What is Edfa

8/13/2019 What is Edfa

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Introduction to the EDFA

A general introduction to the EDFA is presented in this chapter. It starts with an

overview of the implementation of this component in optical communications

networks, then a brief description of the amplifier operation and how to model the

spectral characteristics. Important amplifier parameters such as the optical noise

figure, amplifier bandwidth, and methods to achieve equalisation of the EDFA gain

spectrum are introduced.


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2 Introduction to the EDFA 10

new dopants and glasses to provide amplification at different wavelength bands (see

section 2.4) or by using Raman amplifiers.

EDFAs have been used successfully in WDM transmission systems as all-

optical lumped amplifiers at which the gain is boosted at a point of the transmission

line. On the other hand, the fibre amplifiers based on Raman effect also have

attracted huge research attention nowadays due to its tunability of amplification

band by simply changing pump wavelength, since ever-increasing demand of optical

data transmission capacity expansion in telecommunications has generated

enormous interest in optical communication bands (S-, L-band) [7, 8] outside of a

conventional EDFA gain bandwidth (C-band). The principle of the Raman amplifieris based on the stimulated emission process associated with Raman scattering in

fibre for the amplification of signals. The inelastic non-linear effects can be regarded

as scattering of a pump beam off phonon (molecular vibrational state) and the

transfer of energy into a lower energy beam. The Stokes shift corresponds to the

Eigen-energy of an optical phonon, which is approximately 13.2 THz for optical

fibres. In Raman amplifiers, signal wavelength is longer than pump wavelength by

the equivalent amount of the frequency shift. By using multiple pumps across the

target gain window, over 100nm band Raman amplifiers can be achieved [9]. The

major drawbacks of this technology are the requirement of high pump power or long

length of fibre and the related Rayleigh scattering issue. However, availability of

cheap and high power pump lasers, and highly non-linear fibres enables fibre Raman

amplifiers to be a promising technology for the increase of transmission capacity of

current and future WDM networks.

2.2 Theory

2.2.1 Energy levels

The EDFA absorption and emission cross sections are the signature of the energy

levels of the Er3+

ion in the glass host. When the erbium ion is introduced into a host


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medium the energy levels are modified by local electric fields through Stark-

splitting. These levels are in thermal equilibrium due to rapid nonradiative

transitions between these levels. The amplifier is assumed to have homogeneous

broadening but if the local electric field is different at various sites along or across

the fibre due to impurities, clustering effects, or other glass structural disorders, then

inhomogeneous broadening occurs resulting in different electronic transitions at

respective sites. The incorporation of a network modifier such as Aluminium (Al) to

enhance the solubility of the Er3+

ions in the glass structure changes each energy

levels Stark-splitting and increases the inhomogeneity of the medium. The energy

transitions typically associated with Er

3+

in a silicate glass are the

4

I11/2,

4

I13/2, and4I15/2states, and are illustrated in Figure 2.2.

Figure 2.2 a) Energy level diagram for Er3+

ions showing the dominant transitions. b)

Stark-splitting of the energy levels due to the crystal or glass electric field.

W12, W21are the rates for the stimulated transitions while A32and A21are the rates

for the spontaneous emission. A32is assumed to be essentially nonradiative and A21

essentially radiative [10]. The subscripts 1, 2 and 3 correspond respectively to the

energy levels4I15/2,

4I13/2, and

4I11/2.


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Generally the EDFA is pumped with 980nm radiation, exciting electrons from

the ground state4I15/2 to level

4I11/2 or at 1480nm by exciting electrons from the

ground state to a high-energy Stark-split sublevel of the4

I13/2manifold. Rigorously

this implies, when pumping the EDFA using a wavelength of 980nm, that the

amplifier corresponds to a three-level system while when using a 1480nm pump the

amplifier is a quasi three-level system (as pumping is to a higher-energy Stark-split

state within the I13/2manifold). However, both pumping schemes can be described

effectively in terms of the populations of two levels. This approximation is justified

in the 980nm pumping case due to the nonradiative decay rate A32being much larger

than the stimulated emission rate from 3 to 1, and therefore the population of level 3(4I11/2) can be neglected. In the case of 1480nm pumping the two-level system is

justified due to the rapid thermalisation decay that transfers the higher-energy

electrons of the4I13/2manifold to lower-energy Stark sublevels. The rate equations

for the populations of a two-level system are written as:

