fdtd 弯曲损耗

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用于光互连的聚硅氧烷波导弯曲损耗

用于光互连的聚硅氧烷波导弯曲损
耗
光互连技术是通信领域的重要发展方向，聚硅氧烷波导弯曲损耗是其中一个重要的应用。

聚硅氧烷波导弯曲损耗是指在聚硅氧烷波导中使用弯曲时，光子从弯曲处传播时会发生损耗。

它是由于弯曲处的折射率不均匀以及波导表面不平滑等因素造成的。

聚硅氧烷波导弯曲损耗是由材料特性决定的，也就是说，如果材料的折射率和表面粗糙度都很低，那么聚硅氧烷波导弯曲损耗将会降低。

此外，聚硅氧烷波导弯曲损耗也受到弯曲半径大小的影响。

一般情况下，弯曲半径越大，弯曲损耗越小。

聚硅氧烷波导弯曲损耗是光互连技术中的一个重要指标，它可以直接影响光纤传输系统的性能，因此必须加以重视。

因此，在设计光纤传输系统时，应该考虑到聚硅氧烷波导弯曲损耗的影响，并采取相应的措施降低损耗。

例如，在设计光纤传输系统时，应尽量减少聚硅氧烷波导的弯曲半径，以降低弯曲损耗。

此外，需要使用优质的聚硅氧烷材料，以确保材料折射率和表面粗糙度都达到规定的标准，从而降低聚硅氧烷波导弯曲损耗。

另外，也可以采用表面处理技术来降低聚硅氧烷波导弯曲损耗，例如采用陶瓷填充技术，通过在表面上填充陶瓷材料，可以改善表面的光学性能，有效降低聚硅氧烷波导弯曲损耗。

总之，聚硅氧烷波导弯曲损耗是光互连技术中的一个重要问题，必须加以重视，采取有效的措施来降低损耗，以保证光纤传输系统的正常工作。

FDTD分析光子晶体光纤弯曲

Bending loss analyses of photonic crystalﬁbers based on theﬁnite-difference time-domain methodNgoc Hai Vu,1In-Kag Hwang,1,*and Yong-Hee Lee21Department of Physics,Chonnam National University,300Yongbong-dong,Buk-gu,Gwangju500-757,South Korea 2Department of Physics,Korea Advanced Institute of Science and Technology,373-1Guseong-dong,Yuseong-gu,Daejeon305-701,South Korea*Corresponding author:ikhwang@chonnam.ac.krReceived October8,2007;revised November29,2007;accepted December6,2007;posted December11,2007(Doc.ID88351);published January8,2008This is a report on an effective simulation method for the bending loss analyses of photonic crystalﬁbers. This method is based on the two-dimensionalﬁnite-difference time-domain algorithm and a conformal trans-formation of the refractive index proﬁle.We observed the temporal dynamics of light waves in a bentﬁber in a simulation and obtained the bending loss as a function of bend radius and optical wavelength for the com-mercial photonic crystalﬁbers.The accuracy of this method was veriﬁed by good agreement between the simulation and experimental data.©2008Optical Society of AmericaOCIS codes:060.5295,060.2280,060.2310.First proposed in1995,photonic crystalﬁbers (PCFs),with silica–air microstructures,attract many researchers as theseﬁbers have unique applications in ultrawide-band transmission,supercontinuum generation,high power delivery,optical ampliﬁers, and other functional devices[1].One of the important issues regarding the practical development of these PCFs concerns their bending loss properties.When a ﬁber is bent,the modalﬁeld distorts outwards in the direction of the bend and a radiation loss occurs.The bending loss is usually regarded as an adverse effect in the context of optical transmission.However,the bentﬁbers can also be used as a new and unique op-tical component employable in optical communica-tions or optical sensing[2].It is important to be able to accurately estimate the bending loss of a givenﬁ-ber structure for the design and characterization of various PCFs.The complicated microstructure in a PCF makes the calculation a challenging problem.Most of the analytical methods such as antenna theory developed for conventionalﬁbers with circularly symmetric in-dex proﬁles cannot be directly applied to PCFs.Here, we,for theﬁrst time to our knowledge,adopted a two-dimensionalﬁnite-difference time-domain(2D-FDTD)algorithm[3]for the simulation of optical propagation in a bent PCF.The three-dimensional (3D)structure of the bentﬁber was transformed into a two-dimensional straightﬁber by using conformal mapping of the refractive index proﬁle of the PCF. The temporal evolution of the opticalﬁeld was prop-erly interpreted to yield the bending loss per unit length.We compared the