Estimation of cut-off wavelength of rare earth doped single-mode fibers

A new empirical relation is proposed describing spectral variation of mode-field radius (MFR) as inferred from measurements in the far-field of the fiber. It is shown that using this relation, it is possible to estimate the cut-off wavelength (λ_c) of the fiber. The proposed technique is successfully tested through measurements made on two standard step index single-mode fibers, as well as on an erbium doped fiber (EDF) having λ_c falling within its strong absorption band around 980 nm. This empirical formula is more accurate than the widely used Marcuse's formula to describe spectral dependence of MFR determined through measurements made in the fiber's far-field. The proposed technique is especially suited for estimation of λ_c of doped fibers in which λ_c falls within an absorption band.     

The effects of light–heavy hole transitions on the cutoff wavelengths of far infrared detectors

Results are presented on the effects of doping variation on the cutoff wavelength (λ_c) of homojunction interfacial workfunction internal photoemission far infrared detectors. The behavior at low doping (<10¹⁹ cm⁻³) is well predicted by the free carrier absorption model used previously. However at high doping the observed λ_c is much shorter than the values predicted by the workfunction obtained from Arrhenius plots. An explanation for the reduced λ_c in the high doping region is presented using a model for depletion of the heavy hole band due to direct transitions from the heavy hole to light hole band.     

A practical depth distribution function for angle-resolved Auger/photoelectron spectroscopy

It is shown that, to a good approximation, over the range of energies (single scattering albedo, ω 0.5) and angles (take-off angle >30°) used in angle-resolved AES and XPS spectroscopy, the depth distribution function (DDF) is approximately exponential with decay length Λ = λ_i(1 + λ_i/λ_tr)^−1/2, for inelastic mean free path (IMFP) λ_i, and transport mean free path λ_tr.

As Λ is also the length measured for the attenuation length experimentally (with either the overlayer technique or from backscatter spectra, equivalent to λ_i, using an interpretation which neglects elastic effects), the CDP may be obtained by straightforward Laplace inversion using experimentally determined attenuation lengths. That is, the correct composition depth profile may be obtained from systematically ignoring elastic scattering.     

Spontaneous breaking of scale invariance in a supersymmetric model

The phase structure of a large N, O(N) supersymmetric model in three dimensions is studied. Of special interest is the spontaneous breaking of scale invariance which occurs at a fixed value of the coupling constant, λ₀=λ_c=4π. In this phase the bosons and fermions acquire a mass while a Goldstone boson (dilaton) and Goldstone fermion (“dilatino”) are dynamically generated as massless bound states. The absence of renormalization of the dimensionless coupling constant λ₀ leaves these Goldstone particles massless.     

Generalized Einstein manifolds

A Finslerian manifold is called a generalized Einstein manifold (GEM) if the Ricci directional curvature R(u,u) is independent of the direction. Let F⁰(M, g_t) be a deformation of a compact n-dimensional Finslerian manifold preserving the volume of the unitary fibre bundle W(M). We prove that the critical points g₀ F⁰(g_t) of the integral I(g_t) on W(M) of the Finslerian scalar curvature (and certain functions of the scalar curvature) define a GEM. We give an estimate of the eigenvalues of Laplacian Δ defined on W(M) operating on the functions coming from the base when (M, g) is of minima fibration with a constant scalar curvature H admitting a conformal infinitesimal deformation (CID). We obtain λ ≥ H/(n − 1) (Δf = λf). If M is simply connected and λ = H/(n − 1), then (M, g) is Riemannian and is isometric to an n-sphere. We first calculate, in the general case, the formula of the second variationals of the integral I (g_t) for G = g₀, then for a CID we show that for certain Finslerian manifolds, I″(g₀) > 0. Applications to the gravitation and electromagnetism in general relativity are given. We prove that the spaces characterizing Einstein-Maxwell equations are GEMs.     