2212211122

nAnWnWdt

dN= (2.1a)

21 nnnt += (2.1b)

where ntis the Er3+

ion density and n1and n2the fractional density of the lower and

upper excited levels respectively. These equations hold even for the more complex

system where the manifolds are split into Stark sublevels. In this situation the

transition rates correspond to the sum over all the possible j-k (j,k=1,2) transitions

multiplied by the population weight of the transition, given by the Boltzman

distribution [10]. In practice however the exact energy levels corresponding to the

individual Stark levels are dependent upon the ion distribution and host material.

Thus the population and decay rates for the energy levels of interest, typically have

to be determined experimentally through absorption and emission cross section

measurements.


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2.2.2 Numerical modelling of spectral properties

The wavelength dependent properties of EDFAs can be modelled following the

method proposed by [11] in which the spatial characteristics of the amplifier are

integrated. This model involved dividing the EDFA spectrum into discrete optical

channels of frequency bandwidth, k, centred at the optical wavelength k.

Assuming homogeneous broadening and a uniform distribution of the Er3+

ions

across the fibre core, the amplifier can be characterised by introducing four

measurable fibre parameters: The absorption spectrum, k, the gain spectrum g*k, the

fibre saturation power, PkSat

, and the fibre background loss, lk, that are given by:

tkekk ng =*

(2.2a)

tkakk n= (2.2b)

**)(

kk

k

kk

teffkSat

kg

h

g

nAhP

+=

+=

(2.2c)

Where; ak and ek are respectively the wavelength dependent absorption and

emission cross sections, ntis the total concentration of the erbium ions, =Aeffnt/is

the ratio of the linear density of erbium ions to the fluorescence lifetime, Aeff=b2

eff

is the effective area of the doped region, is the metastable level 2 lifetime, and k

is the overlap integral between the dopant and optical mode distributions that in the

case of uniform doping of the erbium ions (beff=b) is given by:

=

2

0 0

),(

b

kk rdrdrI (2.3)

Where b is the radius of the Er3+

-doped region. If this assumption is unrealistic then

modification of the integral is required to include the Er3+

ion distribution. The


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above overlap integral depends in general on the wavelength channel, k, for which it

is calculated. Under steady-state operation, assuming a uniform distribution for the

excited lower state and upper state populations (n1and n2respectively), the excited

upper state population density for the EDFA is given by [11]:

+

+=

kSat

k

k

kSat

k

k

kk

k

t

P

zP

P

zP

g

n

n

)(1

)(*

2

(2.4a)

21 nnnt += (2.4b)

The equations that describe the propagation of the beams of wavelength kand the

pump through the fibre are [10]:

( ) ( )

+++= )()( 2*2* zPlmh

n

ngzP

n

ngu

dz

dPkkkkk

t

kk

t

kkkk

(2.5a)

( ) ( )

++= )()(2* zPlzP

n

ngu

dz

dPpumppumppumppump

t

pumppumpk

pump (2.5b)

Pk(z) is the signal power at frequency k at a certain position along the amplifier

length; uk represents the direction of the travelling beam uk=1 for a forward

propagating beam and uk=-1 for backward propagation; the term mhkk is the

contribution of the spontaneous emission from the local excited state population n2,

with m=2 corresponding to the number of polarisation modes supported by the fibre,

and h the Plank constant; lk is a wavelength dependent background loss. Thus the

two-level amplifier system can be fully characterised using equations (2.5a) and

(2.5b) that describe the propagation of the signal, ASE and pump along the erbium-

doped fibre and equation (2.4.a) describing the population inversion and saturation

characteristics along the amplifier. When using a pump wavelength of 980nm, the


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gain coefficient is null 0g*

980 = and equation (2.5b) describing the pump evolution

along the EDF can be simplified.