simulation results with the experimental results to validate the accuracy of our method.The FDTD method has some distinct features com-pared with other previous methods such as the efﬁ-cient modal model[4,5]or theﬁnite-element method [6]used for the calculation of bending loss of the PCF. The FDTD algorithm is a very general tool and is ap-plicable to a wide range of electromagnetic problems. It directly solves Maxwell’s equations with minimalassumptions and approximations and thus provides fairly reliable results as long as the spatial and tem-poral resolution are high enough.Recent advance-ment of computer technology allows the use of high spatial and temporal resolution,making this tech-nique more useful and popular.This method enables full access to electromagnetic waves at an arbitrary time and position,so that one can collect any desired information from these waves.Therefore it is distin-guishable from other numerical methods that provide speciﬁc information only.The direct simulation of optical propagation in bentﬁber may be performed by the FDTD method ina complete3D structure ofﬁber loops with an inputof an optical wave from one end of theﬁber loops[2].In this case,we record the optical powers at several locations of theﬁber loops to obtain the bending loss as a function of the propagation length.However,this approach requires huge memory sizes and long com-putation time,which is practically unacceptable.Here,we implemented a time-domain approach for the calculation of the bending loss,instead of the space-domain approach,for computation efﬁciency.First we imagined an inﬁnitely longﬁber with a bendradius of R b as shown in Fig.1(a).At t=0,theﬁber is ﬁlled with an optical wave with a propagation con-stant␤and a uniform intensity along the length.Af-ter t=0,the optical wave starts to attenuate with arate of␣Јdue to the bending loss.Note that the op-tical intensity is always uniform over the wholeﬁber length during the attenuation.Finally the loss coefﬁ-cient per unit time͑␣Ј͒is converted to a loss coefﬁ-cient per unit length͑␣͒using the equation␣=␣Ј/v, where v is the velocity of light in theﬁber.Since the optical wave has no variation along the length except the phase in the above situation,the computation structure for the FDTD method can be reduced to one slice of the bentﬁber with an arbi-trarily small thickness͑⌬z͒as shown in Fig.1(b).Then,the3D structure of the bent piece is again sim-pliﬁed to aﬂat one[Fig.1(c)]by employing an equiva-lent index proﬁle given byJanuary15,2008/Vol.33,No.2/OPTICS LETTERS1190146-9592/08/020119-3/$15.00©2008Optical Society of American eq 2͑x ,y ͒=n 2͑x ,y ͒ͩ1+2x R bͪ,where R b is the radius of curvature and n ͑x ,y ͒is therefractive index proﬁle of the straight ﬁber [6–8].The bottom part of Fig.1(c)shows the transformed refrac-tive index proﬁle of a PCF with a bend radius of 5.5mm.It clearly shows that the transformation su-perimposes a gradient onto the refractive index of the straight ﬁber in the direction of the bend.Therefore the ﬁnal computation structure is effectively a 2D one containing only one grid along the z .The sizes of the computation grids were set to ⌬x =⌬y =⌳/20and ⌬z =⌳/100,where ⌬is the hole pitch.Those param-eters were optimized to maximize the numerical ac-curacy within a reasonable computation time.Figure 1(d)shows the recorded optical intensity E 2at the center of the ﬁber as a function of time.The optical intensity corresponds to I ͑t ͒=͗E 