involving multi-scale dynamical data, showing excellent decomposition results, including sifting the El Niño mode from ocean temperature data. It is further applied to decompose a video data set into separate objects moving at different rates against a slowly varying background. These examples show that the decomposition is an effective dynamical systems tool for data-driven discovery.

math.DS↗

arXiv2014

Hardy spaces $H^p$ over non-homogeneous metric measure spaces and their applications

Let $({\mathcal X},d,μ)$ be a metric measure space satisfying both the geometrically doubling and the upper doubling conditions. Let $ρ\in (1,\infty)$, $0<p\le1\le q\le\infty$, $p\neq q$, $γ\in[1,\infty)$ and $ε\in(0,\infty)$. In this article, the authors introduce the atomic Hardy space ${\widetilde H_{\mathrm{atb},\,ρ}^{p,\,q,\,γ}(μ)}$ and the molecular Hardy space ${\widetilde H_{\rm{mb},\,ρ}^{p,\,q,\,γ,\,ε}(μ)}$ via the discrete coefficient $\widetilde{K}^{(ρ),\,p}_{B,\,S}$, and prove that the Calderón-Zygmund operator is bounded from ${\widetilde H_{\rm{mb},\,ρ}^{p,\,q,\,γ,\,δ}(μ)}$ (or ${\widetilde H_{\rm{atb},\,ρ}^{p,\,q,\,γ}(μ)}$) into $L^p(μ)$, and from ${\widetilde H_{\rm{atb},\,ρ(ρ+1)}^{p,\,q,\,γ+1}(μ)}$ into ${\widetilde H_{\rm{mb},\,ρ}^{p,\,q,\,γ,\,\frac12(δ-\fracν{p}+ν)}(μ)}$ whose genealized fractional versions are also obtained. The authors also introduce the $ρ$-weakly doubling condition, with $ρ\in (1,\infty)$, of the measure $μ$ and construct a non-doubling measure $μ$ satisfying this condition. If $μ$ is $ρ$-weakly doubling, the authors further introduce the Campanato space ${\mathcal E}^{α,\,q}_{ρ,\,η,\,γ}(μ)$ and show that ${\mathcal E}^{α,\,q}_{ρ,\,η,\,γ}(μ)$ is independent of the choices of $ρ$, $η$, $γ$ and $q$; the authors then introduce the atomic Hardy space $\widehat H_{\rm{atb},\,ρ}^{p,\,q,\,γ}(μ)$ and the molecular Hardy space $\widehat H_{\rm{mb},\,ρ}^{p,\,q,\,γ,\,ε}(μ)$, which coincide with each other; the authors finally prove that $\widehat{H}_{\rm{atb},\,ρ}^{p,\,q,\,γ}(μ)$ is the predual of ${\mathcal E}^{1/p-1,\,1}_{ρ,\,ρ,\,1}(μ)$. Moreover, relations of these Hardy spaces are also discussed.

math.CA↗

arXiv2014

Generalized Fractional Integrals and Their Commutators over Non-homogeneous Metric Measure Spaces

Let $({\mathcal X},d,μ)$ be a metric measure space satisfying both the upper doubling and the geometrically doubling conditions. In this paper, the authors establish some equivalent characterizations for the boundedness of fractional integrals over $({\mathcal X},d,μ)$. The authors also prove that multilinear commutators of fractional integrals with ${\mathop\mathrm{\,RBMO(μ)}}$ functions are bounded on Orlicz spaces over $({\mathcal X},d,μ)$, which include Lebesgue spaces as special cases. The weak type endpoint estimates for multilinear commutators of fractional integrals with functions in the Orlicz-type space ${\mathrm{Osc}_{\exp L^r}(μ)}$, where $r\in [1,\infty)$, are also presented. Finally, all these results are applied to a specific example of fractional integrals over non-homogeneous metric measure spaces.

math.CA↗