空分复用光纤研究综述

涂佳静; 李朝晖

doi:doi:10.3788/AOS202141.0106003

光学学报, 2021, 41 (1): 0106003, 网络出版: 2021-02-23

空分复用光纤研究综述下载： 2731次特邀综述

Review of Space Division Multiplexing Fibers

论文大纲

涂佳静 ^1,*李朝晖 ^2,3,**

作者单位

¹ 暨南大学信息科学技术学院, 广东广州 510632

² 中山大学光电材料与技术国家重点实验室, 广东广州 510275

³ 南方海洋科学与工程广东省实验室, 广东珠海 519000

光纤光学空分复用多芯光纤少模/多模光纤少模多芯光纤 fiber optics space division multiplexing multi-core fiber few-mode/multi-mode fiber few-mode multi-core fiber

AI 词云图 AI一句话精读 AI短摘要

注：本部分内容由 AI 自动生成，请您知悉。

摘要

在多媒体和数据应用程序快速扩展和驱动骨干网带宽需求量迅速增长的网络背景下,时分、波分、偏分复用技术与多级调制方式结合,使得大容量传输系统中单模光纤容量快速接近香农理论极限。空分复用(SDM)技术可以突破该限制,为未来光纤容量增长提供新的解决方案。通过讨论多芯光纤、少模/多模光纤和少模多芯光纤三种SDM技术方案,详细介绍了SDM光纤的研究进展及研究方法,同时对三种光纤方案进行对比,阐明了各种方案的优劣性。

Abstract

The rapid growth of multi-media and data applications has driven the bandwidth demand for long-haul fiber-optic links at unprecedented rates. Against this background, the combination of time division multiplexing, wavelength division multiplexing, and polarization division multiplexing with multilevel modulation makes the transmission capacity of single-mode fibers in the large-capacity transmission system rapidly approach the Shannon limit. In view of this problem, the space division multiplexing (SDM) technology that can break through this limit provides new solutions for the growth of fiber capacity in the future. In this paper, we discuss three kinds of SDM fibers, namely, multi-core fiber, few-mode/multi-mode fiber and few-mode multi-core fiber, and introduce the research progress and design method of the SDM fibers. Furthermore, the comparison among the above SDM fibers is also discussed to reveal their advantages and disadvantages.

1 引言

1966年高琨博士利用实验验证了世界上第一根由石英玻璃制成的单模通信光纤,并且首次证明了玻璃中的杂质是引起光纤高损耗的主要因素。经过数十年的光纤工艺优化,1.55 μm波长下的光纤损耗现已下降至0.16 dB/km^[1]。伴随着半导体激光器、掺铒光纤放大器以及波分复用技术的成功应用,基于石英光纤的光通信系统已可以支持大容量长距离的数据传输,逐步发展成为支持互联网的电信基础架构骨干。

在新兴的带宽需求型应用以及遵循摩尔定律持续增长的计算机处理能力的推动下,互联网流量以每十年100倍的速度迅速增长,并且在可预见的未来,这种趋势仍将持续。由于传输带宽扩展以及频谱效率的提升,传统单模光纤传输容量在过去十几年里呈指数型增长。近年来,单模光纤传输系统容量已经达到了100 Tb/s并且传输容量距离乘积已超过100 Pb/s∙km^[2]。然而,由于受到非线性噪声 [图1(a)]^[3]、光纤熔合损伤现象[图1(b)]^[4]和放大器带宽[图1(c)] ^[5]的限制,标准单模光纤已接近香农定理所限定的物理极限,很难继续支撑持续增长的容量要求。可以预测当下的互联网流量增速必将在不远的将来引起容量危机。因此,如何满足持续飞速增长的互连需求,已经成为光纤通信技术研究的核心问题。

图 1. 标准单模光纤容量的物理限制。(a)非线性香农极限^[3];(b)光纤熔合损伤现象^[4];(c)熔融石英光纤的传输窗口图,黑色部分为标准光放大区间^[5]

Fig. 1. Reasons that make the capacity of single-mode fiber approach Shannon limit. (a) Nonlinear Shannon limit^[3]; (b) fiber fuse damage phenomenon^[4]; (c) transmission window of fused-silica fibers, where black region represents the standard optical amplification band^[5]

下载图片查看所有图片

为了进一步增加光纤的通信容量,最直接的方法就是增加纤芯或模式的空间利用率。因此,空分复用(SDM)为光纤传输系统提供了一个新的发展方向,有可能使系统容量增加一个数量级^[6-12]。目前,SDM有三种增加空间信道的实现方式。第一种是多芯光纤(MCF)^[13],即在光纤包层内通过控制纤芯间距合理排布多个纤芯。然而,持续增加 MCF 中的纤芯数量将会导致光纤由于包层直径过大而失去韧性,因此,如何在有限的包层空间内容纳尽可能多的纤芯并同时保证较低的芯间串扰是设计MCF的难点。第二种是少模光纤(FMF)或多模光纤(MMF)^[14]。其中根据光纤内本征矢量模式叠加方式的不同,光纤内传输的模式又可以分为线偏振(LP)模式以及轨道角动量(OAM)模式。多模传输时不可避免地会产生模间干扰,为解决该问题,分别提出了用于接收端直接检测的弱耦合光纤以及利用多入多出(MIMO)数字信号处理算法解调接收的低差分模式群时延(DMGD)光纤^[14]。第三种则是空间和模式两个维度相结合的少模多芯光纤(FM-MCF)^[15]。虽然FM-MCF提升了信道数量,但是如何同时控制芯内和芯间的模式串扰,并且在大纤芯密度多模式数量的基础上保证C+L大带宽则是FM-MCF的设计难点。

本文将详细讨论空分复用光纤的设计方法和实现机理,介绍多芯光纤的分类、芯间串扰计算以及纤芯选取方法;介绍光纤模式、少模/多模光纤分类以及模式调控原理;详细阐述少模多芯光纤的研究进展。最后对比多芯光纤、少模光纤及少模多芯光纤的特性,总结并展望未来亟需发展的SDM技术。

2 多芯光纤

2.1 多芯光纤分类

当提及多芯光纤时,一般是指芯间距大于30 μm的弱耦合单模多芯光纤。该光纤的每个单模纤芯可以作为独立的信道传输信号^[13,16]。首先,弱耦合单模多芯光纤按纤芯种类异同可以分为同质多芯光纤(Homo-MCF)和异质多芯光纤(Hetero-MCF)^[17-19]。下面将从弯曲后芯间串扰的特性来分析Homo-MCF和Hetero-MCF。

图2(a)左侧曲线图表示Homo-MCF的芯间串扰(XT,l_XT)对于弯曲半径(R)的依赖关系。从图中可知,Homo-MCF的串扰随着弯曲半径的增大而增大。图2(a)右侧为弯曲状态下Homo-MCF芯间串扰的分析图。以纤芯6和纤芯7为例:当R趋于最大值时,光纤处于近似笔直状态,同质两芯相位匹配,XT最大;当R逐渐减小时,同质的纤芯6和纤芯7相位失配,XT逐渐减小。从图2(b)左侧曲线图可知,Hetero-MCF的串扰随着弯曲半径的增大先增大后减小,因此存在一个弯曲阈值(R_pk)使得当R > R_pk时光纤对弯曲程度不再敏感。具体地,当R很大时,光纤处于近似笔直状态,异质纤芯6和纤芯7持续处于相位失配状态,XT很小且稳定不变;当R减小到某个阈值R_pk时,纤芯6和纤芯7的有效折射率差(Δn_eff)突变为0,此时XT瞬时达到峰值;当R进一步减小时,纤芯6和纤芯7的相位再次失配,XT再一次逐渐减小。因此,Homo-MCF设计简单,但芯间串扰容易受到外界扰动影响,而Hetero-MCF存在有串扰弯曲不敏感区间,但其纤芯需要巧妙的设计才能使得XT和R_pk折中平衡后相对最优。

图 2. 同质多芯光纤与异质多芯光纤的串扰对比。(a)同质多芯光纤串扰对弯曲半径的依赖关系图以及弯曲状态下有效折射率变化示意图;(b)异质多芯光纤串扰对弯曲半径的依赖关系图以及弯曲状态下有效折射率变化示意图

Fig. 2. Comparison of crosstalk between Homo-MCF and Hetero-MCF. (a) Crosstalk of Homo-MCF dependence on bending radius and change of effective index under bending condition; (b) crosstalk of Hetero-MCF dependence on bending radius and change of effective index under bending condition

下载图片查看所有图片

其次,弱耦合单模多芯光纤按照纤芯外围辅助结构还可以分为沟槽辅助式多芯光纤、空气孔辅助式多芯光纤以及光子晶体多芯光纤,如图3所示^[20]。纤芯外侧的低折射率部分可以抑制纤芯间的能量交叠,从而减小芯间串扰。对于多层纤芯排布的多芯光纤,内部纤芯由于外侧加入了具有强束缚力的低折射率结构,光缆截止波长(λ_cc)将需加长以过滤高阶模式。为了保证C+L波段的工作带宽,需要缩小纤芯的选取范围^[19,21]。图3(a)和图3(b)所示的沟槽辅助式结构可以通过调节沟槽距离纤芯的位置和厚度来调整纤芯选取范围以及串扰大小^[21];图3(c)和图3(f)所示的空气孔辅助式结构可以通过调整空气孔占空比来控制对光的束缚能力。

再次,弱耦合单模多芯光纤按照纤芯排布可以分为单环结构(ORS)、双环结构(DRS)、紧凑六边形结构(HCPS)、三层结构(TLS)、方点阵式结构(SLS)^[22-27]。表1总结了已报道的各种排布的沟道辅助式单模多芯光纤的特性。ORS结构只有一层纤芯,每个纤芯只有两个相邻纤芯,该结构可以有效降低串扰。DRS利用双向交叉通信可以进一步降低芯间串扰。但是ORS和DRS由于内层未排布纤芯或仅排布少量纤芯,纤芯数量有限。TLS、HCPS和SLS结构则是通过更有效地利用空间排布更多的纤芯,但需要注意的是TLS、HCPS和SLS的内侧纤芯将负担周围所有纤芯的总体串扰,而且由于外部多层低折射率沟槽的存在,内侧纤芯的光缆截止波长更长,导致工作带宽比外侧纤芯的带宽要小。