Details of the model used herein for numerical simulations of the EDFA

performance are described in Chapter 7. Briefly though it was implemented by

dividing the full EDFA bandwidth (from 1420nm to 1620nm) into equal segments.

The wavelength dependence of () and g*() were obtained by digitising

absorption and gain parameters measured for an actual EDF as illustrated in Figure

2.3. Using the measured value for the fibre background loss lbgand the ratio of ion

density to the fluorescence lifetime , the rate and propagation equations were

solved until the specified convergence parameters were reached.

0

1

2

3

4

5

6

7

1420 1470 1520 1570 1620

Wavelength (nm)

Abs

orption/Gain(dB/m)

g*()

()

Figure 2.3 Measured absorption and gain parameters for the fibre used in the numerical

simulations.

2.3 Noise figure

The analysis of noise in optical systems is sufficiently complex that it can be

characterised either with simple engineering formulae or by a thorough quantum

theoretical approach. It is not the aim of this section to provide a deep introduction

to noise in optical systems, but rather to give the basic definitions, which quantify

the optical noise generation in the EDFA. These definitions will be used in chapter 6


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to discuss the effect on the EDFA performance, in terms of a noise figure, when the

concept of gain equalising filters is introduced. The optical noise figure is a

parameter used for quantifying the noise penalty added to a signal due to the

insertion of an optical amplifier. That is, before light enters an amplifier the signal to

noise ratio is SNR(0), after amplification it is SNR(z). Thus, optical noise figure can

be defined as:

)(

)0(

zSNR

SNRNF

Opt = (2.6)

If the noise figure of the amplifier were 1, then the initial signal to noise ratio would

be maintained throughout amplification. However it has been shown that the

quantum limit for an optical amplifier [10] is 3dB, therefore the signal to noise ratio

after amplification is half (50%) of the original value. For real optical amplifiers the

noise figure can be as high as 6dB whereby the signal quality is sufficiently

deteriorated that the detectors ability to discriminate signal from noise is

compromised.

The signal to noise ratio can be described as the ratio between the average

signal intensity and the standard deviation of intensity fluctuations from that

average. The definition follows in terms of the average number of photons

and the variance 2=-

2:

)(

)(2

2

z

znSNR

= (2.7)

where z is the position along the amplifier or fibre link. It has also been shown, [10]

that the noise figure of an optical amplifier can be described as:

)(

1

)(

1)(2

zGzG

zGnNF

kk

kspOpt

+

= (2.8)


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where Gk(z) is the amplifier gain at a given position, z, at a wavelength kand where

nspis the spontaneous emission factor that takes the form:

12

2

NN

Nn

ek

aksp

= (2.9)

Here, N1 and N2 are the populations of the ground and excited energy levels

respectively. For a total population inversion N1=0, nsp=1 and therefore the noise

figure is close to 2, which is the quantum limit for the amplifier noise. The

spontaneous emission factor is related to the total power of the amplified

spontaneous emission PASEwithin the bandwidth, k, by the following expression

[10]:

( ) kk

ASEsp

hG

Pn

=

12 (2.10)

2.4 Larger bandwidth

The usable 35nm bandwidth of the EDFA operating in the Conventional band (C-

Band) enabled fibre communications using WDM and DWDM. However growing

demand for increased bandwidth and subsequent research have given rise to fibre

amplification at shorter and longer wavelength bands. The L-band EDFA, where the

EDFA gain is shifted to the longer wavelengths (1560nm-1580nm) [12], in

conjunction with the recently demonstrated Thulium-doped fibre amplifier operating

at the S-band (short wavelengths) around 1490nm [13], provide the basis for future

transmission capacity of 10Tbits/s channels multiplexed across the three amplifier

bands [2]. Figure 2.4 illustrates the three amplification bandwidths covered by the

three types of amplifiers.