2͑t ͒͘.Here we obtained the loss factor per unit time,␣Ј,from curve ﬁtting with the function I ͑t ͒=I 0exp ͑−␣Јt ͒.The veloc-ity of the light was calculated from v =␻/␤,where ␻was the oscillation frequency of Fig.1(d),to get the loss factor per unit length,␣=␣Ј/v .The simulation was performed for the ESM-5PCF (hole pitch,⌳=8␮m;normalized hole diameter,d /⌳=0.46)from Crystal Fibre A/S.The parameters ⌳and d were extracted directly from a scanning electron microscope image of the real ﬁber.The refractive in-dex of the silica was set as 1.444,and no material dispersion was assumed.Figure 2(a)shows the inten-sity distributions of the fundamental mode at ␭=1550nm for the bend in the x direction of the radiusof 3.5mm.It clearly shows that the mode of the bent ﬁber was asymmetric in shape and shifted towards the outside of the bend [4].We generated multiple in-tensity proﬁles at successive time frames in one pe-riod of the optical oscillation to observe the dynamics of the optical ﬁeld,which are shown in Fig.2(b).Here we could observe a “propagating”ﬁeld radiated from the center toward the outside of the bend while the “stationary”core mode was blinking at its optical fre-quency.This energy propagation across the ﬁber was the cause of the bending loss and resulted in the dis-sipation of the optical power in the core mode.The di-rect observation of this phenomenon could not be made by other calculation methods.We calculated the bending losses of the ESM-5PCF for several different bending radii.The plots are denoted with triangles in Fig.3(a).The typical com-putation time was about 2–3h for each data point in our case,although it depends largely on the spatial and temporal resolutions of FDTD.For comparison,the bending losses were experimentally measured us-ing a narrow-linewidth laser and an optical power-meter.Two turns of ﬁber loops were made for a bend radius in the range of 3.0to 7.0mm in incrementsofFig. 1.(Color online)Illustration of the simulation scheme:(a)inﬁnitely-long bent ﬁber model;(b)one sliced piece of the bent ﬁber and its index proﬁle along x ;(c)same as (b)after conformal transformation of the index proﬁle;(d)E 2at the center of the ﬁber as a function of time,show-ing the attenuation of opticalintensity.Fig.2.(Color online)(a)Optical intensity distribution in the cross section of a bent ﬁber with a radius of 5.5mm (log scale)and (b)central regions of intensity proﬁles taken at successive times ͑⌬t =1fs ͒in one period ofoscillation.Fig.3.(Color online)Dependence of bending loss on bend-ing radius for (a)ESM-5PCF and (b)LMA-8PCF.The squares and triangles denote the experimental and simula-tion data,respectively.120OPTICS LETTERS /Vol.33,No.2/January 15,20080.3mm.For a bend radius smaller than 3.0mm,the bent ﬁber was easily broken;while for a radius larger than 7mm,the loss was too low for reliable and re-peatable measurements.Each measurement was re-peated three times,and its average value and devia-tion are shown with squares and error bars,respectively,in Fig.3(a).A comparison was carried out for another PCF,LMA-8(⌳=5.6␮m,d /⌳=0.49)also from Crystal Fibre A/S.The results are shown in Fig.3(b).There was reasonably good agreement be-tween the simulation and experimental results for both ﬁbers.It is interesting to see the small bumps in the experimental curves at the bending radii of ϳ7.8mm for ESM-5PCF and ϳ4.2mm for LMA-8,which did not appear in the simulation results.These loss peaks seemed to