光纤通信中模式耦合理论与影响

需积分: 5 163 浏览量更新于2024-07-16 收藏 2.85MB PDF 举报

"该资源是关于光通信领域中模式耦合的基础理论，主要探讨了电磁波在圆形光波导中的传播模式以及不同模式间的耦合理论。内容来源于 Optical Fiber Telecommunications VIB，由 Elsevier 出版社出版，适用于了解模式分束多路复用（MDM）系统中的耦合效应。" 在光通信系统中，模式耦合是至关重要的一环，特别是在当前对空间复用光通信系统的需求日益增长的背景下。模式耦合涉及的核心概念是不同光纤模式之间的相互作用，这些作用可能导致信号在传输过程中发生随机演变。在长距离系统中，利用相干检测，或者在短距离系统中通过直接检测，通过在多芯光纤（MCFs）或多模光纤（MMFs）的多个核心或模式中复用数据信号，可以增加传输容量，这就是模式分束多路复用（MDM）的基本原理。当光纤中存在指数扰动时，无论有意还是无意，都会诱导不同模式间的信号耦合。耦合强度可被分为弱耦合和强耦合两种类型，这取决于系统的总长度与保持传播场相关性的长度尺度的比较。如果总长度与此相关长度尺度相近，则耦合被认为是弱的；若远大于此长度，则为强耦合。模式耦合对MDM系统的影响是多方面的： 1. **信号质量下降**：耦合可能导致信号质量下降，尤其是在强耦合情况下，由于不同模式间的相互干扰，可能会导致误码率上升。 2. **信道间干扰（Inter-Channel Interference, ICI）**：在多模式光纤中，不同模式的耦合会引发信道间干扰，降低系统性能。 3. **模式色散**：模式耦合还会加剧模式色散问题，模式色散是多模光纤中信号传输速度差异引起的，会影响信号的时序恢复，从而降低系统带宽和传输距离。 4. **系统设计挑战**：理解和控制模式耦合对于优化MDM系统的架构、提高传输效率和稳定性至关重要。设计者需要考虑如何最小化耦合效应，例如通过优化光纤制造工艺来减少不均匀性。 5. **检测与纠错策略**：在耦合影响下，可能需要开发新的检测算法和纠错技术来补偿传输过程中的模式失真和信号衰减。为了克服这些挑战，研究者们正在探索各种方法，如采用更精确的模式匹配理论，发展新型光纤结构，以及利用先进的信号处理技术。例如，使用模式预编码技术可以减少模式间的相互影响，而利用高阶调制格式和先进的数字信号处理算法则有助于恢复因耦合而失真的信号。理解并有效地管理光纤中的模式耦合是提升光通信系统性能的关键，对于实现更高容量、更稳定可靠的通信网络具有重要意义。

503

11.2 Modes and Mode Coupling in Optical Fibers

11.2.3.4 Regimes of mode coupling

Different regimes of mode coupling are familiar from the study of randomly coupled

birefringence and PMD [37,89], and apply as well to mode coupling in MMF

[16,17,82]. These regimes are especially relevant in studying key effects such as

MD (Section 11.3) or MDL (Section 11.4), where operators describing MD or MDL

are deﬁned, whose eigenvalues describe physical properties of interest, i.e. coupled

modal GDs or coupled modal gains.

As stated above, modal ﬁelds are assumed to be strongly correlated over distances

less than or equal to a correlation length, and weakly correlated over distances far

larger than the correlation length. This correlation length is a generalization of the

polarization correlation length deﬁned in the study of PMD [83,90–92].

In the weak-coupling regime, the correlation length is comparable to, or slightly

shorter than, the total system length. In this regime, signal propagation can be mod-

eled using a small number of sections K, where each section should be slightly longer

than the correlation length. If a larger number of sections K is employed, the unitary

matrices

(k)

and

−1)

deﬁned in (11.19) should be correlated to reﬂect correlation

between sections. In the weak-coupling regime, the spread of eigenvalues describ-

ing quantities of interest, such as modal GDs or modal gains, scales linearly with

the number of sections K or the total system length



)

, and each coupled

eigenmode is a linear combination of a small number of uncoupled modes.

In the strong-coupling regime, the correlation length is far shorter than the total

system length. In this regime, signal propagation must be modeled using a large number

of sections K, where each section should be slightly longer than the correlation length.

The unitary matrices

)

and

−

)

should be statistically independent to ensure

independence between sections. In the strong-coupling regime, the spread of eigenvalues

describing quantities of interest, such as modal GDs or modal gains, scales with the

square-root of the number of sections K or the square-root of the total system length L

and each coupled eigenmode is a linear combination of many uncoupled modes.

These regimes of mode coupling are further illustrated and compared in

Section 11.3.1.

()

out

()

…

()

–

()

…

()

Modal

Multiplexer

Multimode

Fiber Sections

Multimode

Fiber Amp.

(a)

(b)

FIGURE 11.2 (a) Matrix model for an MMF system described by the product of a cascade

of matrices. (b) Each matrix in the cascade may represent a section of MMF, a modal

multiplexer or demultiplexer, a multimode optical ampliﬁer or other components.

504 CHAPTER 11 Mode Coupling

11.3 MODAL DISPERSION

In coherent MDM systems, MD poses no fundamental performance limitations.

MIMO equalizer complexity increases with the GD spread [18–20], but if laser phase

noise is sufﬁciently small and the channel does not change too rapidly, MD can

be compensated with no penalty. To date, most long-haul coherent MDM systems

[1–4,70] have operated in the weak-coupling regime. But as transmission distances

and the number of multiplexed modes are increased, equalizer complexity is likely

to become prohibitive unless strong mode coupling is exploited to reduce the GD

spread.

