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Xiaoyan Zhang

Publications and source records attributed to Xiaoyan Zhang.

67 records · Page 4Linked to original sources
arXiv2019

Extremality and Sharp Bounds for the $k$-edge-connectivity of Graphs

Boesch and Chen (SIAM J. Appl. Math., 1978) introduced the cut-version of the generalized edge-connectivity, named $k$-edge-connectivity. For any integer $k$ with $2\leq k\leq n$, the {\em $k$-edge-connectivity} of a graph $G$, denoted by $λ_k(G)$, is defined as the smallest number of edges whose removal from $G$ produces a graph with at least $k$ components. In this paper, we first compute some exact values and sharp bounds for $λ_k(G)$ in terms of $n$ and $k$. We then discuss the relationships between $λ_k(G)$ and other generalized connectivities. An algorithm in $\mathcal{O}(n^2)$ time will be provided such that we can get a sharp upper bound in terms of the maximum degree. Among our results, we also compute some exact values and sharp bounds for the function $f(n,k,t)$ which is defined as the minimum size of a connected graph $G$ with order $n$ and $λ_k(G)=t$.

cs.DM↗
arXiv2018

A photonic crystal-based broadband graphene saturable absorber

The enhanced nonlinear optical response of a one-dimensional (1D) photonic crystal (PC) made from polymers and graphene composites is observed. The graphene PC was fabricated by spin-coating. It shows obvious bandgaps at two wavelengths in transmittance. Femtosecond Z-scan measurement at 515 nm and 1030 nm reveals a distinct enhancement in the effective nonlinear absorption coefficient Beff (and imaginary part of third-order dielectric susceptibility ImX(3)) for graphene nanoflakes embedded in the PC, when compared with the bulk graphene-polymer dispersion. The effect is studied in a wide range of laser intensities. The inclusion of graphene into a 1D-PC remarkably decreases the saturable absorption threshold and saturation intensity, providing a desired solution for an advanced all-optical laser mode-locking device.

physics.optics↗
arXiv2018

Stimulated Brillouin scattering in dispersed graphene

We address the problem of the interaction of powerful laser radiation with a transparent substance containing a low concentration of strongly absorbing nanoparticles under the condition of Stimulated Brillouin scattering (SBS) whose behavior in such media was unexplored. SBS energies in N-methyl-2-pyrrolidone (NMP) and water are measured at the wavelength of 532 nm. An experimental value $g_B = 18.6 \pm 1.8$ cm/GW for a previously unknown Brillouin gain factor of NMP is reported. A strong SBS quenching in the liquids by graphene nanoflakes is found. SBS threshold linear dependences on graphene absorption coefficient (concentration) are established and found suitable for the detection of small nanoparticles quantities in water with a minimal detectable concentration of $5 \cdot 10^{-8}$ g/ml. The effect is considered through an electrostriction - thermal expansion antagonism induced by carbon vapor bubbles formation. It is found to be very sensitive to changes in density, refractive index and acoustic absorption coefficient. Using the SBS method, their determination and the bubbling nanosecond time-scaling can be performed. The effect is advantageous for SBS suppression when it is undesirable in laser technologies and optical telecommunication networks.

physics.optics↗
arXiv2018

Strong Subgraph $k$-connectivity

Generalized connectivity introduced by Hager (1985) has been studied extensively in undirected graphs and become an established area in undirected graph theory. For connectivity problems, directed graphs can be considered as generalizations of undirected graphs. In this paper, we introduce a natural extension of generalized $k$-connectivity of undirected graphs to directed graphs (we call it strong subgraph $k$-connectivity) by replacing connectivity with strong connectivity. We prove NP-completeness results and the existence of polynomial algorithms. We show that strong subgraph $k$--connectivity is, in a sense, harder to compute than generalized $k$-connectivity. However, strong subgraph $k$-connectivity can be computed in polynomial time for semicomplete digraphs and symmetric digraphs. We also provide sharp bounds on strong subgraph $k$-connectivity and pose some open questions.

cs.DM↗
arXiv2017

Directed Hamilton cycles in digraphs and matching alternating Hamilton cycles in bipartite graphs

In 1972, Woodall raised the following Ore type condition for directed Hamilton cycles in digraphs: Let $D$ be a digraph. If for every vertex pair $u$ and $v$, where there is no arc from $u$ to $v$, we have $d^+u)+d^-(v)\geq |D|$, then $D$ has a directed Hamilton cycle. By a correspondence between bipartite graphs and digraphs, the above result is equivalent to the following result of Las Vergnas: Let $G = (B,W)$ be a balanced bipartite graph. If for any $b \in B$ and $w \in W$, where $b$ and $w$ are nonadjacent, we have $d(w)+d(b) \geq |G|/2 + 1$, then every perfect matching of $G$ is contained in a Hamilton cycle. The lower bounds in both results are tight. In this paper, we reduce both bounds by $1$, and prove that the conclusions still hold, with only a few exceptional cases that can be clearly characterized.

math.CO↗
arXiv2017

Minimum size of n-factor-critical graphs and k-extendable graphs

We determine the minimum size of $n$-factor-critical graphs and that of $k$-extendable bipartite graphs, by considering Harary graphs and related graphs. Moreover, we determine the minimum size of $k$-extendable non-bipartite graphs for $k=1,\ 2$, and pose a related conjecture for general $k$.

math.CO↗
arXiv2017

An all optical phase shifter and switch near 1550nm using tungsten disulfide (WS2) deposited tapered fiber