图 3. 单模多芯光纤按照外围辅助结构分类^[20]。(a)沟槽辅助式纤芯折射率分布图;(b)沟槽辅助式多芯光纤横截面图;(c)空气孔辅助式纤芯折射率分布图;(d)空气孔辅助式式多芯光纤横截面图;(e)光子晶体纤芯折射率分布图;(f)光子晶体多芯光纤横截面图

Fig. 3. Classification of single-mode multi-core fiber based on the assisted structure around core^[20]. (a) Refractive index profile of trench-assisted core; (b) cross-section of trench-assisted multi-core fiber; (c) refractive index profile of air-hole-assisted core; (d) cross-section of air-hole-assisted multi-core fiber; (e) refractive index profile of photonic crystal core; (f) cross-section of photonic crystal multi-core fiber

下载图片查看所有图片

表 1. 已报道的沟槽辅助式单模多芯光纤排布方式

Table 1. Core arrangement of the reported trench-assisted single-mode multi-core fibers

Fiber	In Ref. [22]	In Ref. [23]	In Ref. [24]	In Ref. [25]	In Ref. [26]	In Ref. [27]
Cross section of thereported MCFs
Fiber structure	ORS	DRS	HCPS	TLS	New-typeHCPS	SLS
Core number	12	12	19	22	30	32
Core pitch /μm	37	44.6	35	41	30	29
Cladding diameter /μm	225	230	200	260	229	243
Average crosstalk@1550 nm	-32 dB/52 km	<-30 dB/1000 km	-42 dB/1 km	-45 dB/km	-50 dB/9.6 km	<-34.5dB/51.4 km
Loss /(dB·km-1)@1550 nm	0.199	0.186	0.227	0.21	—	0.24
Transmissioncapacity /(Tb·s-1)	1010	409	305	2150	—	—

查看所有表

此外,如果纤芯间距逐渐缩小,弱耦合多芯光纤将演变成强耦合多芯光纤^[28]。强耦合多芯光纤的芯间串扰将增加芯间的能量耦合,从而导致超模的产生,因此强耦合多芯光纤其实是一种少模/多模光纤^[29]。对于强耦合多芯光纤,模式群时延展宽(GDS)的量级将直接决定MIMO算法的复杂度,因此,强耦合多芯光纤的研究重点为如何减小模式的GDS^[30]。文献[ 31-33]优化设计了强耦合3芯光纤和强耦合6芯光纤,通过实验表明GDS与传输距离的平方根成正比。对于强耦合多芯光纤,相邻纤芯的模式耦合系数为10^-1 m^-1量级并且芯间距小于30 μm。

2.2 芯间串扰计算方法

对于弱耦合多芯光纤来说最重要的课题就是减小芯间串扰。芯间串扰理论值可以分别基于模式耦合理论(CMT)^[34-36]和功率耦合理论(CPT)^[35-37]来获得。实际拉制光纤在轴向方向的尺寸,会不可避免地出现随机变化。考虑到这些随机微扰,CMT需要将光纤分成若干相等长度。为了获得精确的串扰值,需要对每段光纤样本进行大量的仿真计算。而CPT则可以通过一次计算获得平均的串扰值,是一种更有效的串扰计算方法。

首先,利用纤芯间的能量交叠积分计算两芯之间的模式耦合系数(κ),表达式为^[21]

κ_{pq} = \frac{ω ε_{0} \overset{+ \infty}{\int_{- \infty}} \overset{+ \infty}{\int_{- \infty}} (N^{2} - N_{q}^{2}) E_{p}^{*} \cdot E_{q} d x d y}{\overset{+ \infty}{\int_{- \infty}} \overset{+ \infty}{\int_{- \infty}} (E_{p}^{*} \times H_{p} + E_{p} \times H_{p}^{*}) d x d y}, (1)

式中,ω是电磁场的角频率,ε₀是材料的介电常数,字母p和q为纤芯的编号,E_p表示纤芯p在纤芯q区域范围内的电场分布,E_q表示纤芯q在纤芯p区域范围内的电场分布。在求解(1)式时,可以利用理论分析方法,也可以利用有限元法。

对于同质阶跃多芯光纤,相邻纤芯的κ解析解为^[38]

κ = \frac{\sqrt[]{Δ}}{a} \frac{u^{2}}{ν^{3} K_{1}^{2} (ω)} \sqrt[]{\frac{π a}{ωD}} ex p (- \frac{ω}{a} D), (2)

式中:Δ和a分别表示阶跃纤芯的纤芯包层折射率差和纤芯半径;u,ω和 $ν$ 分别表示纤芯横向波数、包层横向波数以及归一化频率;D为纤芯间距;K₁表示第二类贝塞尔修正函数。

在目前被报道的多芯光纤中(如图3所示),为了进一步降低芯间串扰,减小相邻纤芯的能量交叠,低折射率沟槽辅助式多芯光纤是最常见的结构^[19]。对于沟槽辅助式多芯光纤,(2)式不再适用,沟槽辅助式双芯的模式耦合系数可表示为^[19]

κ_{pq} = \frac{k (n_{p}^{2} - {n^{2}}_{cl}) W_{1 - p} U_{1 - q} L_{q} \sqrt[]{\frac{π a_{1 - q}}{2 W_{1 - q} D}} \exp (- W_{1 - q} \frac{D}{a_{1 - q}})}{\sqrt[]{n_{p} n_{q}} a_{1 - p} a_{1 - q} V_{1 - p} V_{1 - q} J_{1} (U_{1 - p}) J_{1} (U_{1 - q})} \times \overset{a_{1 - p}}{\int_{0}} J_{0} (U_{1 - p} \frac{r}{a_{1 - p}}) I_{0} (\frac{W_{1 - q}}{a_{1 - q}} - \frac{P_{2} - P_{1} + Y_{2} - Y_{1}}{D - r}) \exp [(P_{2} - P_{1} + Y_{2} - Y) \frac{D}{D - r}] r d r, (3)

式中:k表示纤芯波数;n_p和n_cl分别表示纤芯和包层的折射率;L是振幅系数;U、W和V分别表示纤芯横向波数、包层横向波数以及归一化频率;J₀是0阶贝塞尔函数,I₀是第一类修正贝塞尔函数;P₁= ${W_{1}}_{-}_{q}$ (D- ${a_{3 -}}_{p}$ )/ ${a_{1 -}}_{q}$ ,P₂= ${W_{2 -}}_{q}$ (D- ${a_{3 -}}_{p}$ )/ ${a_{1 -}}_{q}$ , Y₁= ${W_{2 -}}_{q}$ (D- ${a_{2 -}}_{p}$ )/ ${a_{1 -}}_{q}$ , Y₂= ${W_{1 -}}_{q}$ ×(D- ${a_{2 -}}_{p}$ )/ ${a_{1 -}}_{q}$ 。另外,该公式的简化形式可以参考文献[ 39-41]。

在获得模间耦合系数κ之后,利用CPT可以获得功率耦合系数(h)。在求解h值时,文献[ 37]分别采用了三种自相关函数来近似模拟轴向随机扰动,分别为指数自相关函数、高斯自相关函数以及三角自相关函数。其中:已证明基于指数型自相函数所得的仿真计算串扰值与实验测量值的匹配度良好,h的表达式为

h_{pq} (z) = \frac{2 κ_{pq}^{2} d}{1 + (kdδ n_{eff})^{2}}, (4)

式中,k为波数,d表示相关长度,dn_eff为弯曲状态下纤芯p和纤芯q的有效折射率差,其公式可以表示为

\begin{array}{r} δ n_{eff} = & n_{eff, p} [1 + \frac{Λ}{R} \cos θ_{p} (z)] - n_{eff, q} [1 + \frac{Λ}{R} \cos θ_{q} (z)], (5) \end{array}

式中,Λ表示纤芯间距,R为弯曲半径, ${n_{eff,}}_{p}$ 和 ${n_{eff,}}_{q}$ 为纤芯p和q在原始笔直状态下的有效折射率,θ_n(z)表示为γz+θ_c+(n-1)2π/N_core,其中,γ,θ_c,n和N_core分别表示光纤的扭曲率、扭曲补偿、纤芯编号以及纤芯个数。

假设MCF以半径R弯曲并且以扭曲率γ连续扭转,则h的平均值可以表示为^[37]

{\bar{h}}_{pq} = \frac{γ}{2 π} \int^{} 2 π / γ_{0} h_{pq} (z) d z, (6)

此时,串扰关于传播长度L的表达式为^[37]

l_{XT} = \tan h ({\bar{h}}_{pq} L) 。 (7)

2.3 纤芯选取方法

以沟道辅助式异质单模七芯光纤(Hetero-TA-7-core fiber)为例,介绍多芯光纤的纤芯设计方法^[42]。

1) 选取图4(a)的纤芯1。图4(b)中实线和虚线分别表示有效折射率(n_eff)及有效面积(A_eff),点虚线代表同质相邻纤芯间的模式耦合系数κ。位于图4(b)上侧的长虚线是第一高阶模(LP₁₁)的截止线,此时LP₁₁模在波长为1530 nm且弯曲半径R为140 mm的条件下弯曲损耗等于1 dB/m;位于图4(b)下侧的长虚线是基模(LP₀₁)的设计下限,此时LP₀₁模在波长为1625 nm且弯曲半径R为30 mm条件下弯曲损耗等于0.5 dB/100圈。被上下两根点划线相夹的区域被称为单模工作区间(SMOR)。在图4(b)的SMOR中选取第一个有效面积为80 μm²的外侧纤芯1,该纤芯半径r₁=4.76 μm,Δ₁=0.376%,n_eff,1=1.45293068。

外侧纤芯1选取方式[42]。(a)Hetero-TA-7-core fiber的横截面;(b)波长为1550 nm及Λ为35 μm条件下neff和Aeff对于r1和Δ1的函数关系图

图 4. 外侧纤芯1选取方式^[42]。(a)Hetero-TA-7-core fiber的横截面;(b)波长为1550 nm及Λ为35 μm条件下n_eff和A_eff对于r₁和Δ₁的函数关系图

Fig. 4. Core selection of outer core 1^[42]. (a) Cross-section of a Hetero-TA-7-core fiber; (b) n_eff and A_eff as functions of r₁ and Δ₁ at λ =1550 nm and Λ=35 μm for the first outer cores in Hetero-TA-7-core fiber