come from resonant coupling from the core mode to a cladding mode in the multilayer structure of the cladding.Note that the full cladding structure of PCF should be included in the computation structure to investigate this phe-nomenon [9].A detailed study of its origin is under-way.The wavelength dependence of the bending loss was also calculated and measured in this report for ESM-5.In FDTD,the optical wavelength was rede-termined by simultaneous changes of the propaga-tion constant,␤,and the optical frequency,␻.For the experiment,we used an optical spectrum analyzer and a superluminescent diode with a bandwidth of Ͼ50nm.The simulation and experimental data are shown in Fig.4as dashed and solid curves,respec-tively.The strong wavelength dependence was ob-served for a small bending radius,while it was rela-tively ﬂat for a large bending radius.The ﬁne structures in the experimental data seemed to result from the reﬂection of the radiated light at thecladding–jacket or jacket–air boundaries back to the core mode.Note that the exceptionally large bending loss at R ϳ7.7mm in Fig.3(a)was observed again in Fig.4.We also found good agreement between the simulation and experiment,which again veriﬁed the accuracy of our method.We proposed an efﬁcient numerical method for bending loss analyses of PCF,based on the 2D-FDTD method and conformal transformation of the index proﬁle.The time-domain simulation of the optical propagation in a bent ﬁber provided a view of the temporal dynamics of the optical ﬁeld as well as the mode proﬁle,dispersion and the bending loss.The ac-curacy of the method was veriﬁed by good agreement between a simulation and experimental data.The technique outlined here is directly applicable to not only PCFs but also any kind of waveguides with ar-bitrary index proﬁles.It is important to note that this FDTD method can be easily extended by adding new functions to include nonlinear or strain effects in the simulation,which may not be available in other methods.We believe it is a useful tool for analyses and design of various microstructured ﬁbers [10–12].This work was supported by IT R&D program of Ministry of Information and Communication and In-stitute for Information Technology Advancement (2005-S099-03,Development of photonic crystal ﬁ-bers and their application technology for high-speed optical communication system).References1.T.A.Birks,J.C.Knight,and P .St.J.Russell,Opt.Lett.22,961(1997).2.W.Belhadj,F.AbdelMalek,and H.Bouchriha,Mater.Sci.Eng.C 26,578(2006).3.A.Taﬂove and S. C.Hagness,Computational Electrodynamics:the Finite-Difference Time-Domain Method (Artech House,2005).4.J.C.Baggett,T.M.Monro,K.Furusawa,V .Finazzi,and D.J.Richardson,mun.227,317(2003).5.Tanya M.Monro,D.J.Richardson,G.R.Broderick,and P .J.Bennett,J.Lightwave Technol.17,1093(1999).6.Y.Tsuchida,K.Saitoh,and M.Koshiba,Opt.Express 13,4770(2005).7.M. D.Nielsen,N. A.Mortensen,M.Albertsen, A.Bjarklev,and D.Bonacinni,Opt.Express 12,1775(2004).8.D.Marcuse,Appl.Opt.21,4208(1982).9.Q.Wang,G.Farrell,and T.Freir,Opt.Express 13,4476(2005).10.M.Nielsen,J.Folkenberg,N.Mortensen,and A.Bjarklev,Opt.Express 12,430(2004).11.J.M.Fini,Opt.Express 14,69(2006).12.H.Kuniharu,M.Shoichiro,G.Ning,and W.Akira,J.Lightwave Technol.11,3494(2005).Fig.4.(Color online)Loss spectrum of ESM-5PCF with different bend radii.Experimental and simulation data are shown by the solid and dashed curves,respectively.January 15,2008/Vol.33,No.2/OPTICS LETTERS 121。

