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Tian Yang

Publications and source records attributed to Tian Yang.

At least 55 records · Page 3Linked to original sources
arXiv2020

2D-Material-Assisted Bistable Switching of Gap Plasmons Disclosed By Femtosecond Pulse Scattering Spectra

Nanosphere-on-mirror plasmonic antennas, each having a monolayer graphene or MoS2 sheet in the gap, were pumped with a femtosecond laser. Abrupt turnings in the scattering linewidth and peak intensity trends as the laser power changed were experimentally observed. Theoretical modelling of dynamic plasmon evolvement attributes the turning to transitioning between two plasmon states, with a universal switching threshold of four-wave mixing efficiency around 0.14%. This bistability is rendered by a strong feedback from the nonlinear gap current to the gap plasmons, and involvement of both four and high-order wave mixing. This work reveals a pathway to making energy efficient nonlinear plasmonic elements.

physics.optics↗
arXiv2020

A Simple Galerkin Meshless Method, the Fragile Points Method (FPM) Using Point Stiffness Matrices, for 2D Linear Elastic Problems in Complex Domains with Crack and Rupture Propagation

The Fragile Points Method (FPM) is an elementarily simple Galerkin meshless method, employing Point-based discontinuous trial and test functions only, without using element-based trial and test functions. In this study, the algorithmic formulations of FPM for linear elasticity are given in detail, by exploring the concepts of point stiffness matrices and numerical flux corrections. Advantages of FPM for simulating the deformations of complex structures, and for simulating complex crack propagations and rupture developments, are also thoroughly discussed. Numerical examples of deformation and stress analyses of benchmark problems, as well as of realistic structures with complex geometries, demonstrate the accuracy, efficiency and robustness of the proposed FPM. Simulations of crack initiation and propagations are also given in this study, demonstrating the advantages of the present FPM in modeling complex rupture and fracture phenomena. The crack and rupture propagation modeling in FPM is achieved without remeshing or augmenting the trial functions as in standard, extended or generalized FEM. The simulation of impact, penetration and other extreme problems by FPM will be discussed in our future papers.

math.NA↗
arXiv2020

Quadruple-enhanced four-wave mixing in nanometer plasmonic hotspots: classical theory and experiments

Efficiency is a critical factor limiting the applications of nonlinear plasmonic devices. We show by theory and experiments that high efficiency four-wave mixing (FWM) is achieved in nanometer size plasmonic hotspots, which open up opportunities for nanoscale light manipulation. First, we present a classical calculation on the efficiency of frequency conversion by quadruple-enhanced FWM for a Kerr nonlinear material loaded in the plasmonic hotspot of a gold nanosphere dimer. The results indicate the viability to achieve over 10% efficiency in a nanometer volume under milliwatts of pump power consumption or less. Next, we present experimental results which show around 10% linewidth broadening of a 100 fs pulsed laser by a monolayer graphene in a gold nanosphere-plane junction. Such a high efficiency, low power, and nanoscale nonlinear process is a promising candidate for making ultra-compact and high-speed nonlinear optical devices.

physics.optics↗
arXiv2020

Growth of quantum 6j-symbols and applications to the Volume Conjecture

We prove the Turaev-Viro invariants volume conjecture for a "universal" class of cusped hyperbolic 3-manifolds that produces all 3-manifolds with empty or toroidal boundary by Dehn filling. This leads to two-sided bounds on the volume of any hyperbolic 3-manifold with empty or toroidal boundary in terms of the growth rate of the Turaev-Viro invariants of the complement of an appropriate link contained in the manifold. We also provide evidence for a conjecture of Andersen, Masbaum and Ueno (AMU conjecture) about certain quantum representations of surface mapping class groups. A key step in our proofs is finding a sharp upper bound on the growth rate of the quantum $6j-$symbol evaluated at $q=e^{\frac{2πi}{r}}.$

math.GT↗
arXiv2019

A new Fragile Points Method (FPM) in computational mechanics, based on the concepts of Point Stiffnesses and Numerical Flux Corrections

In this paper, a new method, named the Fragile Points Method (FPM), is developed for computer modeling in engineering and sciences. In the FPM, simple, local, polynomial, discontinuous and Point-based trial and test functions are proposed based on randomly scattered points in the problem domain. The local discontinuous polynomial trial and test functions are postulated by using the Generalized Finite Difference method. These functions are only piece-wise continuous over the global domain. By implementing the Point-based trial and test functions into the Galerkin weak form, we define the concept of Point Stiffnesses as the contribution of each Point in the problem domain to the global stiffness matrix. However, due to the discontinuity of trial and test functions in the domain, directly using the Galerkin weak form leads to inconsistency. To resolve this, Numerical Flux Corrections, which are frequently used in Discontinuous Galerkin methods are further employed in the FPM. The resulting global stiffness matrix is symmetric and sparse, which is advantageous for large-scale engineering computations. Several numerical examples of 1D and 2D Poisson equations are given in this paper to demonstrate the high accuracy, robustness and convergence of the FPM. Because of the locality and discontinuity of the Point-based trial and test functions, this method can be easily extended to model extreme problems in mechanics, such as fragility, rupture, fracture, damage, and fragmentation. These extreme problems will be discussed in our future studies.

