Bend radiation in optical fibers

A new, relatively simple way of calculating bend radiation is developed. As is often done in propagation over gently curved surfaces, the fiber curvature is accounted for by placing a straight fiber in a fictitious medium that is inhomogeneous in the plane of the bend. For a gently curved fiber, the medium is slowly varying and the WKB method is used to approximate the radial field dependence. This solution is related to the unperturbed straight fiber solution through an ansatz consistent with the WKB solution. The propagating modes in this approximation remain orthogonal, allowing an immediate generalization to the multimoded case. The radiation loss per unit length is calculated two ways and is consistent with results in the literature.     

Mode conversion and radiation losses in a step-index optical fibre due to bending

Wave propagation in a step-index optical fibre with a curved section is treated theoretically. Mode conversion and radiation take place. The mode coupling coefficients which depend on the polarization of the incident mode are calculated. Radiation losses at the transition between a straight and a curved fibre section and total losses including the continuous radiation loss due to a uniform bend are evaluated. Comparisons are also made between singly and doubly clad fibres. It is shown that the doubly clad fibre can tolerate a sharper bend.Requests for reprints should be sent to Professor G. L. Yip.     

Flow visualization of relaminarization phenomena in curved pipes and the related measurements

Flow visualization results for secondary flow phenomena at the exit of 90° and 180° bends and helically coiled pipes (1, 2 and 5 turns), (radius of curvatureR _c=381 mm, inside pipe diameterd=37.5 mm, curvature ratiod/2R _c=0.049) and in the downstream straight pipe (l/d=30) are presented to study the stabilizing (relaminarization) effect in curved pipes with fully developed entry turbulent air flow and the destabilizing (re-transition from laminar to turbulent flow) effect in the downstream straight region. The entry Reynolds numbers areRe=2200, 3200, 4300 and 5300). The related measurement results using a hot-film anemometer are presented for developing profiles of the time-mean streamwise velocity distribution and the axial turbulence intensity field in the 180° return bend and in the downstream straight pipe for Reynolds numbersRe=3200, 4300, 6300 and 8200. The time traces showing the output of the hot-film sensor are also presented for developing fluctuating velocity field in the 180° bend and in the downstream straight pipe for the same Reynolds number range. Some aspects of the relaminarization phenomena in curved pipes and the re-transition phenomena from laminar to turbulent flow in the downstream straight pipe are clarified by the present experimental investigation.     

新型抗弯曲大模场面积光子晶体光纤

研制出一种新型抗弯曲大模场面积石英光子晶体光纤. 利用光子晶体光纤结构设计的灵活性, 通过规划缺陷的位置及空气孔的尺寸, 实现了大模场面积单模及低弯曲损耗特性.应用建立的实际光子晶体光纤特性分析模型, 研究了研制光纤的模式特性和弯曲特性, 在波长1064 nm处, 平直状态下光纤的模场面积可以达到2812 μm², 基模限制损耗为0.00024 dB/m, 高阶模限制损耗高于1.248 dB/m. 基模和高阶模之间的高传输损耗差, 保证了在获得大模场面积的同时实现单模传输. 弯曲半径和弯曲方向角所带来弯曲损耗变化的研究结果显示, 即使在弯曲半径小到5 cm时, 弯曲损耗也在10^-3 dB/m量级以下, 而且在弯曲半径为30 cm时光纤可承受的弯曲方向角范围扩展至-60°–60°. 研制的光纤具有良好的低弯曲损耗特性, 可有效解决非对称结构所带来的光纤弯曲特性对弯曲方向角敏感的问题. 该光纤在高功率光纤激光器、放大器及高功率传输等技术领域具有重要的应用价值. 关键词： 光子晶体光纤 大模场面积 低弯曲损耗 弯曲方向角     

Quantum graviton creation in a model universe

Quantization in the spatially inhomogeneous, anisotropic, Gowdy three-torus solution of Einstein's equations leads to the production of gravitons from empty space. The creation of pairs of gravitons occurs only in wave modes with wavelength exceeding the horizon size at an initial time. The final number of created gravitons in any mode is proportional to the number of causally unconnected regions at the initial time over the wavelength of that mode. At large times, graviton number is well defined since the solution is in WKB form. The creation process produces the anisotropic collisionless radiation identical to that discussed by Doroshkevich, Zel'dovich, and Novikov which characterizes the large time classical solution. Near the singularity, the model behaves like an empty Bianchi Type I universe at each point in space (local Kasner). The canonical methods of Arnowitt, Deser, and Misner yield a reduced Hamiltonian from which the classical equations of motion are obtained. The quantization of the rapidly varying gravitational field component resembles the procedures used by Parker or Zel'dovich et al. to study particle creation in curved spacetime.     

