光学放大器详解：从半导体到光纤增益介质

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"The Optics Encyclopedia 是一本全面介绍光学放大器的参考书，涵盖了半导体光学放大器、稀土离子掺杂光纤放大器、光纤拉曼放大器和光纤布里渊放大器的物理原理和设备性能，并回顾了这些光学放大器在系统应用中的角色。作者Takaaki Mukai是NTT Electronics Corporation的专家，文章深入探讨了激光放大器的基础属性，如受激与自发跃迁、小信号增益和带宽、增益饱和以及噪声，还详细介绍了各种类型的光学放大器的特点。" 本文主要关注光学放大器这一重要领域，它们在光通信和光信号处理中起到关键作用，能直接放大光信号。光学放大器的种类多样，包括半导体光学放大器（SOA）、稀土离子掺杂光纤放大器（REDFAs）、光纤拉曼放大器（FRAs）和光纤布里渊放大器（BFAs）。半导体光学放大器（SOA）通常由III-V族半导体材料制成，如GaAs或InP，它们利用受激增益机制来放大光信号。SOA具有快速响应时间和小型化的优势，但其增益带宽有限，且易受温度和偏置电流的影响。稀土离子掺杂光纤放大器（REDFAs）是光纤通信系统中的常见组件，通常掺杂有Er3+或Nd3+等离子体。它们具有宽增益谱，适用于多种波长的信号放大，但可能需要泵浦源提供能量。光纤拉曼放大器（FRAs）利用光纤材料的非线性拉曼散射效应实现放大，可以在整个光纤窗口内提供增益，但需要高功率泵浦，并且增益效率相对较低。光纤布里渊放大器（BFAs）依赖于光纤的非线性布里渊散射，可以双向放大信号，但增益带宽较窄，适用于特定频率的信号。光学放大器的噪声特性是设计和应用中必须考虑的关键因素。增益饱和则会影响放大器在高功率输入时的表现，而小信号增益和带宽决定了放大器能够处理的信号类型和速度。文章的介绍涵盖了从基本概念到实际应用的广泛内容，对于理解光学放大器的工作原理及其在光网络中的应用具有重要价值。无论是系统设计师、工程师还是研究人员，都能从中获得宝贵的理论知识和技术细节。

Ampliﬁers, Optical 15

where

eff

1 − exp(−α

.(32)

Solution (31) shows that, because of

pump absorption, the effective interaction

length is l

eff

instead of the actual ﬁber

length l. Note that, for very long ﬁbers,

eff

= 1/α

; while for short ﬁbers (l 

1/α

), l

eff

= l.Foratypicalﬁberloss

value at 1.5

µm(α = 0.2dBkm

−1

), l

eff

is 21.7 km.

If the signal intensity I

(z) at the

Stokes frequency remains much smaller

than the pump intensity, pump depletion

can be ignored. The signal intensity at

the ampliﬁer output at z = l is given

by Eq. (31). Since I

(l) = I

(0) exp(−α

intheabsenceofapumpwave,the

small-signal gain of the FRA is given

by [34]

(l)

(0) exp(−α

=exp



eff



(33)

where P

= I

is the pump power at

the ampliﬁer input and A

is the effective

core area. In a pure-silica ﬁber, g

has a

peak value of about 1 × 10

−13

−1

the Stokes shift frequency ν

∼

450 cm

−1

(≈13.2THz). g

can be enhanced by

doping with GeO

and P

The expression of Eq. (33) assumes the

ideal case in which pump and signal

polarizations are kept parallel throughout

the propagation. When the polarization

is completely scrambled, the average

Raman gain coefﬁcient is reduced by

one half, while the FRA signal gain

becomes polarization insensitive. The FRA

has a fairly broad bandwidth (≈1THz)

due to the amorphous nature of the

glass material.