光纤内模式的弯曲损耗

光纤内模式的弯曲损耗是指光纤因弯曲而导致的光能损失。

具体来说，当光纤弯曲时，部分光纤内的光会因散射而损失掉，造成损耗。

这种损耗与光纤的弯曲程度、弯曲半径以及光纤的材料等因素有关。

在光纤通信中，弯曲损耗是一种重要的损耗类型。

为了减少弯曲损耗，通常需要尽量保持光纤的直线状态，避免过度弯曲，同时选择适当的光纤材料和制造工艺，以提高光纤的抗弯曲性能。

此外，光纤的弯曲损耗还与光纤的制造工艺有关。

例如，光纤制造过程中可能会产生内部应力，这些应力会导致光纤在传输光时产生散射损耗。

为了减少这种损耗，需要采用先进的制造工艺和技术，确保光纤的制造质量和精度。

在实际应用中，为了减少光纤的弯曲损耗，通常需要对光纤进行合理的敷设和固定。

例如，在光纤通信网络中，需要对光纤进行合理的设计和布局，尽量减少光纤的弯曲和扭曲。

同时，在安装过程中也需要避免对光纤进行过度弯曲或扭曲，以免造成光能的损失。

光纤内模式的弯曲损耗是一种常见的光能损失类型，需要通过合理的敷设和固定等措施来减少。

同时，还需要不断改进光纤的制造工艺和技术，提高光纤的质量和性能，以进一步降低光能的损失。

波导弯曲损耗估算

波导弯曲损耗估算下载温馨提示：该文档是我店铺精心编制而成，希望大家下载以后，能够帮助大家解决实际的问题。

文档下载后可定制随意修改，请根据实际需要进行相应的调整和使用，谢谢!并且，本店铺为大家提供各种各样类型的实用资料，如教育随笔、日记赏析、句子摘抄、古诗大全、经典美文、话题作文、工作总结、词语解析、文案摘录、其他资料等等，如想了解不同资料格式和写法，敬请关注!Download tips: This document is carefully compiled by the editor. I hope that after you download them, they can help yousolve practical problems. The document can be customized and modified after downloading, please adjust and use it according to actual needs, thank you!In addition, our shop provides you with various types of practical materials, such as educational essays, diary appreciation, sentence excerpts, ancient poems, classic articles, topic composition, work summary, word parsing, copy excerpts,other materials and so on, want to know different data formats and writing methods, please pay attention!波导是一种有效传输电磁波的结构，在无线通信和光通信等领域有着广泛的应用。

光纤弯曲损耗的测试方案

光纤弯曲损耗的测试方案一．实验目的近些年，光纤的弯曲损耗问题引起众多学者越来越广泛的关注。

除去由于弯曲损耗在光纤通信中的不利影响之外，许多光纤光学传感器也利用了这一传感机理，如在某些传感器中．被测物理量产生一个小位移，该位移又使光纤弯曲半径发生变化，从而改变光衰减。

传统的理论都假设光纤具有无限大的包层．因此得到弯曲损耗随弯曲半径或工作波长单调的关系。

最近的研究发现单模光纤的弯曲损耗随工作波长及弯曲半径变化的振荡现象。

国外的研究人员从上世纪80年代，就已经开始对光纤的弯曲损耗进行比较系统的研究”，但在国内这方面的研究丁作开展较少”，相关的文献报道也比较少。

在本文中，我将分析弯曲损耗在850nm，1310nm和1550三种工作波长，强弯曲状态F的单模光纤弯曲损耗随弯曲半径的变化关系．讨论了弯曲半径、工作波长对单模光纤弯曲损耗的影响。

二．实验仪器光源单模光纤功率计扰模器三．实验原理在早期的研究工作中，对于弯曲的单模光纤，设定其包层为无限大，即光在芯区中传输时，包层及覆层的厚度对光的传输无任何影响%光损耗完全是由纯弯曲引起的，光功率的变化表示为：式中Pi，P分别为光纤弯曲前及弯曲后的光功率，2α是弯曲损耗系数，L是弯曲的长度，其中：将上述公式整理后可得：通过以上的分析，可以看到光纤弯曲引起的损耗依赖于波长和弯曲半径。

四．实验步骤1.测试弯曲半径对弯曲损耗的影响：试验所用光源波长为850nm半导体激光器，将长飞公司的单模光纤沿圆柱弯曲，测量在不同的弯曲半径下的弯曲损耗特性：（1）将光纤与光源连接，保持不要弯曲，测量光纤的输入功率和输出功率（2）将光纤弯曲，使弯曲半径为5mm,用功率计测出光纤的输入光功率和输出光功率，计算损耗：（3）同上，分别用8mm和10mm的弯曲半径测量，计算损耗。

（4）将康宁公司和长飞公司的单模光纤焊接在一起，重复上述步骤，测量损耗，与（3）实验结果比较。

2.测量光源波长对弯曲损耗的影响：选取长飞公司的单模光纤，弯曲半径为8mm,选用不同波长的光源进行测量，算出弯曲损耗：（1）选取850nm波长的光源与光纤连接，使光纤保持不弯曲，测出输入功率和输出功率，再将光纤弯曲，将弯曲半径保持在8mm,测量光纤的输入功率和输出功率，计算损耗（2）将波长变为1310nm,1550nm重复上述步骤，计算损耗。