Modal theory for the two-frequency mutual coherence function in random media: general theory and plane wave solution: II

Abstract

In a previous publication (part I) it has been shown that for an arbitrary statistically isotropic and homogeneous medium the parabolic equation for the two-frequency mutual coherence function can be separated and thereby expressed as a superposition of modes. A parameterization based on the longitudinal part of this representation has also been treated. This paper explores the transverse structure and parameterization of the field solution by employing dimensional, variational and the modified WKB procedures for solving the eigenfunction/eigenvalue problem. General expressions are derived first for a general structure function and then specialized for a power-law structure function with emphasis on quadratic and Kolmogorov media.     

Semi-Analytical Simulation of Titanium-Indiffused Lithium Niobate–Integrated Optic Directional Couplers Consisting of Curved Waveguides

Integrated optic directional couplers consisting of curved waveguides are simulated analytically by solving the Riccati equation. The coupling coefficient between the curved waveguides with a parabolically varying gap and the condition of total power transfer between the waveguides are derived. In order to compute the overall coupling coefficient and hence the power distribution along the waveguides for Ti:LiNbO ₃ curved waveguide directional couplers, the coupling coefficient for straight waveguide couplers is computed for different gaps using the effective-index-based matrix method (EIMM). Finally, the power distribution in the curved waveguides along the length is computed. The method is mostly analytical except the effective-index method and is computationally simple.     

Analysis of curved bends in arbitrary optical devices using cylindrical coordinates

An extension of the beam propagation algorithm based on the method of lines (MoL–BPM) is proposed and substantiated for analysis of curved bends–constituent parts of complicated optical devices, connecting waveguides with different orientation. Cylindrical coordinates are introduced. The formulas are compatible with those in Cartesian coordinates for analysis of straight waveguides. So, in combination concatenations of curved bends and straight waveguides can be examined in a uniform way. For the purpose of analysis in cylindrical coordinates a suitable set of wave equations without any approximation and valid for a general hybrid case is derived. To prove the accuracy of the MoL–BPM in cylindrical coordinates applying the derived formulas, the curvature loss of a rib waveguide was computed and compared with other methods showing very good agreement. As an application of the method two straight waveguides are connected by a curved bend and the power flow is determined.     

Straight and curved disclinations and dislocation equivalents

ABSTRACT

Traditionally, for hard materials, two types of straight disclinations are identified although some Somigliana disclinations with different aspects have been treated theoretically. Here, we consider four physically distinct types of curved generalised disclinations, one of which reduces to two straight types, giving a total of five. We indicate typical applications for the different types.     

The acoustic characteristics of duct bends

The acoustic characteristics of a duct system were studied. The system consisted of a curved bend joined to two straight sections of rigid duct. Solutions of the relevant two-dimensional equations were obtained by numerical methods for a range of bend geometries. The results agreed closely with experimentally obtained data. The effects on the acoustic characteristics of locating a circular arc turning vane in the bend were investigated numerically and experimentally for values of the wave number below that corresponding to the first cut-on mode. Particular attention was paid to the amplitude of the evanescent modes generated at the junction of the bend and the straight sections of duct.     

Nonstationary two-flux model of radiation transport for optical tomography of scattering media

A nonstationary two-flux model is formulated for the transport of radiation in an inhomogeneous scattering medium and is applied to the situation where such a medium is irradiated by the narrow beam of a pulsed laser. It is shown that when the time distribution of the transmitted photons is measured it is possible simultaneously to reconstruct the two spatial functions (the coefficients of absorption coefficient and of scattering of the radiation by the medium) by means of an inverse Radon transformation and the solution of a system of nonlinear differential equations on the projection lines. An analytic solution is obtained in quadratures for these differential equations. The results constitute a method of solving problems in optical tomography in an inhomogeneous scattering medium Zh. Tekh. Fiz. 67, 61–65 (May 1997)     

Evolution of polarization in an inhomogeneous isotropic medium

The depolarization and rotation of the polarization plane of radiation propagating in a two-dimensional graded-index medium is investigated on the basis of the quantum-mechanical method of coherent states. It is shown that the degree of polarization of both linearly and circularly polarized radiation decreases with increasing distance as a result of interaction between the polarization (spin) and the path (orbital angular momentum) of the beam. The wave nature of the depolarization is emphasized. The depolarization decreases as the radiation wavelength decreases. It is found that the degree of polarization exhibits oscillations of pure diffraction origin during the propagation of light in a single-mode optical fiber. It is shown that the rotation of the polarization plane is nonuniform in character and depends on the offset and the tilt angle of the incident-beam axis relative to the fiber axis. The Berry phase is found to undergo oscillations of a wave nature during the propagation of radiation in an inhomogeneous medium. It is shown that the spread in the angle of rotation of the polarization plane increases with distance and can be determined from measurements of the degree of polarization of the radiation. Zh. éksp. Teor. Fiz. 112, 1985–2000 (December 1997)     

Bend radiation of optical fibres

Theoretical and experimental investigations of the radiation far field from a curved optical fibre have been carried out for the lowest order LP-modes. The investigations concern the characteristics of pure bend loss radiation in a direction orthogonal to the plane of the bend. Possible applications involving the bend radiation are briefly discussed.     