Even though more than 50-dB FRA

signal gain was achieved in a Q-

switched pumping experiment [35], max-

imum continuous-wave (cw) signal gain

was 21 dB with a 1.4-W cw-pumping

power [36]. The signal-gain saturation for

FRAs arises from both the pump power

depletion due to the Stokes signal am-

pliﬁcation and the higher-order Stokes

generation. High saturation output power

in FRAs is consistent with the required

high pump power (≈1W).

The 3-dB minimum noise ﬁgure men-

tioned in Sect. 2.4 also holds for ampliﬁers

with parametric interaction processes. The

internal mode ﬂuctuation is the zero-point

ﬂuctuation of a lattice vibrational mode [1].

In the Raman ampliﬁer, the optical

phonon energy hν

is larger than the ther-

mal energy k

T, so the thermal occupation

number, n

= [exp(hν

T) − 1]

−1

,is

much smaller than unity, and the Raman

ampliﬁer operates close to the quan-

tum limit.

3.4

Fiber Brillouin Ampliﬁer

Stimulated Brillouin scattering is analo-

gous to stimulated Raman scattering with

the acoustic phonon mode (sound waves)

playing the role of the lattice vibrations.

Brillouin ampliﬁcation in the optical ﬁber

occurs only in the backward direction

due to wave vector–matching considera-

tions [37]. The frequency shift ν

is given

by ν

= 2(V

/c)ν

,whereV

is the ve-

locity of a longitudinal sound wave in

the medium, c is the speed of light in

the medium, and ν

is the frequency of

the pump wave [4]. For λ = 1.5

µmin

pure silica glass, the Brillouin shift is

= 11 GHz.

The stimulated Brillouin scattering in-

teraction is governed by the following

16 Ampliﬁers, Optical

coupled-intensity equations similar to

Eqs. (28) and (29) in Sect. 3.3 [33].

=−g

+ αI

,(34)

=−g

− αI

.(35)

The only difference is that the sign of

/ dz is reversed to account for the

counterpropagating nature of the Stokes

wave with respect to the pump wave. The

relatively small values of the Brillouin shift

allow two simpliﬁcations to be made:

∼

and α

∼

= α.

The small-signal Brillouin gain is also

given by Eq. (33), by replacing g

with the

Brillouin gain coefﬁcient g

.Inpure-silica

ﬁbers, g

is about 4 × 10

−11

−1

[38],

which is nearly three orders-of-magnitude

larger than the Raman gain coefﬁcient g

Thus, FBAs can achieve the same level of

signal gain with much lower optical pump

power than FRAs. Conversely, this pump-

power advantage results in the smaller

saturation output power, since the FBA

gain saturation originates from the pump-

depletion mechanism. The bandwidth of

the FBA is extremely narrow due to

the long relaxation time of the acoustic

phonon mode. For 1.5-

µm light, the 3-dB

bandwidth is 17 MHz. Such a narrow gain-

bandwidth can be effectively broadened by

sweeping the pump laser frequency back

and forth over the desired bandwidth,

at the expense of additional pumping

power [39, 40].

In the Brillouin ampliﬁer, the internal

mode ﬂuctuation is the zero-point ﬂuc-

tuationofanacousticphononmode[1].

However, the acoustic phonon energy

hν

is smaller than the thermal en-

ergy, so the thermal occupation num-

ber, n

= [exp(hν

T) − 1]

−1

,ismuch

larger than one (typically about 500), and

the Brillouin ampliﬁer operates high above

the quantum limit [39].

System Applications of Optical Ampliﬁers

In this section, we review the applications

of optical ampliﬁers to ﬁber-optic commu-

nications systems.

4.1

Preampliﬁer, In-line Repeater, and Booster

Ampliﬁer

Figure 5 illustrates three applications of

linear optical ampliﬁers: (a) preampliﬁers,

(b) in-line repeaters, and (c) booster ampli-

ﬁers.