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1.46 1.48 1.5 1.52 1.54 1.56 1.58 1.6 1.62

Wavelength (m)

L-Band

S-Band

C-Band

Figure 2.4 Wavelength bandwidth covered by the amplifiers.

2.5 Gain equalisation

Equalisation of an amplifiers gain spectrum is essential for balancing the channel

powers in order to achieve error free detection of the signals transmitted through the

optical fibre link. Several methods for achieving EDFA equalisation, either intrinsic

or extrinsic, have been proposed in the literature. Intrinsic methods constitute

changing the spectroscopic properties of the erbium-doped glass absorption and

emission cross sections by co-doping with other ions, different glass matrices or

special fibre designs. Fluoride-based glasses [14, 15] are known to improve the

flatness of the EDFA gain spectrum. Extrinsic methods are based on filtering

devices that are designed with a wavelength dependent loss spectrum. Several filters

have been demonstrated in the literature [16-26]. These can be divided in active

devices that are re-configurable, which may accommodate changes in the amplifier

gain spectrum due to saturation effects, and passive devices that cannot be tuned.

Active devices reported include; acousto-optic tunable filters [16-19], strain-tuned

fibre Bragg gratings [27], micro mechanical filters [24], and a planar integrated

optical filter [25]. Some passive devices include long period gratings [21, 23], Bragg

gratings [22], and filters using Samarium doped fibres [20]. All these devices have


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characteristic equalisation properties and insertion losses that can be as low as the

splicing loss between the EDF fibre and the filter fibre or as high 8-9dB as reported

in [24, 25].

In chapter 6 an acousto-optic tunable filter based on the profile of a multi-

tapered optical fibre and its spectral transmission properties [18, 19], is discussed.

The amplified spontaneous emission spectrum of an EDFA was equalised for

different saturation levels in order to demonstrate the potential of the device. The

tunable parameters of the device were, the acoustic wave frequency and the filter

loss shape, which was dependent upon the tapered fibre profile. Although this filter

lacks the flexibility of reshaping the spectral profile, it is very easy to tunedepending only on 2 to 4 parameters as opposed to the 12 tuning parameters of other

designs [17].

Figure 2.5 Basic EDFA gain flattening configurations. Top: Filter placed outside the

amplifier. Bottom: Filter placed within the amplifier.

Determination of the ideal filter shape in order to equalise the EDFA is not a

trivial task. The loss spectrum of filters placed outside the EDFA (configuration 1 in

Figure 2.5) can be obtained by inverting the amplifier output gain across the desired

bandwidth. Although the loss due to the insertion of the filter, dependent upon the


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type of filter and the fabrication procedure, can be up to 8-9dB [24, 25], and

therefore another amplification stage is usually required after the filter. If however,

the filter is placed at a certain position inside the EDFA (configuration 2 in Figure

2.5), the penalty in amplifier loss can be reduced but the exact filter shape and

placement is not known. Liaw [20] used the loss spectrum of a samarium-doped

fibre and found the best position at which it should be placed in a given amplifier by

splicing it at different positions along the amplifier. Acoustooptic tunable filters [26]

have also been used in this configuration and optimised by tuning the filter shape

until the desired performance is reached. This is an iterative process and quite time

consuming, as the filters may not be placed in the optimum position along theamplifier. A solution to these problems is proposed in chapter 7, where the

theoretical design of ideal filters that in addition to gain flattening also compensate

for insertion losses, and their position within an amplifier for equalising the EDFA

gain spectrum is discussed. Performance of the above filter configurations is

compared.

2.6 Summary

A brief introduction to the EDFA, one of the most important components in WDM

communications, was given in this Chapter. Starting with fundamental principles of

amplifier operation, a well-known model based on a two-level amplifier system

including the spectral characteristics of the EDFA, was presented. Important issues

relating to the amplifier performance, namely the optical noise figure and amplified

bandwidth were introduced. Finally, the chapter concluded with a review of existing

technologies utilised for equalising the EDFA gain spectrum. The concepts

introduced in this chapter are fundamental to section II where the equalisation of the

EDFA gain spectrum is addressed in more detail.

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