Luminescence-Based Optical Fiber Chemical Sensors

Abstract

A scheme for the simultaneous determination of temperature and analyte concentration for application in luminescence-based chemical sensors is proposed. This scheme is applied to an optical oxygen sensor, which is based on the quenching of the fluorescence of a ruthenium complex. Temperature measurement is performed using the excitation radiation and an absorption long-pass filter. Preliminary results are presented that show the viability of an oxygen measurement that is independent of temperature and optical power level. The possibility of self-referenced temperature measurements with semiconductor nanoparticles is also investigated. In order to optimize the sensor design, several different optical fiber probe geometries for oxygen sensing are tested and compared, including different methods of coupling radiation into the optical fiber system. Polyvinyl alcohol (PVA) and polyacrylamide membranes are tested as supports for sensor immobilization in fiber-optical pH sensing devices in aqueous solution. Some results are presented that show the feasibility of using fiber-optical pH indicators for remote monitoring.     

Multidimensional WKB Approximation for Tunneling Along Curved Escape Paths

Asymptotics of the perturbation series for the ground state energy of the coupled anharmonic oscillators for the positive coupling constant is related to the lifetime of the quasistationary states for the negative coupling constant. The latter is determined by means of the multidimensional WKB approximation for tunneling along curved escape paths. General method for obtaining such approximation is described. The cartesian coordinates (x,y) are choosen in such a way that the x-axis has the direction of the probability flux at large distances from the well. The WKB wave function is then obtained by the simultaneous expansion of the wave function in the coordinate y and the parameter γ determining the curvature of the escape path. It is argued, both physically and mathematically, that these two expansions are mutually consistent. Several simplifications in the integrations of equations are pointed out. It is shown that to calculate outgoing probability flux it is not necessary to deal with inadequacy of the WKB approximation at the classical turning point. The WKB formulas for the large-order behavior of the perturbation series are compared with numerical results and an excellent agreement between the two is found.     

Nonholonomic constraint between the polarization state of light and the twisted angle of a single-mode optical fiber with linear birefringence

The relation between the polarization state of light propagating in a twisted single-mode optical fiber with linear birefringence and the twist angle of the fiber is discussed for the case where the fiber is stretched in a straight line. It is shown that this relation is of the nature of a nonholonomic constraint. Zh. Tekh. Fiz. 68, 128–129 (November 1998)     

Grating-Outcoupled Radiation in Second-Order Fiber Bragg Gratings

Abstract

The experimental results of the radiation for second-order fiber Bragg gratings, which are made of a single-mode photosensitive fiber (PS-1500; Fiber-Core Corp.) and a single-mode fiber (SMF-28; Corning Inc.), by a phase mask writing fabrication technique are explored. For PS-1500 fiber Bragg gratings, the maximum radiation efficiency of ?23.5 dB at resonance λ = 1,539.34 nm with a very narrow bandwidth (about 0.02 nm) are measured from a 10-mm-diameter photo-detector, while for SMF-28 fiber Bragg gratings, the maximum radiation efficiency is ?34.6 dB (λ = 1,538.03 nm) with a bandwidth of 0.06 nm. The total efficiencies of the radiation are about ?16.8 dB for PS-1500 fiber Bragg gratings and ?28.1 dB for SMF-28 fiber Bragg gratings.     

Self-focusing of cosh-Gaussian laser beams in a parabolic medium with linear absorption

The authors have investigated self-focusing of cosh-Gaussian laser beams in a parabolic medium with linear absorption. The field distribution in the medium is expressed in terms of beam-width parameter f, decentred parameter b and absorption coefficient k_i. The differential equation for f parameter is established by following Wentzel–Kramers–Brillouin (WKB) and paraxial approximations through parabolic wave equation approach and analytical solution is obtained for the same. The behavior of f parameter with the normalized distance of propagation η is studied at various values of b with different absorption levels in the medium. The results are presented graphically and discussed.     

Hawking Radiation of Spin-3/2 Particles from Kerr Black Hole

By using dimensional reduction and consistent anomaly method, we calculate the Hawking flux of the spin- 3/2 field in the Kerr black hole background. The results confirm that the Hawking radiation doesn’t depends on the detail of the fields living near the horizon, at least at the semi-classical level. The Hawking temperature is an universality character of black hole which only depends on the information of the horizon. Our calculation agrees with earlier results obtained by the WKB/tunneling method (Yale and Mann, Phys. Lett. B 673(2), 168–172, 2009).