下载图片查看所有图片

2) 在图5(b)中选取如图5(a)所示的纤芯2。需要注意的是纤芯1和纤芯2之间耦合情况,图5(b)中的点虚线代表纤芯1和2之间的平均模式耦合系数K。但是对于异质纤芯,K无法唯一决定XT,需要借助图6通过目标的串扰值来确定K与 ${n_{eff,}}_{q}$ 的最佳组合。如果纤芯2的设置目标为A_eff≥80 μm²,A_eff表示有效面积,最大串扰l_XT,max≤-38 dB/100 km并且光缆截止波长λ_cc≤1530 nm,中心纤芯2的纤芯选取范围(CSR)如图7的填充图所示。

外侧纤芯2选取方式[42]。(a)Hetero-TA-7-core fiber的横截面;(b)波长为1550 nm及Λ为35 μm条件下neff和Aeff对于r1和Δ1的函数关系图

图 5. 外侧纤芯2选取方式^[42]。(a)Hetero-TA-7-core fiber的横截面;(b)波长为1550 nm及Λ为35 μm条件下n_eff和A_eff对于r₁和Δ₁的函数关系图

Fig. 5. Core selection of outer core 2^[42]. (a) Cross-section of a Hetero-TA-7-core fiber; (b) n_eff and A_eff as function of r₁ and Δ₁ at λ=1550 nm and Λ=35 μm for the second outer cores in Hetero-TA-7-core fiber

下载图片查看所有图片

因为纤芯的排布结构直接决定中心纤芯高阶模式的截止条件,使用上述纤芯选取方法时,需要确定纤芯的排布方法^[43]。另外,根据外侧纤芯的有效面积大小可以确定外侧包层厚度(OCT)^[44]。最终,纤芯数量、芯间距以及外侧包层厚度可以确定包层尺寸。为了保证光纤韧性,包层尺寸应尽量控制在220 μm之内^[45]。

图 6. 纤芯1和目标纤芯间串扰对于n_eff,_q和K的函数关系^[42],其中(5)式中的n_eff,_p和n_eff,_q分别代表纤芯1和目标纤芯的有效折射率

Fig. 6. XT between core 1 and the undetermined core as a function of n_eff,_q and K^[42], where n_eff,_p and n_eff,_q in Eq. (5) are effective indexes of refraction of core 1 and the undetermined core, respectively

下载图片查看所有图片

波长为1550 nm及Λ为35 μm条件下neff和Aeff对于r1和Δ1的函数关系图[42],其中CSR为中心纤芯2的纤芯选取区间,最大串扰lXT,max是纤芯2和目标中心纤芯的串扰值

图 7. 波长为1550 nm及Λ为35 μm条件下n_eff和A_eff对于r₁和Δ₁的函数关系图^[42],其中CSR为中心纤芯2的纤芯选取区间,最大串扰l_XT,max是纤芯2和目标中心纤芯的串扰值

Fig. 7. n_effand A_effas functions of r₁ and Δ₁ at λ=1550 nm and λ=35 μm with CSR of center core 2 in Hetero-TA-7-core fiber^[42], where ${l_{XT}}_{, \max}$

下载图片查看所有图片

3 少模/多模光纤

3.1 光纤模式介绍

在设计和分析少模/多模光纤之前,首先需要了解光纤模式的特点。在理想圆对称光纤中本征模式称为柱矢量(CV)模式,CV模式的电场分量表达式可以基于圆柱坐标由亥姆霍兹方程求得,即

\{\begin{array}{l} H E_{l + 1, m}^{even} \\ H E_{l + 1, m}^{odd} \\ E H_{l - 1, m}^{even} \\ E H_{l - 1, m}^{odd} \end{array}\} = F_{l, m} (r) \{\begin{array}{l} \hat{x} \cos (lφ) - \hat{y} \sin (lφ) \\ \hat{x} \sin (lφ) + \hat{y} \cos (lφ) \\ \hat{x} \cos (lφ) + \hat{y} \sin (lφ) \\ \hat{x} \sin (lφ) - \hat{y} \cos (lφ) \end{array}\}, (8)

式中,F_l_,_m(r)为径向电场分布,l是CV模式的角向阶数,m是CV模式径向阶数, $\hat{x}$ 和 $\hat{y}$ 分别表示x和y偏振方向,even和odd分别表示偶模和奇模。当l=1时,E ${H_{l}}_{- 1,}_{m}$ 的奇偶模分别为T ${M_{0,}}_{m}$ 和T ${E_{0,}}_{m}$ 。

线偏振(LP)模式是弱导光纤所支持的模式。当光纤纤芯折射率n₁和包层折射率n₀的比值n₁/n₀≈1时,本征的CV模式HE和EH的传播常数近似,此时简并而成的模式称为LP模式。将n₁/n₀≈1代入矢量模式的色散方程,可以近似得出LP模式的解,这种近似方法被称为弱导近似。LP模式可以由简并的两个CV模式叠加而成^[46],两者之间关系为

\{\begin{array}{l} \hat{x} L P_{l, m}^{even} \\ \hat{y} L P_{l, m}^{even} \\ \hat{x} L P_{l, m}^{odd} \\ \hat{y} L P_{l, m}^{odd} \end{array}\} = F_{l, m} (r) \{\begin{array}{l} \hat{x} \cos (lφ) \\ \hat{y} \cos (lφ) \\ \hat{x} \sin (lφ) \\ \hat{y} \sin (lφ) \end{array}\} = \frac{1}{2} \{\begin{array}{l} 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & - 1 \\ - 1 & 0 & 1 & 0 \end{array}\} \{\begin{array}{l} H E_{l + 1, m}^{even} \\ H E_{l + 1, m}^{odd} \\ E H_{l - 1, m}^{even} \\ E H_{l - 1, m}^{odd} \end{array}\} 。 (9)

轨道角动量(OAM)模式是光纤支持的另一种模式。OAM模式具有螺旋相位波前exp(±ilφ),其中,l代表拓扑荷,与CV的角向阶数一致;φ代表方位角度。OAM模式可以由两个相同传播常数的CV模式变换π/2个相位后叠加而成^[47],两者之间关系可表示为

\{\begin{array}{l} {\hat{σ}}^{+} OA M_{+ l, m} \\ {\hat{σ}}^{-} OA M_{- l, m} \\ {\hat{σ}}^{-} OA M_{+ l, m} \\ {\hat{σ}}^{+} OA M_{- l, m} \end{array}\} = F_{l, m} (r) \{\begin{array}{l} {\hat{σ}}^{+} \exp (+ i lφ) \\ {\hat{σ}}^{-} \exp (- i lφ) \\ {\hat{σ}}^{-} \exp (+ i lφ) \\ {\hat{σ}}^{+} \exp (- i lφ) \end{array}\} = \{\begin{array}{l} 1 & 0 & 0 \\ 1 & - i & 0 & 0 \\ 0 & 0 & 1 & i \\ 0 & 0 & 1 & - i \end{array}\} \{\begin{array}{l} H E_{l + 1, m}^{even} \\ H E_{l + 1, m}^{odd} \\ E H_{l - 1, m}^{even} \\ E H_{l - 1, m}^{odd} \end{array}\}, (10)

式中, ${\hat{σ}}^{\pm} = \hat{x} \pm i \hat{y}$ 表示圆偏振方向的左旋或右旋,OAM下角标的“+/-”则表示波前相位的右旋或左旋。同理,对于弱导近似光纤,OAM模式也可以由LP模式叠加^[48]而成,OAM模式与LP模式的关系可表示为

\{\begin{array}{l} \hat{x} OA M_{- l, m} \\ \hat{y} OA M_{- l, m} \\ \hat{x} OA M_{+ l, m} \\ \hat{y} OA M_{+ l, m} \end{array}\} = F_{l, m} (r) \{\begin{array}{l} \hat{x} \exp (- i lφ) \\ \hat{y} \exp (- i lφ) \\ \hat{x} \exp (+ i lφ) \\ \hat{y} \exp (+ i lφ) \end{array}\} = \{\begin{array}{l} 1 & 0 & - i & 0 \\ 0 & 1 & 0 & - i \\ 1 & 0 & i & 0 \\ 0 & 1 & 0 & i \end{array}\} \{\begin{array}{l} \hat{x} L P_{l, m}^{even} \\ \hat{y} L P_{l, m}^{even} \\ \hat{x} L P_{l, m}^{odd} \\ \hat{y} L P_{l, m}^{odd} \end{array}\} 。 (11)

图8给出CV,LP,OAM三种模式之间的转换关系。

图 8. OAM模式、CV模式及LP模式之间的转关关系

Fig. 8. Conversion relationship between OAM, CV and LP modes

下载图片查看所有图片

3.2 少模/多模光纤分类

首先,基于LP模式的少模/多模光纤按照模式隔离度可以分为弱耦合少模/多模光纤和低差分群时延(DMGD)少模/多模光纤^[14]。弱耦合少模/多模光纤主要通过减少模式耦合来达到模式独立检测或轻量级MIMO技术解复用的目的。低DMGD光纤(也称为全MIMO光纤),通过减小模间的群时延差,利用2N×2N(2个偏振态×N个空间模式)的MIMO技术同时检测接收所有模式。

为实现模式间弱耦合传输,对于传统的阶跃少模光纤,最重要的课题是如何加大LP₀₂和LP₂₁模式间的有效折射率差Δn_eff。中心下陷型阶跃光纤通过纤芯折射率变化影响L ${P_{0}}_{m}$ 圆对称模式的有效折射率,使得LP₀₂和LP₂₁模式有效分离。下一节将详细解释模式调控的方法。图9中分别展示了已报道的弱耦合环芯光纤,其中:图9(a)是弱耦合中心下陷型阶跃6-LP模光纤,该光纤最小Δn_eff(LP₂₁和LP₀₂间)约为1.6×10^-3,基模LP₀₁的衰减损耗为0.25 dB/km,最小有效面积为84 μm²,LP模间最大串扰为-27.6 dB/km ^[49];图9(b)是弱耦合中心下陷型阶跃7-LP模光纤,该光纤最小Δn_eff(LP₂₁和LP₀₂间)约为1.6×10^-3,基模LP₀₁的衰减损耗为0.25 dB/km,最小有效面积为99 μm²,LP模间最大串扰为-25 dB/km^[50];图9(c)是弱耦合中心下陷型阶跃4-LP模光纤,该光纤最小Δn_eff (LP₂₁和LP₀₂间)约为1.8×10^-3,基模LP₀₁的衰减损耗为0.22 dB/km,最小有效面积为100 μm²,LP模间最大串扰为-33.3 dB/km^[51];图9(d)是弱耦合中心下陷型阶跃6-LP模光纤,该光纤最小Δn_eff (LP₂₁和LP₀₂间)约为1.5×10^-3,基模LP₀₁的衰减损耗为0.23 dB/km,最小有效面积为109 μm²,LP模间最大串扰为-28 dB/km^[52]。

