非线性光纤光学基础（第三版）

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"Nonlinear Fiber Optics (Basic Sections) 是一本关于光纤非线性光学的基础教程，由Govind P. Agrawal撰写，是Optics and Photonics系列的一部分。该书详细介绍了光纤中的非线性现象及其应用。" 在光纤通信领域，非线性光纤光学是一个至关重要的主题，因为光在光纤中的传播过程中会受到各种非线性效应的影响。这些效应在高功率传输或高速数据通信中尤其显著，可能导致信号失真、干扰和信道容量限制。以下是该书可能涉及的一些关键知识点： 1. **光纤的基本原理**：书中可能首先介绍光纤的基本结构，包括芯、包层和涂覆层，以及单模和多模光纤的区别。此外，还会讨论光纤的传播常数、衰减和色散等基本特性。 2. **非线性效应**：光纤中的非线性效应主要包括自相位调制（SPM）、交叉相位调制（XPM）、四波混频（FWM）和受激布里渊散射（SBS）。这些效应是由于光强依赖的折射率变化导致的，会影响光脉冲的形状和频率。 3. **自相位调制（SPM）**：SPM是指光脉冲在其自身内部由于强度依赖的折射率变化而引起的相位变化，可能导致脉冲展宽或压缩。 4. **交叉相位调制（XPM）**：XPM发生在两个不同强度的光脉冲在同一条光纤中传播时，一个脉冲的相位会受到另一个脉冲的影响。 5. **四波混频（FWM）**：FWM是四个光波在光纤中相互作用，生成新的频率成分的过程。这个过程可以用于频率转换，也是光孤子通信和超连续谱生成的基础。 6. **受激布里渊散射（SBS）**：SBS是一种声光效应，其中光能与光纤中的声波相互作用，导致反向散射光。SBS限制了光纤放大器的输出功率，并可用于布里渊激光器和光频梳的生成。 7. **孤子通信**：非线性光纤中的孤子是一种特殊的光脉冲，其形状保持不变，能够在长距离内无失真传输。孤子通信是利用非线性效应来维持脉冲质量的一种方法。 8. **光孤子碰撞**：在光纤中，孤子可能会相互碰撞，这种现象对理解光脉冲的传播行为至关重要。 9. **光纤非线性应用**：非线性光纤光学在光通信、光学信号处理、光谱学和量子信息处理等领域有广泛应用。例如，FWM用于光频率转换，SBS用于光限幅和光学采样，非线性光纤也可以用作光学参量振荡器和光学滤波器。 10. **实验方法和测量技术**：书中可能还涵盖了检测和研究非线性效应的实验技术，如光时域反射计（OTDR）、光谱分析和脉冲测量。《Nonlinear Fiber Optics (Basic Sections)》第三版提供了关于光纤非线性光学的深入理解，对理解现代光纤通信系统中的挑战和解决方案至关重要。通过学习这些概念，读者能够掌握如何优化系统性能并解决实际问题。

2 Introduction

teristics [5]–[8]. The idea that optical ﬁbers would beneﬁt from a dielectric

cladding was not obvious and has a remarkable history [1].

The ﬁeld of ﬁber optics developed rapidly during the 1960s, mainly for the

purpose of image transmission through a bundle of glass ﬁbers [9]. These early

ﬁbers were extremely lossy (loss

1000 dB/km) from the modern standard.

However, the situation changed drastically in 1970 when, following an earlier

suggestion [10], losses of silica ﬁbers were reduced to below 20 dB/km [11].

Further progress in fabrication technology [12] resulted by 1979 in a loss of

only 0.2 dB/km in the 1.55-

m wavelength region [13], a loss level limited

mainly by the fundamental process of Rayleigh scattering.

The availability of low-loss silica ﬁbers led not only to a revolution in the

ﬁeld of optical ﬁber communications [14]–[17] but also to the advent of the

new ﬁeld of nonlinear ﬁber optics. Stimulated Raman- and Brillouin-scattering

processes in optical ﬁbers were studied as early as 1972 [18]–[20]. This work

stimulated the study of other nonlinear phenomena such as optically induced

birefringence, parametric four-wave mixing, and self-phase modulation [21]–

[25]. An important contribution was made in 1973 when it was suggested that

optical ﬁbers can support soliton-like pulses as a result of an interplay between

the dispersive and nonlinear effects [26]. Optical solitons were observed in a

1980 experiment [27] and led to a number of advances during the 1980s in the

generation and control of ultrashort optical pulses [28]–[32]. The decade of the

1980s also saw the development of pulse-compression and optical-switching

techniques that exploited the nonlinear effects in ﬁbers [33]–[40]. Pulses as

short as 6 fs were generated by 1987 [41]. Several reviews and books cover

the enormous progress made during the 1980s [42]–[52].

The ﬁeld of nonlinear ﬁber optics continued to grow during the decade

of the 1990s. A new dimension was added when optical ﬁbers were doped

with rare-earth elements and used to make ampliﬁers and lasers. Although

ﬁber ampliﬁers were made as early as 1964 [53], it was only after 1987 that

their development accelerated [54]. Erbium-doped ﬁber ampliﬁers attracted

the most attention because they operate in the wavelength region near 1.55

and can be used for compensation of losses in ﬁber-optic lightwave systems

[55], [56]. Such ampliﬁers were used for commercial applications beginning

in 1995. Their use has led to a virtual revolution in the design of multichannel

lightwave systems [14]–[17].

The advent of ﬁber ampliﬁers also fueled research on optical solitons [57]–

[60] and led eventually to the concept of dispersion-managed solitons [61]–

4 Introduction

core-cladding index difference

∆



;

(1.2.1)

and the so-called V parameter deﬁned as

(



)

;

(1.2.2)

where k

, a is the core radius, and

is the wavelength of light.

The V parameter determines the number of modes supported by the ﬁber.

Fiber modes are discussed in Section 2.2, where it is shown that a step-index

ﬁber supports a single mode if V

405. Optical ﬁbers designed to sat-

isfy this condition are called single-mode ﬁbers. The main difference between

the single-mode and multimode ﬁbers is the core size. The core radius a is

typically 25–30

m for multimode ﬁbers. However, single-mode ﬁbers with

∆



003 require a to be

m. The numerical value of the outer radius b

is less critical as long as it is large enough to conﬁne the ﬁber modes entirely.

A standard value of b

m is commonly used for both single-mode

and multimode ﬁbers. Since nonlinear effects are mostly studied using single-

mode ﬁbers, the term optical ﬁber in this text refers to single-mode ﬁbers un-

less noted otherwise.

1.2.1 Material and Fabrication

The material of choice for low-loss optical ﬁbers is pure silica glass synthe-

sized by fusing SiO

molecules. The refractive-index difference between the

core and the cladding is realized by the selective use of dopants during the fab-

rication process. Dopants such as GeO

and P

increase the refractive index

of pure silica and are suitable for the core, while materials such as boron and

ﬂuorine are used for the cladding because they decrease the refractive index of

silica. Additional dopants can be used depending on speciﬁc applications. For

example, to make ﬁber ampliﬁers and lasers, the core of silica ﬁbers is codoped

with rare-earth ions using dopants such as ErCl

and Nd

. Similarly, Al

is sometimes added to control the gain spectrum of ﬁber ampliﬁers.

The fabrication of optical ﬁbers involves two stages [75]. In the ﬁrst stage,

a vapor-deposition method is used to make a cylindrical preform with the de-

sired refractive-index proﬁle and the relative core-cladding dimensions. A typ-

ical preform is 1-m long with 2-cm diameter. In the second stage, the preform

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