An optical preampliﬁer [Fig. 5(a)] is a

front-end device of an optical receiver, in

which a weak optical signal is ampliﬁed

before photodetection so that SNR degra-

dation due to thermal noise generated in

an electronic circuit can be suppressed [2,

7]. An optical preampliﬁer provides a larger

ampliﬁcation factor and a broader band-

width than other front-end devices, such

as the avalanche photodiode and the opti-

cal heterodyne detector. A 1.3-

µm TW-SOA

preampliﬁer receiver has achieved a 3.7-dB

improvement in sensitivity over the best

performance recorded for a conventional

avalanche photodiode receiver at a bit rate

of 8 Gbps [41].

An optical in-line repeater ampliﬁer

[Fig. 5(b)] compensates for ﬁber loss and

can extend the spacing between two regen-

erative repeaters [2, 7, 42]. Compared with

a conventional repeater, which employs

optical-to-electrical signal conversion and

has regenerating, reshaping, and retim-

ing functions, an optical in-line repeater

ampliﬁer features data rate and mod-

ulation format versatility. Furthermore,

Ampliﬁers, Optical 19

low-noise ﬁgure and succeeding ampliﬁers

with high saturation output powers.

Second, consider the case of L

= 1.

This is a cascaded in-line repeater system,

where each transmission line loss L

compensated for by the ampliﬁer gain G

Thetotalnoiseﬁgureofthesystemis

given by

total

= G

+ G

+···

+ G

, =



i=1

.(39)

Equation (39) indicates that, in the com-

pensated in-line repeater system, the noise

ﬁgures for all ampliﬁers contribute equally

to the total SNR degradation of the sys-

tem. Furthermore, if the ampliﬁer gain

and noise ﬁgure of all repeaters are identi-

cal with each other, Eq. (39) reduces to the

simple formula

total

= GFk.(40)

When allowable SNR degradation,

total

= [(S/N)

/(S/N)

], is given for a

system and both the ampliﬁer gain G

and noise ﬁgure F are known, the

maximum number of cascaded repeaters

max

is easily calculated using Eq. (40). The

SNR degradation in the cascaded linear

ampliﬁer repeater system is illustrated in

the lower part of Fig. 6. An abrupt SNR

degradation occurs at the ﬁrst repeater

output, which amounts to GF,theproduct

of the repeater gain and the noise ﬁgure.

Then, it gradually decreases as k

−1

the number of repeaters k increases.

Therefore, once in-line repeaters are

introduced into a transmission line, the

maximum number of repeaters (i.e., the

maximum system length) is achieved

by utilizing the last ampliﬁer as the

preampliﬁer, instead of the in-line repeater

that follows the transmission ﬁber. It is

important to reduce the ampliﬁer noise

ﬁgure F when increasing k

max

.Sincethe

(S/N)

value is proportional to the signal

power in the shot noise limit, it is also

important to operate ampliﬁer repeaters

in the high-power region, which is limited

by the saturation output power P

3dB

4.3

Ampliﬁers for Advanced Photonic Networks

Development of optical communications

systems has been started from the point-

to-point links, such as long-haul terrestrial

and submarine systems. The dramatic

growth of the Internet is accelerating to

increase the transmission capacity using

WDM technology as well as to extend

the optical ﬁbers to each subscriber (i.e.,

FTTH: Fiber-To-The-Home). WDM sys-

tem employs a large number of optical

carriers with different wavelengths into a

single transmission ﬁber, where the trans-

mission capacity can be increased by the

number of optical carriers. Most transmis-

sion ﬁbers have low absorption coefﬁcients

(e.g., <0.3 dB km

−1

) at wavelengths of

1450 to 1650 nm. The bandwidth of op-

tical ampliﬁers is now required to be

wide enough to amplify WDM signals

simultaneously. In advanced photonic net-

works, channel and packet destinations

can be routed by switching the chan-

nel/packet wavelength from one to the

other. All-optical signal processing, such

as optically controlled optical gate, will

be required in the node of high-capacity

photonic networks.

4.3.1 Wideband DFAs for WDM Systems

For realizing wideband optical ampliﬁers

so as to support WDM signals simulta-

neously, there are two approaches: one

is to expand the doped ﬁber ampliﬁer

(DFA) gain-bandwidth itself, and the other

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