图 9. 已报道的弱耦合中心下陷型阶跃光纤。(a)弱耦合中心下陷型阶跃6-LP模光纤^[49];(b)弱耦合中心下陷型阶跃7-LP模光纤^[50];(c)弱耦合中心下陷型阶跃4-LP模光纤^[51];(d)弱耦合中心下陷型阶跃6-LP模光纤^[52]

Fig. 9. Reported inner-depressed step-index few mode fibers with the weak coupling. (a) Inner-depressed step-index 6-LP-mode fiber with the weak coupling^[49]; (b) inner-depressed step-index 7-LP-mode fiber with the weak coupling^[50]; (c) inner-depressed step-index 4-LP-mode fiber with the weak coupling^[51]; (d) inner-depressed step-index 6-LP-mode fiber wi

下载图片查看所有图片

在设计全MIMO光纤时,最重要的是保证全部高阶模式与基模LP₀₁模式的群速度尽量相等且保证在设计要求的波长范围内DMGD斜率尽量小^[53-58]。图10展示了减小模间DMGD的三种光纤解决方案。图10(a)为低折射率沟槽辅助式双层阶跃光纤,此类光纤利用两层阶跃结构来调控模式n_eff从而达到控制DMGD的目的^[54];图10(b)为低折射率沟槽辅助式渐变折射率光纤,此类光纤通过调控渐变折射率的形变因子α来控制模式的群速度,从而达到控制DMGD的目的^[55];图10(c)为按一定长度比例熔接正DMGD光纤与负DMGD光纤以达到零DMGD的补偿方法^[57]。

图 10. 减小模间DMGD的三种光纤解决方案。(a)低折射率沟槽辅助式双层阶跃光纤^[54];(b)低折射率沟槽辅助式渐变折射率光纤^[55];(c)按一定长度比例熔接正DMGD光纤与负DMGD光纤以达到0DMGD的补偿方法^[57]

Fig. 10. Fiber solutions for reducing DMGD between modes. (a) Trench-assisted dual-cladding step fiber with low refractive index^[54]; (b) trench-assisted graded-index fiber with low refractive index^[55]; (c) 0DMGD compensation method to connect positive DMGD fiber (p) and negative DMGD fiber(n) with low refractive index^[57]

下载图片查看所有图片

其次,基于OAM模式的少模/多模光纤按照本征模式分离程度可以分成OAM强导环芯光纤和OAM模组通信环芯光纤^[59-68]。支持OAM模式的光纤多具有环芯结构,环芯结构使得各阶模式模场的重叠度增加,从而加大了各阶模式的隔离度,而且可以通过减小环芯厚度来抑制径向高阶的传输。

OAM强导环芯光纤具有非常大的纤芯包层折射率差,通过调节环芯厚度以及纤芯包层边界的折射率,可以调控本征CV模式的隔离度,被认为是一种弱耦合光纤。表2中展示了近年报道的支持OAM传输的实芯和光子晶体环芯光纤。空心的环芯光纤由于中心包层折射率下降为1.0,使得纤芯包层的相对折射率差大幅增大,从而使同一阶相同拓扑荷的两个不同波前相位旋转方向的OAM模式可以以低耦合的形式独立传播^[59-60]。负曲率渐变折射率光纤可以通过设计负曲率系数来调控CV模式之间的Δ ${n_{eff}}^{[61]}$ 。除了实芯环芯光纤,光子晶体环芯光纤由于具有天然高的纤芯包层相对折射率差,可以有效地加大CV模式间的间隔^[62-64]。

表 2. 已报道的OAM强导弱耦合环芯光纤

Table 2. Reported OAM strongly-guiding and weakly-coupling ring-core fibers

Fiber	In Ref. [59]	In Ref. [60]	In Ref. [61]	In Ref. [62]	In Ref. [63]
Cross sectionof strongly-guidedOAM fiber			—
Refractiveindexdistribution				—	—
OAM modegroup	OAM5,1,OAM5,1,OAM7,1(12 OAMmodes in all)	OAM0,1,OAM1,1,OAM2,1 ,…,OAM7,1 (28 OAMmodes in all)	OAM1,1(2 OAMmodes in all)	OAM+1,1,OAM+2,1,OAM+3,1,OAM+4,1(4 OAMmodes in all)	OAM+1,1,OAM+2,1 (2 OAMmodes in all)
Min Δneff /10-4	~1	1.1	2.1	~2	~7

查看所有表

OAM模组通信的设计思路是把模组间的有效折射率加大,而模组内本征CV模式依然保持简并状态。由于OAM模组从2阶拓扑荷开始每个模组内具有固定的4个简并模式,因此,接收端可以采用固定的4×4量级的MIMO技术来解调2阶及以上OAM的组内模式,且每个模组可以直接用于检测接收。图11展示了3个实现OAM模组通信的实验系统。其中:图11(a)给出基于低损耗低串扰的环芯光纤(RCF)和4×4 MIMO处理技术,利用2~3阶8个OAM模式以及10个波长,共传输80个通道16 Gband QPSK信号100 km,总容量达到2.56 Tb/s,光谱效率达到10.24 bit/(s · Hz),容量距离乘积达到256 (Tbit/s) · km^[65];图11(b)基于渐变折射率多模光纤实现了2.6 km无需MIMO的OAM模组传输(OAM_0,1,OAM_+1,1/OAM_-1,1, OAM_+2,1, OAM_+3,1)^[66];图11(c)基于环芯光纤实现了13个OAM模组的弱耦合传输^[67]。

OAM模组通信的实验系统。(a)基于低损耗、低串扰的环芯光纤和4×4 MIMO处理技术,利用8个OAM模式以及10个波长,共传输80个通道16 Gbaud QPSK信号100 km[65];(b)基于渐变折射率多模光纤实现了2.6 km无需MIMO的4个OAM模组传输[66];(c)基于环芯光纤实现了13个OAM模组的弱耦合传输[67]

图 11. OAM模组通信的实验系统。(a)基于低损耗、低串扰的环芯光纤和4×4 MIMO处理技术,利用8个OAM模式以及10个波长,共传输80个通道16 Gbaud QPSK信号100 km^[65];(b)基于渐变折射率多模光纤实现了2.6 km无需MIMO的4个OAM模组传输^[66];(c)基于环芯光纤实现了13个OAM模组的弱耦合传输^[67]

Fig. 11. OAM mode groups multiplexing transmission system. (a) Low crosstalk and low attenuation ring-core fiber with 4×4 MIMO based OAM multiplexing transmission experiment involving ten wavelengths and eight OAM modes over a distance of 100 km, transmitting 16-Gbaud QPSK signals over all 80 channels^[65]; (b) graded-index multi-mode fiber without MIMO based OAM multiplexing transmission over 2.6 km transmitting 4 OAM mode groups^{[ 下载图片查看所有图片}

3.3 模式调控机理

图12(a)展示的是传统的阶跃弱导光纤,图12(b)表示的是阶跃弱导光纤的色散曲线,其中横坐标V表示归一化频率,b表示归一化传播常数。V和b的表达式为

\begin{array}{l} V = k n_{1} a \sqrt[]{2 Δ}, (12) \\ b = \frac{{n^{2}}_{eff} - n_{2}^{2}}{n_{1}^{2} - n_{2}^{2}}, (13) \end{array}

式中,k,n₁,n₂,a,Δ分别表示自由空间的波数、纤芯折射率、包层折射率、纤芯半径以及纤芯包层间的相对折射率差。从图12(b)可以看出,LP₀₂和LP₂₁模的有效折射率非常接近^[68]。设计LP弱耦合少模光纤和OAM径向一阶少模光纤时,最重要的是调控LP₀₂模式。对于前者,需要调大LP₀₂和LP₂₁模的Δn_eff间隔;对于后者,需要彻底抑制径向高阶LP₀₂模式以减小其在复用解复用时对于径向一阶模式的串扰。

图 12. 阶跃光纤的横截面、折射率分布及色散曲线。(a)阶跃光纤的横截面及折射率分布;(b)阶跃弱导光纤的色散曲线图^[68]

Fig. 12. Cross-section, refractive index distribution and dispersion curves of step-index fiber. (a) Cross-section and refractive index distribution of step-index fiber; (b) dispersion curves of weakly-guiding step-index fiber^[68]

下载图片查看所有图片

为了调控弱导光纤中的模式,需要在标准阶跃光纤折射率上引入微扰项Δn来选择性地影响模式的传播常数。加入微扰后的传播常数的表达式^[69-70]为

β \approx \bar{β} + δβ = \bar{β} + k \frac{\overset{}{\int_{A}} Δ n {|\bar{e}|}^{2} d A}{\overset{}{\int_{A}} {|\bar{e}|}^{2} d A}, (14)

式中, $\bar{β}$ 、δβ和 $\bar{e}$ 表示阶跃光纤的标准模式传播常数、传播常数的修正项和电场分布,A表示光纤的有限横截面区域。从(14)式中可以看出,若想使得目标模式传播常数发生变化,需要使电场分布区域的折射率突变。由于径向高阶模式在纤芯中心处呈高斯分布,因此,在纤芯中心设置折射率下限,引入微扰项Δn,则可以很大程度上地减小径向高阶模式的传播常数。

图13(a)表示纤芯中心折射率下限的环芯光纤,其中,d,a,n₁,n₂,Δ分别表示中心下限部分直径、环形纤芯半径、纤芯折射率、包层折射率以及纤芯包层相对折射率差。图13(b)~(d)分别表示环芯不同厚度条件下光纤的色散曲线,其中环芯厚度用d/(2a)表示,d/(2a)越大,说明环芯厚度越薄。当d/(2a)从0.2以0.05为步长增加到0.3时,径向高阶LP₀₂模式的传播常数逐渐变小。因此,在设计基于LP模式的弱耦合少模光纤时,可以通过调控折射率下限部分的大小来控制径向高阶模式与其他模式的隔离程度^[68]。

