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Erbium doped fibre amplifier with dynamic
gain flatness for WDM
J. Nilsson, Y.W. Lee and W.H. Choe
The authors have designed and numerically analysed an erbium
doped fibre amplifier for wavelength division multiplexing with a
wavelength-independentgain, irrespective of operating conditions.
Furthermore, under some assumptions, they show that this
property cannot he attained without a gain-flattening filter. A
gain flat to within I % over a bandwidth of 6nm is demonstrated.
Introduction: An undesirable feature of erbium doped fibre amplifiers (EDFAs) for wavelength division multiplexing (WDM) is
that the gain is normally different for different channels (see e.g.
[I, 21 and references therein). This can be characterised by the
locked inversion (LI) gain spectrum, which is measured at a constant population inversion [ 2 ] . Several methods have been used for
obtaining a flat LI gain spectrum [ I , 21, with various degrees of
complexity and applicability. One approach is to modify the composition of the glass used for the EDFA [I - 31. A gain-flattening
filter can also he used [I, 41. A difficulty arises in that if the population inversion of an EDFA changes, the gain at different wavelengths will change by different amounts [I, 2 , 51. Therefore, the
gain flatness of an EDFA depends on the operating gain, which
consequently has to he considered in the EDFA design. However,
the gain depends on, for example, the signal and pump powers,
both of which may vary. Furthermore, for cascades with many
EDFAs, the average gain approximately equals the average loss
between amplifiers [6], which a150 may be unknown and even
time-varying. Clearly. it can be difficult or even impossible to
know for what gain level a gain-flattened EDFA should be
In this Letter, we numerically explore the spectral characteristics
of a newly designed type of EDFA that exhibits a flat LI gain
spectrum irrespective of the operating gain (dynamic gain flatness,
DGF). The EDFA is based on an E D F (erbium doped fibre)
where the shape of the LI gain spectrum does not change with the
population inversion over a wavelength region. A low AP+-content
ErZ+:Al3’:Ge4’:SiO, fibre can be used for this purpose. The resulting constant-shape gain is then flattened by a passive filter. We
believe that this type of EDFA can be useful in WDM networks.
It will also eliminate AC gain tilt and tilt variations in EDFAs for
analogue AM CATV [7]. Another possible application is for tunable fibre lasers. We also argue that under certain assumptions,
D G F cannot be achieved unless a filter is used.
EDFA design: For a homogeneously broadened gain medium, the
EDFA gain G (in dB) can be written as
G ( ~ L z ,=
X )[ y * ( X ) n a -.(X)(1
- na)]L- f(X)
where h is the wavelength, L is the fibre length, a(h)is the absorption spectrum in decibels per metre, g’(h) is the gain, in decibels
per metre, at complete inversion [2, 31,flh) is the attenuation of an
optional filter in decibels, and n2 is the degree of excitation, i.e. the
ratio of ErJ+ ions in the excited (metastable) state to the total
number of ErZ+ions. n, is directly related to the population inversion. Since we assume that the erbium is confined to the central
regions of the core, n, is wavelength-independent [SI. Only the
ground and metastable states of Er” are assumed populated.
According to eqn. 1, the LI gain spectrum changes with n, as
If the quantity [g’(h)+a(A)]
= g, ,(A) is equal for two wavelengths,
the gain (in dB) at these wavelengths will change by equal
amounts as n2 changes. The product Lgp,(h) also equals the gain
difference between a completely inverted and an unpumped
EDFA; i.e. the gain swing. Central to this Letter is that for the
must be constant over an
design of a DGF EDFA, g&)
extended wavelength range. We found that this can be achieved in
an ErZ+:Al’+:Ge4*:Si0,glass fibre with -1% AI,O, by weight, for
wavelengths around 1.55p.m [I, 31. However, the gain will not be
flat without a filter. A Mach-Zehnder filter with maximum attenu-
ation at 1570nm. a free spectral range of 34nm, zero insertion
loss, and a peak attenuation of 0.373dB per metre of E D F was
used to flatten the gain. The resulting D G F EDFA is further studied below.
First, however, we show that D G F is impossible in an EDFA
without a filter, under the assumption that the following expression by McCumber [8] is valid:
g’(X) = a(X)exp[(hc/X,- h c / X ) / k T ]
In eqn. 3, h is Planck’s constant, c is the speed of light, k is Boltzmann’s constant, T i s the temperature, and h, is a crossover wavelength, where the sires of the gain at complete inversion and
absorption are equal. Ifg‘(h) is constant over a wavelength region,
it follows from eqn. 3 that a@), and hence g,,,,(h). must vary.