Outer curvature and conformal geometry of an imbedding

The differential geometry of an imbedded (e.g. string or membrane world sheet) surface in a higher-dimensional background is shown to be conveniently describable (except in the null limit case) in terms of what are designated as its first, second, and third fundamental tensors, which will have the respective symmetry properties η_μν = η_(μν) as a trivial algebraic identity, K_μν^ρ = K_(μν)^ρ as the “generalised Weingarten identity”, which is the (Frobenius type) integrability condition for the imbedding, and Ξ_λμν^ρ = Ξ_(λμν)^ρ as a “generalised Codazzi equation”, which depends on the background geometry being flat or of constant curvature, needing replacement by a more complicated expression for a generic value of the background curvature B_κλ^μ_ν. The “generalised Gauss equation” expressing the dependence on this background curvature of the internal curvature tensor R_κλ^μ_ν of the imbedded surface is converted into terms of the first and second fundamental tensors, and it is thereby demonstrated that the vanishing of the (conformally invariant) “conformation tensor”, i.e. the trace free part C_μν^ρ of the second fundamental tensor K_μv^ρ, is a sufficient condition for conformal flatness of the imbedded surface (and thus in particular for the vanishing of its (Weyl type) conformal curvature tensor C_κλ^μ_ν) provided the background is itself conformally flat. In a trio of which the first two members are the generalised Gauss and Codazzi equations, the “third” member is shown to give an expression in terms of C_μν^ρ for the (trace free, conformally invariant) “outer curvature” tensor Ω_κλ^μ_ν whose vanishing is the condition for feasibility of the natural generalisation of the Walker frame transportation ansatz. The vanishing of C_μν^ρ is shown to be sufficient in a conformally flat background for the vanishing also of Ω_κλ^μ_ν.     

Size dependence of light-field enhancement caused by surface plasmon excitation

A theory is presented for the light-field enhancement (LFE) near a metal sphere when surface plasmons are excited. Both the spatial dispersion and electromagnetic retardation effects are shown to suppress the LFE if the sphere radius a becomes comparable with the screening length l_TF or the light wavelength λ, respectively. The maximum value of the LFE close to the result of quasi-electrostatics without spatial dispersion is achieved at a≈50 Å, in which case l_TFaλ/2π.     

The temperature dependence of the short wavelength transmittance limit of vacuum ultraviolet window materials—I. Experiment

The short wavelength transmittance limit or cut-off wavelength, λ_co, of LiF, MgF₂, CaF₂, LaF₃, BaF₂, sapphire, synthetic crystal quartz and fused quartz has been measured from about 100°C to about 10°K. λ_co is not a well denned quantity, so for the purpose of this experiment it has been arbitrarily taken as the wavelength where transmittance could just be measured, usually 0.1-0.5 per cent. With one exception λ_co shifted to shorter wavelengths as the sample was cooled; the shift varied from about 40 to 80 Å over the temperature range from 100°C to 10°K, depending on the material, with the largest shift occurring in BaF₂;. The exception was LaF₃ which showed no measurable change in λ_co wth temperature. Over the temperature range from 20° to 100°C the slope of λ_co, with temperature for all materials was fairly constant, but below 20°C it decreased, approaching zero as the temperature approached 20°-10°K. In the case of synthetic crystal quartz, for example, the slope changed from about 0.28 Å/°K at room temperature to about 0.055 Å/°K at 80°K.     

光纤截止波长的依赖关系

光纤截止波长是单模光纤的一个重要参数，它与许多因素如模场直径、长度、弯曲、衰减等有关。本文分析研究与截止波长相关的这些因素后，指出在制造光纤光缆时要尽可能减少对光纤截止波长不利的因素，将最小工作波长提高到60－70nm作为设计光纤的截止波长上限，从而有利于降低光纤弯曲损耗。     

Itinerant-localized duality description of the spin fluctuations in the normal state of high-Tc cuprates. An explanation of neutron scattering experiments

On the basis of the itinerant-localized duality theory of spin fluctuations, the puzzling aspects of the neutron scattering experiments in the normal state of high-T_c cuprates are clarified from a global point of view. The dynamical spin structure factor exhibits two different aspects depending on the energy transfer ω. At lower energies, ω < ω_c, where ω_c is the fermion coherence energy, the spectrum is coherent so that the characteristic scales for wavevector and energy are temperature dependent, while at higher energies, ω > ω_c, the spectrum is incoherent so that those characteristic scales are temperature independent. The integrated weight of the coherent part of the spectrum exhibits the so-called “spin gap” behavior when the Fermi surface of the itinerant fermion is technically nested, even though there is no excitation gap in the spectrum at all.     