physics.comp-ph↗
arXiv2018

On type-preserving representations of the thrice punctured projective plane group

In this paper we consider type-preserving representations of the fundamental group of the three--holed projective plane into $\mathrm{PGL}(2, \R) =\mathrm{Isom}(\HH^2)$ and study the connected components with non-maximal euler class. We show that in euler class zero for all such representations there is a one simple closed curve which is non-hyperbolic, while in euler class $\pm 1$ we show that there are $6$ components where all the simple closed curves are sent to hyperbolic elements and $2$ components where there are simple closed curves sent to non-hyperbolic elements. This answer a question asked by Brian Bowditch. In addition, we show also that in most of these components the action of the mapping class group on these non-maximal component is ergodic. In this work, we use an extension of Kashaev's theory of decorated character varieties to the context of non-orientable surfaces.

math.GT↗
arXiv2018

Volume conjectures for the Reshetikhin-Turaev and the Turaev-Viro invariants

We consider the asymptotics of the Turaev-Viro and the Reshetikhin-Turaev invariants of a hyperbolic $3$-manifold, evaluated at the root of unity $\exp({2π\sqrt{-1}}/{r})$ instead of the standard $\exp({π\sqrt{-1}}/{r})$. We present evidence that, as $r$ tends to $\infty$, these invariants grow exponentially with growth rates respectively given by the hyperbolic and the complex volume of the manifold. This reveals an asymptotic behavior that is different from that of Witten's Asymptotic Expansion Conjecture, which predicts polynomial growth of these invariants when evaluated at the standard root of unity. This new phenomenon suggests that the Reshetikhin-Turaev invariants may have a geometric interpretation other than the original one via $SU(2)$ Chern-Simons gauge theory.

math.GT↗
arXiv2018

Turaev-Viro invariants, colored Jones polynomials and volume

We obtain a formula for the Turaev-Viro invariants of a link complement in terms of values of the colored Jones polynomial of the link. As an application we give the first examples for which the volume conjecture of Chen and the third named author\,\cite{Chen-Yang} is verified. Namely, we show that the asymptotics of the Turaev-Viro invariants of the Figure-eight knot and the Borromean rings complement determine the corresponding hyperbolic volumes. Our calculations also exhibit new phenomena of asymptotic behavior of values of the colored Jones polynomials that seem not to be predicted by neither the Kashaev-Murakami-Murakami volume conjecture and various of its generalizations nor by Zagier's quantum modularity conjecture. We conjecture that the asymptotics of the Turaev-Viro invariants of any link complement determine the simplicial volume of the link, and verify it for all knots with zero simplicial volume. Finally we observe that our simplicial volume conjecture is stable under connect sum and split unions of links.

math.GT↗
arXiv2017

Stepwise quantum phonon pumping in plasmon-enhanced Raman scattering

Plasmon-enhanced Raman scattering (PERS) becomes nonlinear when phonon pumping and phonon-stimulated scattering come into play. It is fundamental to the understanding of PERS and its photobleaching behavior. By quantization of the molecular vibration coherent state into phonon number states, we theoretically predict a stepwise dependence of PERS intensity on laser power. Experimental evidence is presented by measuring a monolayer of malachite green isothiocyanate molecules sandwiched in individual gold nanosphere-plane antennas, under radially polarized laser excitation of sub-microWatt powers.

cond-mat.mes-hall↗
arXiv2015

Reproducible Ultrahigh Electromagnetic SERS Enhancement in Nanosphere-Plane Junctions

Surface enhanced Raman scattering (SERS) in nanoscale hotspots has been placed great hopes upon for identification of minimum chemical traces and in-situ investigation of single molecule structures and dynamics. However, previous work consists of either irreproducible enhancement factors (EF) from random aggregates, or moderate EFs despite better reproducibility. Consequently, systematic study of SERS at the single and few molecules level is still very limited, and the promised applications are far from being realized. Here we report EFs as high as the most intense hotspots in previous work yet achieved in a reproducible and well controlled manner, that is, electromagnetic EFs (EMEF) of 10^9~10 with an error down to 10^+/-0.08 from gold nanospheres on atomically flat gold planes under radially polarized (RP) laser excitation. In addition, our experiment reveals the EF's unexpected nonlinearity under as low as hundreds of nanowatts of laser power.