Therefore, if eqn. 3 holds, g,,(A) can he constant over a finite
wavelength interval only if g‘(h), and thus the gain for n, = 1,
varies in the same interval. In other words, if eqn. 3 is valid, it is
impossible to have a gain that is flat and stays flat as the degree of
excitation changes, if the only wavelength-dependent gain and loss
stem from the lasing transition of Er?’, and the gain is bomogeneously broadened. A filter is then needed to attain a flat gain for all
n,. If g,,,,(h) is not constant, the filter attenuation flh) has to
change with nl. This in turn requires that flh) is tunable, and that
light powers in the EDFA are monitored. On the other hand, if
g,>,(A) is constant, the sameflh) results in a flat gain for all n2,and
/(A) need not be tunable, nor does any light power need to be
monitored (independent of whether eqn. 3 is valid or not). This is
the approach adopted in this Letter. Note, however, that a coilstant shape gain spectrum can he beneficial even without a flattening filter, since it will be easier to implement pre-emphasis for a
WDM system or pre-distortion for optical AM TV signals [I].
wavelength, nm
Fig. 1 Spectra for. unalysed
EDFAs Spectra for reference EDFA (left axis):
(i) g (A)
(iii) ~ * ( h )
Spectra for DGF EDFA (right axis):
(iv) s,,(h)
(v) a(h,
(vi) g . 6 )
(vii) Attenuation Ah) of Mach-Zehnder filter for DGF EDFA (per
metre of EDF)
Results and discussion: Returning to our proposed D G F EDFA,
its spectra a@),g’(A) and g,) J h ) , and the filter attenuation.f(h) are
shown in Fig. 1. For comparisons to an EDFA of the type normally considered for a flat gain spectrum, we used a thoroughly
investigated, high AI’+ content Er”:Al’+:Ge“:SiO, glass EDFA as
a reference [7]. Its spectra are also drawn in Fig. 1. This reference
EDFA exhibited a relatively flat gain over a wide wavelength
range of 1540 1565nm even without a filter. However, g&)
not constant in the same region. On the other hand, for the D G F
EDFA, g’(h) is not flat, hut from 1545 to 1552nm, g,,(h) is
almost constant. For both fibres, a(A) were measured and g’(h)
were found from eqn. 3.
The gain flatness for different n? is shown in Fig. 2. The gain
was calculated using eqn. 1. The curves show the relative deviations of the gain (in dB) from a reference level corresponding to
the maximum gain in the long wavelength end of the gain spectra;
i.e. outside the gain peak around 1535nm. I n a real EDFA, the
peak around 1535nm may need to be filtered out to prevent saturation by ASE and gain peaking at 1535nm in a cascade. The following can be seen from Fig. 2: The reference EDFA exhibits a
flat gain (to within 3%) over a wide bandwidth for all three different values of n2 used. At n, = 0.8, the wavelength range is from
31stAugust 7995
Vol. 37
No. I8
wavelength, nm
Fig. 2 Relutive Ruin deviation uguinst nuvelengrh,for d $ j k m t degrea o/
ODA. K., FUKUTOKU. M., F U K U I . M . , KITOH.T., and TOBA.H.: ‘10channel x IO-Gbitk optical FDM transmission over a 500-km
dispersion-shifted fiber employing unequal channel spacing and
amplifier-gain equalisation’. Optical Fiber Communications Conf.,
1995, Vol. 8. 1995 OSA Technical Digest Series, (Optical Society of
America, Washington, DC. 1995),pp. 27-29
GILES. c R . and DESURVIRE. E.: ‘Modeling erbium-doped fiber
amplifiers’. J. Lighrivave Techno/., 1991, LT-9, pp. 271-283
IIESTHIEUX. B M., SUYAMA. M and CHIKAMA, T.: ‘Theoretical and
experimental study of self-filtering effect in concatenated erbiumdoped fiber amplifiers’, J. Lightivave Techno/., 1994, LT-12, pp.
N I L S S 0 N . J . K 1 M . S . L L E E S H , and CHOE. W.H.: ‘AC gain tilt
variations with gain compression in erbium doped fiber amplifiers’.
Topical Meeting on Optical Amplifiers and Their Applications,
Davos. Switzerland, 1995
MCCUMBER, D.E.: ‘Theory of phonon-terminated optical masers’,
Phys Rev. A , 1964, 134, pp. 299-306
The maximum gains for h > I , 5 4 0and
~ for h > 1.545 pm were used
as reference values for the reference and DGF BDFA, respectively
DGF EDFA for n2 = 0.6, 0.8, and 1.0; curves are almost coincident
Reference EDFA for:
- - ~
n, = I
n2 = 0.8
n? = 0.6
1538 to 1554nm. Thus, for an EDFA with a 30dB gain, a flatness
of *0.4SdB can be obtained in this range. For a cascade of
EDFAs with a total gain of IOOdB (333dB) and with n? = 0.8
(averaged over all EDFAs), the same wavelength range represents
the 3dB (1OdB) bandwidth. However, the wavelength range
changes with n2; at n2 = 0.6, it is 1552 1563nm. The overlap with
the wavelength range at n2 = 0.8 is only 1 - 2nm. The overlap
increases for less stringent flatness criteria. For the D G F EDFA,
the curves for different nl are close to each other, and the bandwidth is smaller. However, the range of flat gain wavelengths that
overlap is relatively large, e.g. l0nm at 10% flatness and 7nm at
3% flatness, even as n, changes from 1 to 0.6. This corresponds to
gain compression of -75%. There is even a region of 6nm where
the gain is flat to within 1%. However, neither the accuracy of the
original measurements nor the assumption of eqn. 3 allows for the
gain to be calculated to within 1 %.