Study on the bend characteristics of single mode-multimode-single mode optical fiber structure

In this paper, the bend characteristics of the single mode-multimode-single mode (SMS) fiber structure are experimentally investigated. SMS fiber structure is very sensitive to the bend. The central wavelength shifts to shorter wavelength with the increasing of fiber bend angle. The central wavelength shift changes with the changing of multimode fiber(MMF) bend section length. The shorter bend MMF has higher sensitivity to the bend angle.     

Computer simulations of ion scattering and recoiling blocking patterns for surface structure analysis

A three-dimensional classical ion trajectory simulation code has been developed and applied to ion scattering and recoiling patterns on a large-area detector. The test systems used for the patterns were as follows: (1) Pt{110})-(1 × 2) and −(1 × 3) as an example of a reconstructed metal surface; (2) Ni{100}, {110}, and {111} surfaces as an example of different crystal faces: and (3) Ni{110}−(2 × 1)−O as an example of adsorbate recoiling. The optimum experimental configurations for collecting data for structural analysis have been considered. Three configurations have been identified; these include collection of both in- and out-of-plane scattering and recoiling data. The anisotropic patterns obtained for the scattered I_S, and recoiled I_R flux in azimuthal δ and exit β angle space are produced by blocking cones and are unique for the specific substrate and adsorbate structures. Critical exit β_c and azimuthal δ_c angles can be identified from these patterns. The interatomic spacings d along specific azimuths are determined from measurements of β_c and δ_c. Simulated patterns for the three test systems listed above are presented and their features are analyzed in terms of the surface structures. The advantages and new features available through the use of large-area detectors are described and compared to conventional ion scattering spectrometry (ISS). In the case of Pt, for which comparable experimental scattering data are available, the agreement between simulations and experimental results is good.     

Determination of the inelastic mean free path of electrons in silver and copper by measurement and calculation of the elastic scattering coefficient

The inelastic mean free paths, λ, of electrons in polycrystalline Ag and Cu samples were determined for electron energies in the range 250–1500 eV by means of elastic peak electron spectroscopy (EPES). In this method the coefficient of elastic scattering of electrons, η_e, is measured. η_e is also calculated theoretically for different assumed values of λ. The value of λ giving the best agreement between the measured and calculated η_e is taken as the experimental one. the η_e measurements were performed for Ag and Cu samples cleaned by mechanical scraping only and for samples cleaned by ion bombardment in order to estimate the eventual influence of surface roughness on the η_e values. Additionally, different methods to calculate η_e theoretically are compared.     

Dielectric and ferroelectric properties of the mixed crystals system (CH3NH3)5Bi2(1 − x)Sb2xCl11

Dielectric and pyroelectric properties of the mixed crystals system, (CH₃NH₃)₅Bi_{2(1 − x)}Sb_2xCl₁₁ (0 < x < 0.25) were systematically investigated. Temperature dependencies of ′_c in the vicinity of ferro-paraelectric phase transition were measured for the mixed crystals with x = 0.05, 0.07, 0.11, 0.13 and 0.25 in the frequency region 1 kHz–1 MHz. The substitution of bismuth atoms by antimony drastically reduces the magnitude of ′_c and shifts the ferro-paraelectric phase transition towards higher temperatures. The dielectric dispersion of the complex electric permittivity, _c^*, in x = 0.05 crystals was studied in the frequency range from 30 to 1000 MHz. Around 321 K phase transition, two dielectric relaxators are postulated; a low-frequency one in the megahertz region showing a critical slowing down and a high-frequency one in the gigahertz region.     

Anisotropic dielectric properties of PbYb1/2Ta1/2O3 single crystals

PbYb_1/2Ta_1/2O₃ single crystals were obtained for the first time. They were grown by the flux method. The PbOPbF₂B₂O₃ system was used as a solvent. Dielectric investigations were carried out in 1 0 0_c, 1 1 0_c and 1 1 1_c pseudocubic directions. These studies pointed to anisotropy of dielectric properties. Frequency-independent ε′(T) and ε″(T) maxima related to the antiferroelectric–paraelectric (AFE—PE) phase transition are observed for all directions at 562 K. The frequency-dependent ε′(T) and ε″(T) maxima near 400 K related to the ferroelectric (FE)–AFE phase transition are observed only in 1 1 1_c direction. The hysteresis loops were observed in this direction only. These results point that ferroelectric relaxor properties appear only in 1 1 1_c direction. We propose to consider the ferroelectric phase as ferrielectric one.     