Optical phase shifters and switches play an important role for various optical applications including optical signal processing, sensing and communication. In this paper, we demonstrate a fiber all optical phase shifter using few-layer 2D material tungsten disulfide (WS2) deposited on a tapered fiber. WS2 absorbs injected 980 nm pump (control light) and generates heat which changes the refractive index of the tapered fiber due to thermo-optic effect and achieves a maximum phase shift of 6.1π near 1550 nm. The device has a loss of 3.7 dB. By constructing a Mach-Zehnder interferometer with WS2 based phase shifter in one arm, an all optical switch is also obtained with an extinction ratio of 15 dB and a rise time of 7.3 ms. This all fiber low-cost and compact optical phase shifter and switch demonstrates the potential of 2D transition metal dichalcogenides for all optical signal processing devices.

physics.optics↗
arXiv2015

Giant Two-Photon Absorption in Monolayer MoS2

Strong two-photon absorption (TPA) in monolayer MoS2 is demonstrated in contrast to saturable absorption (SA) in multilayer MoS2 under the excitation of femtosecond laser pulses in the near infrared region. MoS2 in the forms of monolayer single crystal and multilayer triangular islands are grown on either quartz or SiO2/Si by employing the seeding method through chemistry vapor deposition. The nonlinear transmission measurements reveal that monolayer MoS2 possesses a giant nonsaturation TPA coefficient, larger than that of conventional semiconductors. As a result of TPA, two-photon pumped frequency up-converted luminescence is observed directly in the monolayer MoS2. For the multilayer MoS2, the SA response is demonstrated with the ratio of the excited-state absorption cross section to ground-state cross section of 0.18. In addition, the laser damage threshold of the monolayer MoS2 is 97 GW/cm2, larger than that of the multilayer MoS2 of 78 GW/cm2.

physics.optics↗
arXiv2015

Direct Observationof DegenerateTwo-Photon Absorption and Its Saturation in WS2 and MoS2 Monolayer and Few-Layer Films

The optical nonlinearity of WS2, MoS2 monolayer and few-layer films was investigated using the Z-scan technique with femtosecond pulses from the visible to the near infrared. The dependence of nonlinear absorption of the WS2 and MoS2 films on layer number and excitation wavelength was studied systematically. WS2 with 1~3 layers exhibits a giant two-photon absorption (TPA) coefficient. Saturation of TPA for WS2 with 1~3 layers and MoS2 with 25~27 layers was observed. The giant nonlinearity of WS2 and MoS2 is attributed to two dimensional confinement, a giant exciton effect and the band edge resonance of TPA.

physics.optics↗
arXiv2015

Optical Limiting and Theoretical Modelling of Layered Transition Metal Dichalcogenide Nanosheets

Nonlinear optical property of transition metal dichalcogenide (TMDC) nanosheet dispersions, including MoS2, MoSe2, WS2, and WSe2, was performed by using Z-scan technique with ns pulsed laser at 1064 nm and 532 nm. The results demonstrate that the TMDC dispersions exhibit significant optical limiting response at 1064 nm due to nonlinear scattering, in contrast to the combined effect of both saturable absorption and nonlinear scattering at 532 nm. Selenium compounds show better optical limiting performance than that of the sulfides in the near infrared. A liquid dispersion system based theoretical modelling is proposed to estimate the number density of the nanosheet dispersions, the relationship between incident laser fluence and the size of the laser generated micro-bubbles, and hence the Mie scattering-induced broadband optical limiting behavior in the TMDC dispersions.

physics.optics↗
arXiv2014

WS2 as a saturable absorber for ultrafast photonic applications of mode-locked and Q-switched lasers

Two-dimensional (2D) nanomaterials, especially the transition metal sulfide semiconductors, have drawn great interests due to their potential applications in viable photonic and optoelectronic devices, such as saturable absorbers (SAs) and optical switches, etc. In this work, tungsten disulfide (WS2) based SA for ultrafast photonic applications was demonstrated. WS2 nanosheets were prepared using liquid-phase exfoliation method and embedded in polyvinyl alcohol (PVA) thin film for the practical usage. Saturable absorption was observed in the WS2-PVA SA at the telecommunication waveband near 1550 nm. By incorporating WS2-PVA SA into a fiber laser cavity, both stable mode locking operation and Q-switching operation were achieved. In the mode locking operation, the laser obtained femtosecond output pulse width and high spectral purity in the radio frequency spectrum. In the Q-switching operation, the laser had tunable repetition rate and output pulse energy of a few tens of nano joule. Our findings suggest that few-layer WS2 nanosheets embedded in PVA thin film are promising nonlinear optical materials for ultrafast photonic applications as a mode locker or Q-switcher.

physics.optics↗
arXiv2005

New versions of the all-ones problem

We study three new versions of the All-Ones Problem and the Minimum All-Ones Problem. The original All-Ones Problem is simply called the Vertex-Vertex Problem, and the three new versions are called the Vertex-Edge Problem, the Edge-Vertex Problem and the Edge-Edge Problem, respectively. The Vertex-Vertex Problem has been studied extensively. For example, existence of solutions and efficient algorithms for finding solutions were obtained, and the Minimum Vertex-Vertex Problem for general graphs was shown to be NP-complete and for trees it can be solved in linear time, etc. In this paper, for the Vertex-Edge Problem, we show that a graph has a solution if and only if it is bipartite, and therefore it has only two possible solutions and optimal solutions. A linear program version is also given. For the Edge-Vertex Problem, we show that a graph has a solution if and only if it contains even number of vertices. By showing that the Minimum Edge-Vertex Problem can be polynomially transformed into the Minimum Weight Perfect Matching Problem, we obtain that the Minimum Edge-Vertex Problem can be solved in polynomial time in general. The Edge-Edge Problem is reduced to the Vertex-Vertex Problem for the line graph of a graph.

math.CO↗