图 13. 环芯光纤的横截面、折射率分布及色散曲线^[68]。(a)环芯光纤的横截面及折射率分布;(b)d/(2a)=0.20时,环芯弱导光纤的色散曲线图;(c)d/(2a)=0.25时,环芯弱导光纤的色散曲线图;(d)d/(2a)=0.30时,环芯弱导光纤的色散曲线图

Fig. 13. Cross-section, refractive index distribution and dispersion curves of ring-core fiber^[68]. (a) Cross-section and refractive index distribution of ring-core fiber; (b) dispersion curves of weakly-guiding ring-core fiber, when d/(2a)=0.20; (c) dispersion curves of weakly-guiding ring-core fiber, when d/(2a)=0.25; (d) dispersion curves of weakly-guiding ring-core fiber, when d/(2a)=0.30

下载图片查看所有图片

在设计本征模式分离的OAM光纤时,需要调控各个CV模式的传播常数,使得CV模式分离。径向一阶本征矢量模式(m=1)各个CV模式的传播常数修正项见表3^[70]。表中,I₁和I₂分别表示为

\begin{array}{l} I_{1} = \frac{Δ}{2 k n_{1} r_{0}^{2}} \frac{\overset{\infty}{\int_{0}} r E_{l} (r) \frac{\partial E_{l} (r)}{\partial r} \frac{\partial n (r)}{\partial r} d r}{\overset{\infty}{\int_{0}} r E_{l}^{2} (r) d r}, (15) \\ I_{2} = \frac{lΔ}{2 k n_{1} r_{0}^{2}} \frac{\overset{\infty}{\int_{0}} E_{l}^{2} (r) \frac{\partial n (r)}{\partial r} d r}{\overset{\infty}{\int_{0}} r E_{l}^{2} (r) d r}, (16) \end{array}

式中,r是光纤径向坐标,r₀是纤芯半径,E_l(r)表示角向l阶CV模式的电场分布,n(r)是径向上的折射率分布。在折射率突变处由于入射波偏振方向的改变,模式的相位会发生相应的变化,从而导致传播常数改变。从(15)式和(16)式可以看出,如果想要让CV模式独立传播,需要在折射率突变处增大 $\frac{\partial E_{l} (r)}{\partial r}$ 和E_l(r)。因此,环形结构可以使模式靠近折射率突变处,能够有效调控CV模式传播常数。另外,增大n₁/n₀可以改变原本简并的本征CV模式各自的传播常数 $\bar{β}$ ,打破弱导近似,有效加大组内CV模式的间隔,但是这也会带来本征的自旋轨道耦合现象,增加本征串扰^[71-72]。因此,在设计OAM光纤时需要在本征模式分离与减小本征串扰之间做折中处理。

表 1. 已报道的沟槽辅助式单模多芯光纤排布方式

Table 1. Core arrangement of the reported trench-assisted single-mode multi-core fibers

Fiber	In Ref. [22]	In Ref. [23]	In Ref. [24]	In Ref. [25]	In Ref. [26]	In Ref. [27]
Cross section of thereported MCFs
Fiber structure	ORS	DRS	HCPS	TLS	New-typeHCPS	SLS
Core number	12	12	19	22	30	32
Core pitch /μm	37	44.6	35	41	30	29
Cladding diameter /μm	225	230	200	260	229	243
Average crosstalk@1550 nm	-32 dB/52 km	<-30 dB/1000 km	-42 dB/1 km	-45 dB/km	-50 dB/9.6 km	<-34.5dB/51.4 km
Loss /(dB·km-1)@1550 nm	0.199	0.186	0.227	0.21	—	0.24
Transmissioncapacity /(Tb·s-1)	1010	409	305	2150	—	—

查看所有表

4 少模多芯光纤

少模多芯光纤将空间和模式两个维度结合,是更进一步提升光纤传输容量的空分复用方案^[73-80]。在设计少模多芯光纤时,需要在包层尺寸限制下考虑纤芯排布以及芯内模式的调控,其设计机理与上述多芯光纤和少模光纤类似,在此不再赘述。

2015年,日本情报通信研究机构(NICT)报道了异质沟槽辅助式阶跃折射率36芯3模光纤,利用该光纤的108个空间信道共传输了100 Gb/s的双偏振四相绝对相移调制(DP-QPSK)信号^[76]。2018年,日本KDDI研究所制备了一种同质沟槽辅助式渐变折射率19芯6模光纤,并且利用该光纤首次通过实验验证传输容量可达10 Pb/s,每个空间信道的平均速率为89.1 Tb/s,平均频谱效率为1099.9 bit·s^-1·H ${z^{- 1}}^{[79]}$ 。2020年,日本NICT利用368-WDM、波特率为24.5 Gband、64和256正交振幅调制(QAM)信号在38芯3模光纤上传输13 km,频谱效率达到1158.7 bit·s^-1·Hz^-1,总容量为10.66 Pb/s^[80]。该容量是目前报道的少模多芯光纤中的最大容量,该结果体现出未来基于少模多芯光纤的大容量空分复用系统的巨大潜力。

5 光纤性能对比

在制备方面,MCF的制备技术较为成熟,损耗与SMF接近,通过调整芯数和芯间距可以维持低串扰,但芯数受到包层尺寸上限的约束,目前已有7芯光纤商用化产品^[81];FMF需要控制纤芯预制棒掺杂浓度和厚度,制备较复杂,FMF的损耗主要来自高阶模式。目前等离子体化学气相沉积(PCVD)技术可以较为准确地控制掺杂浓度,产业界也推出了2~4个LP模式的FMF产品^[82];FM-MCF的设计与制备相对而言复杂度更高。在对准方面,MCF、FM-MCF需要采用Marker标识来辅助对准熔接,还需要采用具有端面观测功能的熔接机,而FMF则可以直接使用现有设备进行熔接,但是熔接时其纤芯的主轴偏离容易导致熔接损耗以及模式串扰^[83]。在复用方面,MCF有商用的扇入扇出设备,FMF有基于相位模板空间光耦合器、光子灯笼波导耦合器等不同解决方案,两者都有商业化产品,支持4~6个LP模式转换与复用,而FM-MCF需要先扇入扇出再耦合,现在尚处于实验室研究阶段。在放大方面,MCF有芯区和包层泵浦,其中包层泵浦集成度高,但是泵浦效率较低,增益控制困难,FMF同样有芯区和包层泵浦两种,需要进行模间增益控制^[84],而FM-MCF主要为包层泵浦,其中FM-MCF同样需要控制模间增益差。在数字信号处理(DSP)方面,MCF如果考虑偏振态,单个纤芯需要2×2简单的MIMIO-DSP,全MIMO的FMF或FM-MCF中单芯则需要2N_core×2N_core量级的计算,其中N_core为纤芯数量,因此模式数N_mode越多,计算量越复杂^[85-86]。

上述对比光纤皆为传统LP模式的空分复用光纤,对于OAM模式空分复用光纤来说,制备难点来自于光纤折射率分布变化增多从而导致的预制棒掺杂层数增加,因此需要更精确地控制沉积的厚度。目前报道的OAM环芯光纤低阶模式的损耗可以低至0.2 dB/km量级,串扰可以达到-55 dB/km^[87],而高阶模式的损耗和串扰目前尚未报道。OAM环芯光纤熔接对准存在与上述LP少模光纤同样的难点,光纤熔接时若存在纤芯偏离则很容易导致模式串扰和熔接损耗。然而,OAM环芯光纤也具有一定的发展潜力。首先,一般OAM环芯光纤传输的是径向一阶模式,各阶径向一阶OAM模式的光强分布相似,因此,在模式复用调控以及放大增益均衡方向均更有优势;其次,OAM环芯光纤可以采用模组通信方案,即模组分离,而组内强耦合。对于模组可以采用直检的方式接收,而对于组内简并的4个模式可以使用4×4固定量级的MIMO-DSP进行处理。

综上所述,多芯光纤虽然损耗低,但是在如何对接、如何提高放大功率等问题上亟需突破;少模光纤熔接虽然可以兼容现有单模设备,但是熔接时会引入模式串扰,且目前模式复用/解复用设备仍处于实验状态,传输系统难度较大。上述多芯光纤、少模光纤及少模多芯光纤在应用与系统方面均尚未完全成熟,日后何种光纤能成为空分复用主流商用技术主要取决于光纤周边器件及工程问题的解决。

表 2. 已报道的OAM强导弱耦合环芯光纤

Table 2. Reported OAM strongly-guiding and weakly-coupling ring-core fibers

Fiber	In Ref. [59]	In Ref. [60]	In Ref. [61]	In Ref. [62]	In Ref. [63]
Cross sectionof strongly-guidedOAM fiber			—
Refractiveindexdistribution				—	—
OAM modegroup	OAM5,1,OAM5,1,OAM7,1(12 OAMmodes in all)	OAM0,1,OAM1,1,OAM2,1 ,…,OAM7,1 (28 OAMmodes in all)	OAM1,1(2 OAMmodes in all)	OAM+1,1,OAM+2,1,OAM+3,1,OAM+4,1(4 OAMmodes in all)	OAM+1,1,OAM+2,1 (2 OAMmodes in all)
Min Δneff /10-4	~1	1.1	2.1	~2	~7

查看所有表

6 结束语

空分复用技术作为提升光纤通信系统的关键技术,被认为是继波分复用技术之后的光纤传输技术的第二次技术革命。近年来,世界各国科研机构都开展了关于SDM相关技术的深入研究。本文主要着眼于空分复用光纤,分别从光纤分类与传输机理方面介绍了三种主流的空分复用光纤,并总结了光纤的设计原理和方法。对于多芯光纤,从芯间串扰计算与纤芯选取的角度介绍了设计方法。对于少模/多模光纤,详细介绍了模式分类和模式调控机理。最后对比了多芯、少模及少模多芯三种方案,阐述了各自的优缺点。

虽然SDM技术在标准化方面尚不明确,研究发展和推广应用也存在着诸多瓶颈,但是世界各国的研究团队仍然在积极探索可行可靠的技术路线以推动SDM的发展。2019年日本住友电工集团与拉奎拉大学合作在意大利拉奎拉市的地下隧道首次铺设了包含18根多芯光纤的6.29 km光缆。现场测试得知空分复用光纤部署于现实环境后仍然具有非常低的损耗和空间模式色散,这标志着空分复用传输从实验室理想环境走向了更复杂的现场实时传输。因此,可以预想,未来随着SDM相关技术的不断发展,SDM将成为下一代超大容量光纤通信的重要解决方案。

参考文献

[1] Li T Y. Lightwave telecommunication[J]. Physics Today, 1985, 38(5): 24-31.