physics.optics↗
arXiv2015

Plasmonic Crystal Cavity on Single-Mode Optical Fiber End Facet for Label-Free Biosensing

All surface plasmon resonance (SPR) devices on single-mode optical fibers' (SMF) end facets, as reported up to date, are limited by severely broad and shallow resonance spectra. The consequent poor performance when they are used as refractive index sensors, together with the challenge of nanofabrication on fiber end facets, has prohibited the development of such devices for label-free biosensing. Meanwhile, the planewave coupled, multimode fiber and fiber sidewall SPR counterparts are extensively employed for label-free biosensing. In this paper, we report the design, fabrication and characterization of a plasmonic crystal cavity on a SMF end facet, which shows high performance label-free sensing capability that comes from a steep cavity resonance near the plasmonic bandedge. The experimental figure-of-merit is 68 RIU^-1, which is over twenty times improvement to previous reports. The refractive index detection limit is 3.5*10^-6 RIU at 1 s integration time. We also describe a novel glue-and-strip process to transfer gold nano structures onto fiber end facets.

physics.optics↗
arXiv2015

Gap plasmon resonator arrays for unidirectional launching and shaping of surface plasmon polaritons

We report the design and experimental realization of a kind of miniaturized devices for efficient unidirectional launching and shaping of surface plasmon polaritons (SPPs). Each device consists of an array of evenly spaced gap plasmon resonators with varying dimensions. Particle swarm optimization is used to achieve a theoretical two dimensional launching efficiency of about 51%, under the normal illumination of a 5-μm waist Gaussian beam at 780 nm. By modifying the wavefront of the SPPs, unidirectional SPPs with focused, Bessel and Airy profiles are launched and imaged with leakage radiation microscopy.

physics.optics↗
arXiv2015

On type-preserving representations of the four-punctured sphere group

We give counterexamples to a question of Bowditch that if a non-elementary type-preserving representation $ρ:π_1(Σ_{g,n})\rightarrow PSL(2;\mathbb R)$ of a punctured surface group sends every non-peripheral simple closed curve to a hyperbolic element, then must $ρ$ be Fuchsian. The counterexamples come from relative Euler class $\pm1$ representations of the four-punctured sphere group. We also show that the mapping class group action on each non-extremal component of the character space of type-preserving representations of the four-punctured sphere group is ergodic, which confirms a conjecture of Goldman for this case. The main tool we use is Kashaev-Penner's lengths coordinates of the decorated character spaces.

math.GT↗
arXiv2014

Angle structures and hyperbolic $3$-manifolds with totally geodesic boundary

This notes explores angle structures on ideally triangulated compact $3$-manifolds with high genus boundary. We show that the existence of angle structures implies the existence of a hyperbolic metric with totally geodesic boundary, and conversely each hyperbolic $3$-manifold with totally geodesic boundary has an ideal triangulation that admits angle structures.

math.GT↗
arXiv2014

Volume and rigidity of hyperbolic polyhedral $3$-manifolds

We investigate the rigidity of hyperbolic cone metrics on $3$-manifolds which are isometric gluing of ideal and hyper-ideal tetrahedra in hyperbolic spaces. These metrics will be called ideal and hyper-ideal hyperbolic polyhedral metrics. It is shown that a hyper-ideal hyperbolic polyhedral metric is determined up to isometry by its curvature and a decorated ideal hyperbolic polyhedral metric is determined up to isometry and change of decorations by its curvature. The main tool used in the proof is the Fenchel dual of the volume function.

math.GT↗
arXiv2013

Generation of Diffraction-Free Optical Beams Using Wrinkled Membranes

We report the first demonstration of wrinkled membranes as a kind of optical focusing devices, which are low cost, light weight and flexible. Our device consists of concentric wrinkle rings on a gold-PDMS bilayer membrane, which converts collimated illuminations to diffraction-free focused beams. Beam diameters of 300-400 μm have been observed in the visible range. By comparing the theoretically calculated and experimentally measured focal spot profiles, we predict a focal spot size as small as around 50 μm if fabrication eccentricity can be eliminated.

physics.optics↗
arXiv2012

The skein algebra of arcs and links and the decorated Teichmüller space

We define an associative algebra AS_h(S) generated by framed arcs and links over a punctured surface S which is a quantization of the Poisson algebra C(S) of arcs and curves on S. We then construct a Poisson algebra homomorphism from C(S) to the space of smooth functions on the decorated Teichmuller space endowed with the Weil-Petersson Poisson structure. The construction relies on a collection of geodesic lengths identities in hyperbolic geometry which generalize Penner's Ptolemy relation, the trace identities and Wolpert's cosine formula. As a consequence, we derive an explicit formula for the geodesic lengths functions in terms of the edge lengths of an ideally triangulated decorated hyperbolic surface.

math.GT↗