光纤的弯曲损耗及其在对线器上的应用

光纤的弯曲损耗及其在对线器中的应用内容摘要光纤是光波导的一种，光纤的弯曲损耗理论也有了很大的进步。

本文就对光纤弯曲损耗做了详细的阐述，并列出了多模光纤和单模光纤的几种微弯和宏弯损耗的计算公式。

经分析了光纤弯曲损耗随弯曲半径，工作波长，以及纤芯半径变化的关系。

弯曲损耗随曲率增大而减小，随工作波长增大增加，弯曲损耗与纤芯半径也有一定的关系。

同时光的截止波长也受光弯曲损耗的影响。

本文还介绍了减小弯曲损耗的一般办法。

弯曲损耗其实质是光能量因光纤弯曲而辐射到媒介中或者损耗在包层内，本文介绍了计算弯曲损耗的简化模型——天线模型。

在光纤弯曲损耗理论的基础上，本文还介绍了光纤在线检测工具光纤对线器对弯曲损耗的应用。

可为光纤弯曲损耗的应用作为参考实例。

【关键词】截止波长光纤对线器弯曲损耗Fiber bending loss and its application on linedeviceAbstractOptical fiber is a kind of optical waveguide, optical fiber technology in recent years and rapid development, optical fiber manufacturing technology in developing and perfecting quality, performance, optical fiber also is rising ceaselessly, optical fiber application more and more widely. Optical fiber bending loss of paper also presents high requirements. This article is to optical fiber bending loss do detail, lists the multimode fiber and single-mode optical fiber several slightly bend and macro bending loss calculation formula. By analyzing the fiber bending loss with bending radius, operating wavelength, and fiber core radius of the relationship of change. Bending loss with curvature and decreases with the increasing operating wavelength, increase, with the increase of fiber core radius, high-order mode loss more than low order mode. At the same time also cutoff wavelength of light by light bending loss influence. This paper also introduces the general way to decrease bending loss. In fiber bending loss based on the theory of optical fiber, this paper also introduces the on-line detection tools to line of optical fiber is bending loss of applications. For the application of optical fiber bending loss as the reference for the example. 【Key Words】the cutoff wavelength optical fiber to the line devicebending loss目录一、引言 (5)二、弯曲损耗 (5)（一）影响光纤传输损耗的因素 (5)（二）弯曲损耗的机理 (6)（三）光纤弯曲损耗与相应截止波长的关系 (11)三、弯曲损耗在对线器上的应用 (12)（一）天线模型 (12)（二）光纤对线器 (12)四、结束语 (13)参考文献 (13)致谢 (14)光纤的弯曲损耗及其在对线器中的应用一、引言光纤的弯曲损耗是由于光纤发生弯曲，使得本来在光纤中传输的能量辐射到光纤外的媒介中或者损耗到包层中的一种现象。

光纤弯曲损耗的研究应用

光纤弯曲损耗的研究应用光纤是一种高速传输信息的重要工具，它被广泛应用于通信、医疗、军事、航空航天等领域，是现代科学技术的重要组成部分。

然而，在光纤传输信息的过程中，由于光纤的弯曲，会引起信号传输的信号损失，这对光纤的传输质量和传输距离都会产生较大的影响。

为了提高光纤的传输性能，研究光纤弯曲损耗成为了目前研究的热点之一。

光纤弯曲损耗指的是光在弯曲光纤中传输时，由于折射率的变化，光的能量因损耗而减弱的现象。

这种损失会导致光的强度减弱，从而影响光信号在光纤中的传输质量，损失的程度取决于光纤的半径、曲率、波长等因素。

研究光纤弯曲损耗通常采用实验和理论相结合的方法。

实验可以通过在不同曲率、半径及材料的光纤上研究光纤弯曲损耗，从而了解其影响因素及损失程度。

理论方面，主要采用电磁波传输理论、光学传输理论和数值计算方法等，根据光纤折射率分布、几何形状等参数，计算出适当曲率下的光纤弯曲损耗，从而为光纤的设计和优化提供理论指导。