[2] Saitoh K, Matsuo S. Multicore fiber technology[J]. Journal of Lightwave Technology, 2016, 34(1): 55-66.

[3] Essiambre R J, Kramer G, Winzer P J, et al. Capacity limits of optical fiber networks[J]. Journal of Lightwave Technology, 2010, 28(4): 662-701.

[4] Wang J, Gray S, Walton D, et al. Fiber fuse in high power optical fiber[J]. Proceedings of SPIE, 2008, 7134: 71342E.

[5] Desurvire E B. Capacity demand and technology challenges for lightwave systems in the next two decades[J]. Journal of Lightwave Technology, 2006, 24(12): 4697-4710.

[6] MoriokaT. New generation optical infrastructure technologies: “EXAT initiative” towards 2020 and beyond[C]∥2009 14th OptoElectronics and Communications Conference, July 13-17, 2009, Vienna, Austria. New York: IEEE Press, 2009: 1- 2.

[7] Richardson D J, Fini J M, Nelson L E. Space-division multiplexing in optical fibres[J]. Nature Photonics, 2013, 7(5): 354-362.

[8] Li G F, Bai N, Zhao N B, et al. Space-division multiplexing: the next frontier in optical communication[J]. Advances in Optics and Photonics, 2014, 6(4): 413-487.

[9] Mizuno T, Miyamoto Y. High-capacity dense space division multiplexing transmission[J]. Optical Fiber Technology, 2017, 35: 108-117.

[10] . E102-[J]. Awaji Y. Review of space-division multiplexing technologies in optical communications. IEICE Transactions on Communications, 2019, B(1): 1-16.

[11] Winzer P J. Making spatial multiplexing a reality[J]. Nature Photonics, 2014, 8(5): 345-348.

[12] 裴丽, 王建帅, 郑晶晶, 等. 空分复用光纤的特性及其应用研究[J]. 红外与激光工程, 2018, 47(10): 1002001.

Pei L, Wang J S, Zheng J J, et al. Research on specialty and application of space-division-multiplexing fiber[J]. Infrared and Laser Engineering, 2018, 47(10): 1002001.

[13] Saitoh K, Matsuo S. Multicore fibers for large capacity transmission[J]. Nanophotonics, 2013, 2: 441-454.

[14] Sillard P, Bigot-Astruc M, Molin D. Few-mode fibers for mode-division-multiplexed systems[J]. Journal of Lightwave Technology, 2014, 32(16): 2824-2829.

[15] Sasaki Y, Takenaga K, Matsuo S, et al. Few-mode multicore fibers for long-haul transmission line[J]. Optical Fiber Technology, 2017, 35: 19-27.

[16] Saitoh K, Koshiba M, Takenaga K, et al. Crosstalk and core density in uncoupled multicore fibers[J]. IEEE Photonics Technology Letters, 2012, 24(21): 1898-1901.

[17] SaitohK, KoshibaM, TakenagaK, et al.Homogeneous and heterogeneous multi-core fibers[C]∥2012 IEEE Photonics Society Summer Topical Meeting Series, July 9-11, 2012, Seattle, WA, USA.New York: IEEE Press, 2012: 210- 211.

[18] Koshiba M, Saitoh K, Kokubun Y. Heterogeneous multi-core fibers: proposal and design principle[J]. IEICE Electronics Express, 2009, 6(2): 98-103.

[19] Tu J, Saitoh K, Koshiba M, et al. Design and analysis of large-effective-area heterogeneous trench-assisted multi-core fiber[J]. Optics Express, 2012, 20(14): 15157-15170.

[20] HayashiT. Multi-core fibers for space division multiplexing[M] ∥Handbook of Optical Fibers. Singapore: Springer Singapore, 2019: 1- 47.

[21] Tu J J, Saitoh K, Koshiba M, et al. Optimized design method for bend-insensitive heterogeneous trench-assisted multi-core fiber with ultra-low crosstalk and high core density[J]. Journal of Lightwave Technology, 2013, 31(15): 2590-2598.

[22] TakaraH, SanoA, KobayashiT, et al. ( 12 SDM/222 WDM/456Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency[C]∥ 2012European Conference on Optical Communication, September 16-20, 2012, Amsterdam, Netherlands. Washington, D.C.: Optical Society of America, 2012: Th.3.C.1.

[23] Sano A, Takara H, Kobayashi T, et al. 409-Tb/s+409-Tb/s crosstalk suppressed bidirectional MCF transmission over 450 km using propagation-direction interleaving[J]. Optics Express, 2013, 21(14): 16777-16783.

[24] SakaguchiJ, Puttnam BJ, KlausW, et al. 19-core fiber transmission of 19×100×172-Gb/s SDM-WDM-PDM-QPSK signals at 305 Tb/s[C]∥ 2012 Optical Fiber Communication Conference, March 4-8, 2012, Los Angeles, California, USA. Washington, D.C.: Optical Society of America, 2012: PDP5C. 1.

[25] Puttnam BJ, Luís RS, KlausW, et al.2.15 Pb/s transmission using a 22 core homogeneous single-mode multi-core fiber and wideband optical comb[C]∥2015 European Conference on Optical Communication (ECOC), September 27 - October 1, 2015, Valencia, Spain.New York: IEEE Press, 2015: 1- 3.

[26] AmmaY, SasakiY, TakenagaK, et al. High-density multi-core fiber with heterogeneous core arrangement[C]∥ 2015 Optical Fiber Communication Conference, March 9-14, 2015, San Francisco, California, USA. Washington, D.C.: Optical Society of America, 2015: Th4C. 4.

[27] MizunoT, ShibaharaK, OnoH, et al. 32-core dense SDM unidirectional transmission of PDM-16QAM signals over 1600 km using crosstalk-managed single-mode heterogeneous multicore transmission line[C]∥2016 Optical Fiber Communications Conference and Exhibition (OFC), March 20-24, 2016, Anaheim, CA, USA. Washington, D.C.: Optical Society of America, 2016: Th5C. 3.

[28] Xia C, Bai N, Ozdur I, et al. Supermodes for optical transmission[J]. Optics Express, 2011, 19(17): 16653-16664.

[29] Ho K P, Kahn J M. Statistics of group delays in multimode fiber with strong mode coupling[J]. Journal of Lightwave Technology, 2011, 29(21): 3119-3128.

[30] Arik S O, Kahn J M, Ho K P. MIMO signal processing for mode-division multiplexing: an overview of channel models and signal processing architectures[J]. IEEE Signal Processing Magazine, 2014, 31(2): 25-34.

[31] RyfR, SierraA, Essiambre RJ, et al. 1200-km 6 × 6 MIMO mode-multiplexed transmission over 3-core microstructured fiber[C]∥ 2011 European Conference on Optical Communication and Exhibition, September 18-22, 2011, Geneva, Switzerland. Washington, D.C.: Optical Society of America, 2011: Th.13.C.1.

[32] RyfR, Essiambre RJ, Gnauck AH, et al. Space-division multiplexed transmission over 4200-km 3-core microstructured fiber[C]∥OFC/NFOEC, March 4-8, 2012, Los Angeles, CA, USA. Washington, D.C.: Optical Society of America, 2012: PDP5C. 2.

[33] RyfR, Fontaine NK, GuanB, et al.1705-km transmission over coupled-core fibre supporting 6 spatial modes[C]∥2014 The European Conference on Optical Communication (ECOC), September 21-25, 2014, Cannes, France.New York: IEEE Press, 2014: 1- 3.

[34] Hayashi T, Taru T, Shimakawa O, et al. Design and fabrication of ultra-low crosstalk and low-loss multi-core fiber[J]. Optics Express, 2011, 19(17): 16576-16592.

[35] Koshiba M, Saitoh K, Takenaga K, et al. Multi-core fiber design and analysis: coupled-mode theory and coupled-power theory[J]. Optics Express, 2011, 19(26): B102-B111.

[36] Takenaga K, Arakawa Y, Tanigawa S, et al. An investigation on crosstalk in multi-core fibers by introducing random fluctuation along longitudinal direction[J]. IEICE Transactions on Communications, 2011, 94(2): 409-416.

[37] Koshiba M, Saitoh K, Takenaga K, et al. Analytical expression of average power-coupling coefficients for estimating intercore crosstalk in multicore fibers[J]. IEEE Photonics Journal, 2012, 4(5): 1987-1995.

[38] OkamotoK. Fundamentals of optical waveguides[M]. 2nd ed. London: Elsevier Inc, 2006.

[39] Ye F H, Tu J J, Saitoh K, et al. Design of homogeneous trench-assisted multi-core fibers based on analytical model[J]. Journal of Lightwave Technology, 2016, 34(18): 4406-4416.

[40] Ye F H, Tu J J, Saitoh K, et al. Wavelength-dependence of inter-core crosstalk in homogeneous multi-core fibers[J]. IEEE Photonics Technology Letters, 2016, 28(1): 27-30.

[41] Ye F, Tu J, Saitoh K, et al. Simple analytical expression for crosstalk estimation in homogeneous trench-assisted multi-core fibers[J]. Optics Express, 2014, 22(19): 23007-23018.

[42] Tu J J, Long K P, Saitoh K. An efficient core selection method for heterogeneous trench-assisted multi-core fiber[J]. IEEE Photonics Technology Letters, 2016, 28(7): 810-813.

[43] Xie X Q, Tu J J, Zhou X, et al. Design and optimization of 32-core rod/trench assisted square-lattice structured single-mode multi-core fiber[J]. Optics Express, 2017, 25(5): 5119-5132.

[44] Takenaga K, Arakawa Y, Sasaki Y, et al. A large effective area multi-core fiber with an optimized cladding thickness[J]. Optics Express, 2011, 19(26): B543-B550.

[45] Matsuo S, Takenaga K, Arakawa Y, et al. Large-effective-area ten-core fiber with cladding diameter of about 200 μm[J]. Optics Letters, 2011, 36(23): 4626-4628.

[46] Zhang W D, Huang L G, Wei K Y, et al. Cylindrical vector beam generation in fiber with mode selectivity and wavelength tunability over broadband by acoustic flexural wave[J]. Optics Express, 2016, 24(10): 10376-10384.

