Numerical simulation of a truncated cladding negative curvature fiber sensor based on the surface plasmon resonance effect

A refractive index(RI)sensor based on the surface plasmon resonance effect is proposed using a truncated cladding negative curvature fiber(TC-NCF).The influences of the TC-NCF structure parameters on the sensing performances are investigated and compared with the traditional NCF.The simulation results show that the proposed TC-NCF RI sensor has an ultra-wide detection range from 1.16 to 1.43.The maximum wavelength sensitivity reaches 12400 nm/RIU,and the corresponding R^(2)of the polynomial fitting equation is 0.9999.The maximum and minimum resolutions are 2.56×10^(-5)and 8.06×10^(-6),respectively.In addition,the maximum amplitude sensitivity can reach-379.1 RIU^(-1)when the RI is chosen as 1.43.The proposed TC-NCF RI sensor could be useful in biochemical medicine,environmental monitoring,and food safety.

Single-polarization single-mode hollow-core negative curvature fiber with nested U-type cladding elements

Hollow-core negative curvature fibers(HC-NCFs)have become one of the research hotspots in the field of optical fiber because of their potential applications in the data and energy transmissions.In this work,a new kind of single-polarization single-mode HC-NCF with nested U-type cladding elements is proposed.To achieve the single-polarization single-mode transmission,we use two different silica tubes in thickness,which satisfy the resonance and anti-resonance conditions on the U-type cladding elements and the cladding tubes,respectively.Besides,the elliptical elements are introduced to achieve good single-mode performance.By studying the influences of the structure parameters on the propagation characteristics,the optimized structure parameters are obtained.The simulation results show that when the wavelength is fixed at 1550 nm,the single-polarization single-mode transmission is achieved,with the polarization extinction ratio of 25749 and minimum high-order mode extinction ratio of 174.Furthermore,the confinement loss is only 0.0015 dB/m.

An Interpolation of Hardy Inequality and Moser–Trudinger Inequality on Riemannian Manifolds with Negative Curvature

Let M be a complete, simply connected Riemannian manifold with negative curvature. We obtain an interpolation of Hardy inequality and Moser-Trudinger inequality on M. Furthermore, the constant we obtain is sharp.

On the Negativity of Ricci Curvatures of Complete Conformal Metrics

A version of the singular Yamabe problem in bounded domains yields complete conformal metrics with negative constant scalar curvatures.In this paper,we study whether these metrics have negative Ricci curvatures.Affirmatively,we prove that these metrics indeed have negative Ricci curvatures in bounded convex domains in the Euclidean space.On the other hand,we provide a general construction of domains in compact manifolds and demonstrate that the negativity of Ricci curvatures does not hold if the boundary is close to certain sets of low dimension.The expansion of the Green’s function and the positive mass theorem play essential roles in certain cases.

A NONMONOTONE SECOND-ORDER STEPLENGTH METHOD FOR UNCONSTRAINED MINIMIZATION

In this paper, a nonmonotone method based on McCormick＇s second-order Armijo＇s step-size rule [7] for unconstrained optimization problems is proposed. Every limit point of the sequence generated by using this procedure is proved to be a stationary point with the second-order optimality conditions. Numerical tests on a set of standard test problems are presented and show that the new algorithm is efficient and robust.