1、光通信系统中的应用在光通信系统中，传输距离和传输带宽是非常关键的因素，而光纤的弯曲损耗是影响它们的重要障碍。

因此，在光纤的选择、安装和调试过程中，需要根据实际情况，选用合适的光纤以及控制弯曲半径和曲率等参数，以减小光纤的信号损失，保证光信号的传输质量和距离。

其次，利用光纤弯曲损耗的特性可以实现光纤传感器的设计和制造，在光纤表面附上压电陶瓷、光纤光栅等传感器，可以快速高效地检测压力、温度、形变等信息，而不影响光纤传输的质量。

2、医疗影像中的应用光纤在医疗影像中扮演着至关重要的角色，它可以实现光学成像和控制，其优点包括较高的分辨率、无线电磁辐射和安全等特性，受到了广泛的关注。

同时，光纤的弯曲损耗也是医疗影像中不可忽视的因素之一。

通过研究光纤弯曲损耗，可以在光学成像中减少图像失真、提高图像质量和分辨率，同时有效地降低光纤的信号损失，从而提高医疗成像的精度和安全性。

3、航空航天中的应用光纤在航空航天中的应用主要涉及到通信、导航和飞行控制等领域。

光纤的弯曲损耗、抗弯曲光纤标准G.657及试验

一、光纤弯曲损耗的理论和计算
1、宏弯损耗的计算：对折射率突变型单模光纤，设曲率半径为R，则每单位长度的弯曲损耗由下式给出[1]： 1
c AC R 2 exp(UR)
3 2

(dB / m)
..............(1)
近似公式
当1≤λ/λcf≤2时准确率
（2）
（3）
(n) 3 U 0.705 (2.748 0.996 ) cf 1 1 3 cf 2 AC 30( n ) 4 2 ( )
二、光纤弯曲与截止波长的关系
光纤的截止波长受诸多因素的影响（甚至包括测量条件）。同样，弯曲直径和光纤长度也影响单模光纤的截止波长，可表达为[2]：
L2 1 1 c 2 c1 C log S ( ) …………………….(6) L1 D2 D1
式中，λ c2和λ c1分别是在弯曲直径D2和长度L2与弯曲直径D1和长度L1时的截止波长，C是长度相关常数，S是弯曲相关常数。研究证明，对于匹配包层光纤，其截止波长对弯曲的依赖性更大。由（6）式可以看出，弯曲半径减小，截止波长也将减小。
再取R=10mm，计算得到弯曲损耗α c=6.13dB/m，折合每弯曲 10圈宏弯损耗为3.8dB，这比前者上升了75倍，这种非常急剧的增加明显是由于（1）式中的指数项引起的。此计算结果与实测值相比有比较好的近似程度。
一、光纤弯曲损耗的理论和计算
针对给定的折射率差、工作波长和截止波长，可以定义一个临界曲率半径Rc，当实际曲率半径接近Rc时，弯曲损耗从可以忽略的程度急剧增加到不可容忍的数值。在通常波段(1000nm附近)，Rc近似公式为：
在33dBm的实验之后，光纤跳线的损耗恢复不到其初始损耗值。这是因为温度增加导致光纤跳线前几圈的严重损坏。

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FDTD（时域有限差分法）是一种用于模拟电磁波传播和散射的数值方法。

在光纤或其它波导中，由于弯曲带来的传输损耗是光纤光学中常见的问题。

当光纤被弯曲时，会有附加的传输损耗。

这个损耗被称为弯曲损耗。

通常情况下，一旦光纤达到某一个临界曲率半径后，损耗便会迅速上升。

这个临界曲率半径对于不同的光纤差别很大：对于具有较好导波特性的光纤（即具有高数值孔径的光纤），这个临界值就很小（几毫米）；但是对于普通模式面积很大的单模光纤，这个临界值通常很大（几十厘米）。

弯曲损耗对于波长越长的分量的影响越大。

在长波段高的弯曲损耗通常都会限制单模光纤的可传输光的波长范围。

另外，弯曲还会导致双折射。

以上内容仅供参考，建议查阅专业光纤书籍获取更全面和准确的信息。