[47] Han Y, Liu Y G, Wang Z, et al. Controllable all-fiber generation/conversion of circularly polarized orbital angular momentum beams using long period fiber gratings[J]. Nanophotonics, 2018, 7(1): 287-293.

[48] Han Y, Liu Y G, Huang W, et al. Generation of linearly polarized orbital angular momentum modes in a side-hole ring fiber with tunable topology numbers[J]. Optics Express, 2016, 24(15): 17272-17284.

[49] Bigot-AstrucM, Trinel JB, MaertenH, et al. Weakly-coupled 6-LP-mode fiber with low differential mode attenuation[C]∥Optical Fiber Communication Conference (OFC) 2019, San Diego, California. Washington, D.C.: Optical Society of America, 2019: M1E. 3.

[50] Bigot AM, MolinD, Jongh KD, et al. Next-generation multimode fibers for space division multiplexing[C]∥ 2017 Advanced Photonics Congress, July 24-27, 2017, Zurich, Switzerland. Washington, D.C.: Optical Society of America, 2017: NeM3B. 4.

[51] MaL, Jiang SL, Du JB, et al. Ring-assisted 7-LP-mode fiber with ultra-low Inter-mode crosstalk[C]∥Asia Communications and Photonics Conference, November 2-5, 2016, Wuhan, China. Washington, D.C.: Optical Society of America, 2016: AS4A. 5.

[52] Ge DW, Li JH, Zhu JL, et al. Design of a weakly-coupled ring-core FMF and demonstration of 6-mode 10-km IM/DD transmission[C]∥2018 Optical Fiber Communications Conference and Exposition (OFC), March 11-15, 2018, San Diego, CA, USA. Washington, D.C.: Optical Society of America, 2018: W4K. 3.

[53] Tu J, Saitoh K, Takenaga K, et al. Heterogeneous trench-assisted few-mode multi-core fiber with low differential mode delay[J]. Optics Express, 2014, 22(4): 4329-4341.

[54] Sasaki Y, Amma Y, Takenaga K, et al. Few-mode multicore fiber with 36 spatial modes (three modes (LP01, LP11a, LP11b)×12 cores)[J]. Journal of Lightwave Technology, 2015, 33(5): 964-970.

[55] Sillard P, Molin D, Bigot A M, et al. Low-differential-mode-group-delay 9-LP-mode fiber[J]. Journal of Lightwave Technology, 2016, 34(2): 425-430.

[56] Tu J, Saitoh K, Amma Y, et al. Heterogeneous trench-assisted few-mode multi-core fiber with graded-index profile and square-lattice layout for low differential mode delay[J]. Optics Express, 2015, 23(14): 17783-17792.

[57] Maruyama R, Kuwaki N, Matsuo S, et al. Two mode optical fibers with low and flattened differential modal delay suitable for WDM-MIMO combined system[J]. Optics Express, 2014, 22(12): 14311-14321.

[58] SakamotoT, MoriT, YamamotoT, et al. Differential mode delay managed transmission line for wide-band WDM-MIMO system[C]∥Optical Fiber Communication Conference, Los Angeles, California. Washington, D.C.: Optical Society of America, 2012: OM2D. 1.

[59] GreggP, KristensenP, Ramachandran S. Conservation of orbital angular momentum in air core optical fibers[EB/OL]. ( 2014-12-03)[2020-08-24]. https:∥arxiv.org/abs/1412. 1397.

[60] Brunet C, Vaity P, Messaddeq Y, et al. Design, fabrication and validation of an OAM fiber supporting 36 states[J]. Optics Express, 2014, 22(21): 26117-26127.

[61] Ung B, Vaity P, Wang L, et al. Few-mode fiber with inverse-parabolic graded-index profile for transmission of OAM-carrying modes[J]. Optics Express, 2014, 22(15): 18044-18055.

[62] Tu J, Liu Z, Gao S, et al. Ring-core fiber with negative curvature structure supporting orbital angular momentum modes[J]. Optics Express, 2019, 27(15): 20358-20372.

[63] Tandjè A, Yammine J, Dossou M, et al. Ring-core photonic crystal fiber for propagation of OAM modes[J]. Optics Letters, 2019, 44(7): 1611-1614.

[64] Tu J J, Gao S C, Wang Z, et al. Bend-insensitive grapefruit-type holey ring-core fiber for weakly-coupled OAM mode division multiplexing transmission[J]. Journal of Lightwave Technology, 2020, 38(16): 4497-4503.

[65] Zhang J W, Liu J Y, Shen L, et al. Mode-division multiplexed transmission of wavelength-division multiplexing signals over a 100-km single-span orbital angular momentum fiber[J]. Photonics Research, 2020, 8(7): 1236-1242.

[66] Zhu L, Wang A, Chen S, et al. Orbital angular momentum mode groups multiplexing transmission over 2.6-km conventional multi-mode fiber[J]. Optics Express, 2017, 25(21): 25637-25645.

[67] Chen S, Li S, Fang L, et al. OAM mode multiplexing in weakly guiding ring-core fiber with simplified MIMO-DSP[J]. Optics Express, 2019, 27(26): 38049-38060.

[68] Kasahara M, Saitoh K, Sakamoto T, et al. Design of three-spatial-mode ring-core fiber[J]. Journal of Lightwave Technology, 2014, 32(7): 1337-1343.

[69] May AR, Zervas MN. Few-mode fibers with improved mode spacing[C]∥2015 European Conference on Optical Communication (ECOC), September 27 - October 1, 2015, Valencia, Spain.New York: IEEE Press, 2015: 1- 3.

[70] Snyder AW, Love JD. Optical waveguide theory[M]. Arrowsmith W J, Transl. 1 st ed. London: Chapman and Hall Ltd , 1983: 312- 313.

[71] Zhang Z, Gan J, Heng X, et al. Optical fiber design with orbital angular momentum light purity higher than 99.9[J]. Optics Express, 2015, 23(23): 29331-29341.

[72] Gregg P, Kristensen P, Rubano A, et al. Enhanced spin orbit interaction of light in highly confining optical fibers for mode division multiplexing[J]. Nature Communications, 2019, 10: 4707.

[73] Watanabe T, Kokubun Y. Ultra-large number of transmission channels in space division multiplexing using few-mode multi-core fiber with optimized air-hole-assisted double-cladding structure[J]. Optics Express, 2014, 22(7): 8309-8319.

[74] Tu J J, Long K P, Saitoh K. Design and optimization of 3-mode×12-core dual-ring structured few-mode multi-core fiber[J]. Optics Communications, 2016, 381: 30-36.

[75] MizunoT, KobayashiT, TakaraH, et al. 12-core×3-mode dense space division multiplexed transmission over 40 km employing multi-carrier signals with parallel MIMO equalization[C]∥ 2014 Optical Fiber Communication Conference, March 9-13, 2014, San Diego, California, USA. Washington, D.C.: Optical Society of America, 2014: Th5B. 2.

[76] SakaguchiJ, KlausW, Mendinueta J M D, et al. Realizing a 36-core, 3-mode fiber with 108 spatial channels[C]∥2015 Optical Fiber Communications Conference and Exhibition (OFC), March 22-26, 2015, Los Angeles, CA, USA. Washington, D.C.: Optical Society of America, 2015: Th5C. 2.

[77] UdenR, Correa RA, Lopez EA, et al. 2014European Conference on Optical Communication and Exhibition, September 22-24, 2014, Cannes, France. New York: IEEE, 2014: Mo.3.3. 4.

[78] SakamotoT, MatsuiT, SaitohK, et al. Low-loss and low-DMD few-mode multi-core fiber with highest core multiplicity factor[C]∥2016 Optical Fiber Communications Conference and Exhibition (OFC), March 20-24, 2016, Anaheim, CA, USA. Washington, D.C.: Optical Society of America, 2016: Th5A. 2.

[79] Soma D, Wakayama Y, Beppu S, et al. 10.16-peta-B/s dense SDM/WDM transmission over 6-mode 19-core fiber across the C+L band[J]. Journal of Lightwave Technology, 2018, 36(6): 1362-1368.

[80] RademacherG, Puttnam BJ, Luís RS, et al. 10.66 peta-bit/s transmission over a 38-core-three-mode fiber[C]∥2020 Optical Fiber Communications Conference and Exhibition (OFC), March 8-12, 2020, San Diego, CA, USA. Washington, D.C.: Optical Society of America, 2020: Th3H. 1.

[81] 杨晨, 李博睿, 童维军. 多芯光纤制备技术与应用的新进展[EB/OL]. ( 2017-06-15) [2017-06-15]. https:∥www.yofc.com/view/1548.html.

YangC, Li BR, Tong W J. Progress of multi-core fiber fabrication technology and application[EB/OL]. ( 2017-06-15) [2017-06-15]. https:∥www.yofc.com/view/1548.html.

[82] 沈磊, 陈苏, 孙雪婷, 等. 长飞少模光纤分析[J]. 电信技术, 2017( 4): 30- 32.

ShenL, ChenS, Sun XT, et al. Analysis of YOFC few-mode fibers[J]. Telecommunications Technology, 2017( 4): 30- 32.

[83] 陈威成, 胡贵军, 刘峰, 等. 少模光纤熔接点处模式耦合测量[J]. 光学学报, 2017, 37(12): 1206005.

Chen W C, Hu G J, Liu F, et al. Measurement of mode coupling at a splice point between few-mode fiber[J]. Acta Optica Sinica, 2017, 37(12): 1206005.

[84] 张振振, 郭骋, 张一弛, 等. 增益均衡的远程遥泵少模光纤放大器[J]. 光学学报, 2019, 39(10): 1006004.

Zhang Z Z, Guo C, Zhang Y C, et al. Gain-equalized remotely pumped few-mode fiber amplifier[J]. Acta Optica Sinica, 2019, 39(10): 1006004.

[85] 赖俊森, 汤瑞, 吴冰冰, 等. 光纤通信空分复用技术研究进展分析[J]. 电信科学, 2017, 33(9): 118-135.

Lai J S, Tang R, Wu B B, et al. Analysis on the research progress of space division multiplexing in optical fiber communication[J]. Telecommunications Science, 2017, 33(9): 118-135.

[86] 王瑜浩, 武保剑, 万峰, 等. 少模光纤通信系统中模间非线性相位调制的补偿分析[J]. 光学学报, 2019, 39(12): 1206006.