Even though impressive system experiments in a narrow bandwidth have been reported [4], the narrow bandwidth of the D G F
EDFA is a limitation. Other host materials may provide a constant g , ,(h) over a larger bandwidth. Furthermore, the spectral
shapes can also be modified by changing the geometries of the
refractive index and the Er3+-dopingof the EDF.
Conclusions: We have designed and analysed a new type of EDFA
that exhibits a flat gain irrespective of the operating conditions.
and shown that if the McCumber relation [SI holds and the
medium is homogeneously broadened, this is impossible without a
filter. The bandwidth of the flat gain is small, but can perhaps be
larger in other host materials.
Acknowledgments: The E D F used for the D G F EDFA was made
by V.F. Khopin, Institute of Chemistry of High Purity Substances,
Nizhni Novgorod, and its absorption spectrum was provided by
A.V. Belov, General Physics Institute, Moscow.
0 IEE 1995
30 June 1995
Electronics Lerrers Online No. 19951059
J. Nilsson, Y.W. Lee and W.H. Choe (Opro-Devlce Laboratories.
Samsung Advanced Institute of Technology, P O Box 111, Suwon 440600, Koreu)
DESURVIR€. E.: ‘Erbium-doped fiber amplifiers’ (Wiley, New York,
Chichester. Brisbane, Toronto, Singapore. 1994)
2 CLESCA. B., BAYART, D., and BEYLAT, J.L.: ‘l.5-)ml fluoride-based
fiber amplifiers for wideband multichannel transport networks’,
Opt. Fiber Techno/., 1995. 1, pp, 135-157
3 WYATT. R.: Spectroscopy Of rare-earth doped fibres’ in FRANCE, P.W
(Ed.): ’Optical fibre lasers and amplifiers’ (CRC Press, Glasgow
and London; Bldckie and Boca Raton, 1991)
Vol. 31
Mechanism for high singlemode stability of
gain-coupled DFB lasers with periodically
etched quantum wells
T. Makino
Indexing termx Dirtributrrd ferrdhuck /users, Luser mudes.
Semiconductor Quantum wells
The sidemode suppression ratio of gain-coupled DFB lasers with
periodically etched quantum wells is analysed by a more accurate
model for amplified spontaneous emission. It is shown that the
periodic etching of quantum wells is very effective for providing a
high side-mode suppression. The mechanism for the high
singlemode stability is explained by the effective modal gain,
which has an enhancement at the longer wavelength side of the
Bragg stopband.
Introduction: Recently, we have developed partly gain-coupled
DFB lasers with periodically etched MQWs [I, 21. The lasers have
exhibited a high singlemode yield with an oscillation at the long
wavelength side of the Bragg stopband [I, 21 owing to gain coupling effects. The wide-temperature-range singlemode operation
has also been achieved by lasers with high sidemode suppression
[2, 31. Since this type of gain-coupled DFB laser structure consists
of two grating sections with larger and smaller numbers of QWs,
which produce two different modal gains, the conventional threshold gain difference may not be a relevant measure for singlemode
selectivity. Therefore, the sidemode suppression ratio (SMSR)
needs to be analysed in a more accurate manner. In this Letter, we
present an analysis of the SMSR of the gain coupled DFB lasers
by an amplified spontaneous emission model based on the localnormal-mode transfer-matrix method. The physical mechanism for
the strong side-mode suppression is explained by the effective
modal gain of the gain-coupled DFB laser structure.
Anulysis: It has been shown that the average amplified spontaneous emission power pISp(w)Awfrom the facet within angular frequency Aw is given by [4]
p a s p ( w ) A w = h w r ~ , ~ l Ai2Anw/(2rr,)
where fi is Planck’s constant divided by 2rr, n,# is the spontaneous
emission factor, q is a quantity which at threshold becomes the
differential quantum efficiency of the other facet, and A , is the
transmission coefficient of the whole structure. We denote the
complex effective indices of the grating sections with the larger
number of QWs and the smaller number of QWs by N H and Nr,
respectively. Then, we can express N H and N L as N , = n, + jm, ( i =
H , L), where n, and m , are the real and the imaginary parts, of N,
respectively. The imaginary part m , can be expressed as m , = r,g/
2k, where Ti is the optical confinement factor for section i (i = H ,
L), g is the material gain and k is the wavenumber. The transfer
matrix T,,, for one grating period can be obtained in terms of N H
and N L [5]. The transmission coefficient A , can be expressed in
terms of the elements of the matrix T,, [5].
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