Vortex penetration depth of κ-(ET)2Cu[N(CN)2]Br

The magnetic field dependence of the in-plane penetration depth λ_|(H) for single crystal κ-(ET)₂Cu[N(CN)₂]Br has been measured at 3, 9.6, and 36 MHz. Over a limited range, λ_| scales with a characteristic field H^*(T) that coincides with a shoulder in the λ_| vs. H curves. Above that field, λ_| increases sharply toward a second inflection point at H^**(T) that coincides with is close to the irreversibility line measured by magnetization. For fields larger than H^** the penetration depth diverges, suggesting that the vortex lattice has melted. The field dependence at one frequency agrees qualitatively with a model of pinned vortices at low fields giving way to flux flow at higher fields. However, the observed frequency dependence deviates significantly from the predictions of this model, suggesting that collective effects play a major role. Our technique also yields a new measurement for the interplane penetration depth λ 300 μm, implying an anisotropy λ/λ_| > 200.     

掺铒孔辅助导光光纤的特性研究与优化设计

掺铒孔辅助导光光纤是由掺铒的高折射率纤芯、低折射率包层和少量的空气孔组成. 采用有限元法分析了掺铒孔辅助导光光纤的模式特性；给出了数值计算截止波长和模场直径的方法；提出了改进的平均粒子数反转度迭代算法来数值计算掺铒光纤放大器的增益和噪声系数. 研究空气孔对掺铒孔辅助导光光纤的截止波长、模场直径和放大器的增益系数的影响. 发现：减小相对孔芯距的值，可使截止波长向短波长移动，减小模场直径的值；当孔的相对大小较大时，截止波长、模场直径和增益的最大值基本上不随孔的相对大小的增大而改变. 最后，综合考虑掺铒光纤基模和二阶模的截止波长、与普通单模光纤的熔接损耗、放大器的增益和噪声系数等因素，优化设计了掺铒孔辅助导光光纤的四个结构参量——纤芯半径、纤芯与包层的折射率差、相对孔芯距和孔的相对大小. 关键词： 孔辅助导光光纤 掺铒光纤 光纤放大器 有限元法     

Tuning, attenuating, and switching by controlled flexure of long-period fiber gratings

Azimuthal variations in the refractive index that are inherent in CO(2) -laser-induced long-period fiber gratings (LPFG's) coupled to small controlled flexure of the LPFG produce a wide variety of transmission characteristics as a function of LPFG curvature. The particularly useful cases of (1) wavelength tuning at a constant attenuation and (2) variable attenuation (switching) at a constant wavelength are demonstrated by flexing of LPFG's that have been appropriately axially rotationally oriented relative to the plane of curvature.     

The dispersion properties of surface acoustic wave devices on AlN/LiNbO3 film/substrate structure

Highly c-axis oriented aluminum nitride (AlN) films were deposited on z-cut LiNbO₃ substrates by reactive rf magnetron sputtering. The crystalline properties investigated by X-ray diffraction (XRD) revealed that AlN film with (0 0 2) preferred orientation was improved by an increase of the deposition time within the experimental range. However, the surface morphology of AlN film measured by scanning probe microscopy (SPM) showed that the roughness was getting worse with increase of deposition time. Surface acoustic wave (SAW) properties, measured by a network analyzer in the structure consisting of highly c-axis AlN films on z-cut LiNbO₃ substrates, were investigated. The phase velocity (V_P) was significantly increased by the increase of h/λ, where h is the thickness of AlN film and λ is the wavelength. However, the insertion loss (IL) of SAW filters was also increased by the increase of h/λ. Experimental results on the temperature characteristics of SAW devices are also presented.     

Interesting effect of optical Kerr nonlinearity in expanding single-mode regime of optical fibers using dispersion-flattened profiles

An interesting effect of optical Kerr nonlinearity is reported from theoretical investigation on the fundamental and first higher mode cutoff frequencies in single-mode fibers doped with highly nonlinear materials like CdS_xSe_1−x with W-type dispersion-flattened profiles. It is observed that whereas the single-mode regime decreases absolutely for dispersion-shifted profiles due to reduction of the first higher order mode cutoff frequency as is evident from earlier studies, it increases for W-type profiles for such nonlinearity taking its effect on the nonzero fundamental mode cutoff frequency into consideration. Thus, one can go further down below the fundamental mode cutoff frequency while using W-fibers in single mode nonlinear fiber devices involving evanescent field coupling in the low V region.