Wang Y H, Wu B J, Wan F, et al. Analysis of compensation for inter-mode nonlinear phase modulation in few-mode optical fiber communication systems[J]. Acta Optica Sinica, 2019, 39(12): 1206006.

[87] Shi CM, ShenL, Zhang JW, et al.Ultra-low inter-mode-group crosstalk ring-core fiber optimized using neural networks and genetic algorithm[C]∥2020 Optical Fiber Communications Conference and Exhibition (OFC), March 8-12, 2020, San Diego, CA, USA.New York: IEEE Press, 2020: W1B. 3.

涂佳静, 李朝晖. 空分复用光纤研究综述[J]. 光学学报, 2021, 41(1): 0106003. Jiajing Tu, Zhaohui Li. Review of Space Division Multiplexing Fibers[J]. Acta Optica Sinica, 2021, 41(1): 0106003.

空分复用光纤研究综述 下载： 2731次特邀综述

1 引言

图 1. 标准单模光纤容量的物理限制。(a)非线性香农极限[3];(b)光纤熔合损伤现象[4];(c)熔融石英光纤的传输窗口图,黑色部分为标准光放大区间[5]

Fig. 1. Reasons that make the capacity of single-mode fiber approach Shannon limit. (a) Nonlinear Shannon limit[3]; (b) fiber fuse damage phenomenon[4]; (c) transmission window of fused-silica fibers, where black region represents the standard optical amplification band[5]

2 多芯光纤

2.1 多芯光纤分类

图 2. 同质多芯光纤与异质多芯光纤的串扰对比。(a)同质多芯光纤串扰对弯曲半径的依赖关系图以及弯曲状态下有效折射率变化示意图;(b)异质多芯光纤串扰对弯曲半径的依赖关系图以及弯曲状态下有效折射率变化示意图

Fig. 2. Comparison of crosstalk between Homo-MCF and Hetero-MCF. (a) Crosstalk of Homo-MCF dependence on bending radius and change of effective index under bending condition; (b) crosstalk of Hetero-MCF dependence on bending radius and change of effective index under bending condition

表 1. 已报道的沟槽辅助式单模多芯光纤排布方式

Table 1. Core arrangement of the reported trench-assisted single-mode multi-core fibers

2.2 芯间串扰计算方法

2.3 纤芯选取方法

图 4. 外侧纤芯1选取方式[42]。(a)Hetero-TA-7-core fiber的横截面;(b)波长为1550 nm及Λ为35 μm条件下neff和Aeff对于r1和Δ1的函数关系图

Fig. 4. Core selection of outer core 1[42]. (a) Cross-section of a Hetero-TA-7-core fiber; (b) neff and Aeff as functions of r1 and Δ1 at λ =1550 nm and Λ=35 μm for the first outer cores in Hetero-TA-7-core fiber

图 5. 外侧纤芯2选取方式[42]。(a)Hetero-TA-7-core fiber的横截面;(b)波长为1550 nm及Λ为35 μm条件下neff和Aeff对于r1和Δ1的函数关系图

Fig. 5. Core selection of outer core 2[42]. (a) Cross-section of a Hetero-TA-7-core fiber; (b) neff and Aeff as function of r1 and Δ1 at λ=1550 nm and Λ=35 μm for the second outer cores in Hetero-TA-7-core fiber

图 6. 纤芯1和目标纤芯间串扰对于neff,q和K的函数关系[42],其中(5)式中的neff,p和neff,q分别代表纤芯1和目标纤芯的有效折射率

Fig. 6. XT between core 1 and the undetermined core as a function of neff,q and K[42], where neff,p and neff,q in Eq. (5) are effective indexes of refraction of core 1 and the undetermined core, respectively

图 7. 波长为1550 nm及Λ为35 μm条件下neff和Aeff对于r1和Δ1的函数关系图[42],其中CSR为中心纤芯2的纤芯选取区间,最大串扰lXT,max是纤芯2和目标中心纤芯的串扰值

Fig. 7. neff and Aeff as functions of r1 and Δ1 at λ=1550 nm and λ=35 μm with CSR of center core 2 in Hetero-TA-7-core fiber[42], where lXT,max

3 少模/多模光纤

3.1 光纤模式介绍

图 8. OAM模式、CV模式及LP模式之间的转关关系

Fig. 8. Conversion relationship between OAM, CV and LP modes

3.2 少模/多模光纤分类

图 9. 已报道的弱耦合中心下陷型阶跃光纤。(a)弱耦合中心下陷型阶跃6-LP模光纤[49];(b)弱耦合中心下陷型阶跃7-LP模光纤[50];(c)弱耦合中心下陷型阶跃4-LP模光纤[51];(d)弱耦合中心下陷型阶跃6-LP模光纤[52]

图 10. 减小模间DMGD的三种光纤解决方案。(a)低折射率沟槽辅助式双层阶跃光纤[54];(b)低折射率沟槽辅助式渐变折射率光纤[55];(c)按一定长度比例熔接正DMGD光纤与负DMGD光纤以达到0DMGD的补偿方法[57]

表 2. 已报道的OAM强导弱耦合环芯光纤

Table 2. Reported OAM strongly-guiding and weakly-coupling ring-core fibers

3.3 模式调控机理

图 12. 阶跃光纤的横截面、折射率分布及色散曲线。(a)阶跃光纤的横截面及折射率分布;(b)阶跃弱导光纤的色散曲线图[68]

Fig. 12. Cross-section, refractive index distribution and dispersion curves of step-index fiber. (a) Cross-section and refractive index distribution of step-index fiber; (b) dispersion curves of weakly-guiding step-index fiber[68]

图 13. 环芯光纤的横截面、折射率分布及色散曲线[68]。(a)环芯光纤的横截面及折射率分布;(b)d/(2a)=0.20时,环芯弱导光纤的色散曲线图;(c)d/(2a)=0.25时,环芯弱导光纤的色散曲线图;(d)d/(2a)=0.30时,环芯弱导光纤的色散曲线图

表 1. 已报道的沟槽辅助式单模多芯光纤排布方式

Table 1. Core arrangement of the reported trench-assisted single-mode multi-core fibers

4 少模多芯光纤

5 光纤性能对比

表 2. 已报道的OAM强导弱耦合环芯光纤

Table 2. Reported OAM strongly-guiding and weakly-coupling ring-core fibers

6 结束语

Article Outline

相关论文

相关资讯

关于本站 Cookie 的使用提示

全站搜索

空分复用光纤研究综述下载： 2731次特邀综述

图 1. 标准单模光纤容量的物理限制。(a)非线性香农极限^[3];(b)光纤熔合损伤现象^[4];(c)熔融石英光纤的传输窗口图,黑色部分为标准光放大区间^[5]

Fig. 1. Reasons that make the capacity of single-mode fiber approach Shannon limit. (a) Nonlinear Shannon limit^[3]; (b) fiber fuse damage phenomenon^[4]; (c) transmission window of fused-silica fibers, where black region represents the standard optical amplification band^[5]

图 4. 外侧纤芯1选取方式^[42]。(a)Hetero-TA-7-core fiber的横截面;(b)波长为1550 nm及Λ为35 μm条件下n_eff和A_eff对于r₁和Δ₁的函数关系图

Fig. 4. Core selection of outer core 1^[42]. (a) Cross-section of a Hetero-TA-7-core fiber; (b) n_eff and A_eff as functions of r₁ and Δ₁ at λ =1550 nm and Λ=35 μm for the first outer cores in Hetero-TA-7-core fiber

图 5. 外侧纤芯2选取方式^[42]。(a)Hetero-TA-7-core fiber的横截面;(b)波长为1550 nm及Λ为35 μm条件下n_eff和A_eff对于r₁和Δ₁的函数关系图

Fig. 5. Core selection of outer core 2^[42]. (a) Cross-section of a Hetero-TA-7-core fiber; (b) n_eff and A_eff as function of r₁ and Δ₁ at λ=1550 nm and Λ=35 μm for the second outer cores in Hetero-TA-7-core fiber

图 6. 纤芯1和目标纤芯间串扰对于n_eff,_q和K的函数关系^[42],其中(5)式中的n_eff,_p和n_eff,_q分别代表纤芯1和目标纤芯的有效折射率

Fig. 6. XT between core 1 and the undetermined core as a function of n_eff,_q and K^[42], where n_eff,_p and n_eff,_q in Eq. (5) are effective indexes of refraction of core 1 and the undetermined core, respectively

图 7. 波长为1550 nm及Λ为35 μm条件下n_eff和A_eff对于r₁和Δ₁的函数关系图^[42],其中CSR为中心纤芯2的纤芯选取区间,最大串扰l_XT,max是纤芯2和目标中心纤芯的串扰值

Fig. 7. n_effand A_effas functions of r₁ and Δ₁ at λ=1550 nm and λ=35 μm with CSR of center core 2 in Hetero-TA-7-core fiber^[42], where ${l_{XT}}_{, \max}$

图 9. 已报道的弱耦合中心下陷型阶跃光纤。(a)弱耦合中心下陷型阶跃6-LP模光纤^[49];(b)弱耦合中心下陷型阶跃7-LP模光纤^[50];(c)弱耦合中心下陷型阶跃4-LP模光纤^[51];(d)弱耦合中心下陷型阶跃6-LP模光纤^[52]

图 10. 减小模间DMGD的三种光纤解决方案。(a)低折射率沟槽辅助式双层阶跃光纤^[54];(b)低折射率沟槽辅助式渐变折射率光纤^[55];(c)按一定长度比例熔接正DMGD光纤与负DMGD光纤以达到0DMGD的补偿方法^[57]

图 12. 阶跃光纤的横截面、折射率分布及色散曲线。(a)阶跃光纤的横截面及折射率分布;(b)阶跃弱导光纤的色散曲线图^[68]

Fig. 12. Cross-section, refractive index distribution and dispersion curves of step-index fiber. (a) Cross-section and refractive index distribution of step-index fiber; (b) dispersion curves of weakly-guiding step-index fiber^[68]

图 13. 环芯光纤的横截面、折射率分布及色散曲线^[68]。(a)环芯光纤的横截面及折射率分布;(b)d/(2a)=0.20时,环芯弱导光纤的色散曲线图;(c)d/(2a)=0.25时,环芯弱导光纤的色散曲线图;(d)d/(2a)=0.30时,环芯弱导光纤的色散曲线图