In this section, ﬁeld coupling models are used to study the effect of mode coupling

on MD. PMs, which are coupled modes having well-deﬁned GDs, are described. Of

greatest relevance to long-haul MDM systems, the statistics of the GDs of the PMs

in the strong-coupling regime are analyzed.

11.3.1 Coupled modal dispersion

The effect of mode coupling on MD was studied for the two-mode case in the context

of PMD in SMF [36–40,89–91], where coupled polarization states having well-deﬁned

GDs were called PSPs. The theory was extended to the multimode case in [41], where

coupled modes having well-deﬁned GDs were called PMs. Following [41], we assume

MDL is negligible (the combined impact of MD and MDL is studied in Sections

11.4.6 and 11.6.2). We further neglect mode-averaged loss or gain to simplify the

notation here, although that assumption was not made in [38,41]. In this case, the

total propagation operator deﬁned in (11.20) becomes unitary:

(t)

∗

(ω)M

(t)

(ω) = I

where

is a

D × D

identity matrix. We restrict attention to optical signals occupying

a narrow bandwidth near angular frequency ω. We deﬁne a set of D input PMs as a

set of input ﬁeld patterns deﬁned by vectors

PM,

(

)

, µ

1, ...,

. These input PMs

are linear combinations of the uncoupled modes that have special properties. If an

input PM is launched, the ﬁeld at the ﬁber output is described by the corresponding

output PM

PM,(out)

(t)

(ω)A

PM,(in

)

. Each of the input PMs is deﬁned such that

if we ﬁx the input ﬁeld pattern to be

PM,(in)

and vary ω slightly, the output ﬁeld

pattern

PM,(out)

remains unchanged to ﬁrst order in

. One can deﬁne a Hermitian

GD operator:

where

(t)

(ω)/dω

denotes differentiation with respect to

. As shown

in [41], the D input PMs are mutually orthogonal eigenmodes of the GD operator

whose eigenvalues are the coupled GDs:

In general, each input PM differs from the corresponding output PM, since the

operators

)

and G do not commute.

(11.21)

G =

(t)

(t)∗

(ω)

(11.22)

PM,

(

)

PM,

(

)

, µ

1, ..., D.

505

11.3 Modal Dispersion

For signals occupying a sufﬁciently narrow bandwidth near angular frequency

the overall input-output relationship of a ﬁber can be expressed as:

where

(

and

)

are unitary matrices that are independent of frequency (to ﬁrst

order), whose columns represent the input PMs and the output PMs, respectively, in

the basis of ideal modes. The matrix

describes propagation of the PMs. The matrix (11.24) describes no crosstalk, since it

is diagonal, and describes differential delay but no distortion, since its phase depends

linearly on ω. Many factorizations of the form (11.23) are possible mathematically,

but this choice is unique in yielding frequency-independent

(

and

(t)

and a diago-

nal



(t)

(ω)

with well-deﬁned GDs.

In [17], the effect of spatial- and polarization-mode coupling on the modal

GDs in graded-index MMF was studied. A ﬁber of ﬁxed total length L

was

divided into a ﬁxed number of sections K, and each section was given a random

curvature to induce spatial-mode coupling and birefringence. Successive sections

were rotated by a random angle to induce polarization-mode coupling. By chang-

ing the standard deviation (STD) of the curvature

, different regimes of mode

coupling can be obtained. Figure 11.3 shows the coupled GDs of the PMs in

a 1-km-long, graded-index MMF supporting D = 110 modes in two polariza-

tions. In the weak-coupling regime (

0. 3

), modes form groups having GD

degeneracies of 2, 4, 6, …, and the GD spread scales linearly with K or L. In the

medium-coupling regime (

0. 3

<σ

), these GD degeneracies are broken, and

each coupled PM is a linear combination of a small number of uncoupled modes.

In the strong-coupling regime (

<σ

), the GD spread is reduced substan-

tially, scaling in proportion to

√

, and each coupled PM is a linear com-

bination of many uncoupled modes. The reduction of the GD spread, while not

commonly observed in glass MMFs of 1-km length, is analogous to that observed

in plastic MMF. The regimes of mode coupling were explained previously using

a power coupling model in [16]. The power coupling model, while intuitively

appealing, may not be capable of providing the quantitative predictions required

for MDM systems.

The ﬁeld pattern of each PM varies with optical frequency ω, and is correlated

over a coherence bandwidth that depends, in principle, on the uncoupled modes and

GDs and the mode coupling [30,82]. In the absence of coupling and MDL, the PMs

are essentially equivalent to the ideal modes [41], so the coherence bandwidth is

extremely large, of the order of THz. In [17], the coherence bandwidths of the PMs

(11.23)

(t)

(ω)

(t)



(t)

(ω)U

(t)

∗

(11.24)



(t)

(ω) =







−jωτ

0 e

−jωτ







剩余77页未读，继续阅读

hanshubiao

粉丝: 0
资源: 3

光纤通信中模式耦合理论与影响

13.Coupling of Boundary Element Methods and Fi.pdf

C++标准库（第二版）英文版.pdf

论文研究-Experimental Examination of Multi-Mode Coupling Theory of a Coaxial Bragg Reflector.pdf

论文研究-Multi-mode Coupling in a Coaxial Bragg Reflector.pdf

System Coupling Users Guide.pdf

Probability Estimates for Multi-class Classification by Pairwise Coupling.pdf

USB4 1.0 ECN - Clarify AC Coupling Requirements.pdf

molecular dynamics with coupling to an external bath.pdf

21ic下载_IEEEStd519-2014.pdf.pdf

Spatial-mode-coupling-based dispersion engineering for integrated optical waveguide

最新资源