Research Journal of Applied Sciences, Engineering and Technology 2(4): 381-386, 2010
ISSN: 2040-7467
© M axwell Scientific Organization, 2010
Submitted Date: April 21, 2010
Accepted Date: May 05, 2010
Published Date: July 05, 2010
Study the Effect of Temperature on the Optimum Length of Er3+ Doped
Almino-germanosilicate, Aluminum-Oxide and Yattria-Silicate Glass
Osama M ahran
Faculty of Science, University of Alexandria, Alexandria, Egypt
Abstract: In this study the effect of temperature on the optimum fiber length for maximum gain of Erbium
doped almino-germanosilicate, aluminum oxide and yattria-silicate glass, with fixed pump power. The optimum
length depe nds strongly on the temperature and increases as the temperature increases. The maximum gain also
depends on the wavelen gth an d power of the sig nal which v alidate our findings throug h distribu ted gain
measurements and so optimum length too.
Key word: EDFA , optical amplifiers, optimum length, temperature effect
Arellano, 2003) that these equ ations, dedu ced in principle
for single-c hannel am plifiers, could be easily extended to
the case of EDFAs operating under W avelength Division
Mu ltiplexing (WD M) cond itions.
In this article, we study the effect of temperature on
the optimum fiber length for maximum gain of Erbium
doped almino-germanosilicate, aluminum-oxide and
yattria-silicate glass, with fixed pum p pow er.
INTRODUCTION
In order to increase the transmission capacity of
W avelength Division Multiplexing (WD M) systems,
optical amplification outside the conventional band
(C-band, 1540-1560 nm) and L-band (1560-1610 nm) is
required and the various parameters which affected the
gain such op timum length of the fiber and the temperature
must be studied. The short wavelength band (S-band,
1480-1520 nm) is particularly attractive, being
characterized by low loss in silica optical fiber. Many
techniques have been deve loped to realize S-band
amplification such as thulium-doped fluoride fiber
amplifier (TDFFA) and a fiber Raman amplifier
(Gerlas et al., 1997; Ch eng and Min, 2005).
W hile these amplifiers have enabled impressive gain,
noise figure and sy stem perform ance , they have not
matched conven tional Erbium-Doped Fiber A mplifiers
(EDFA s) in terms of efficiency , simplicity, reliability
and cost.
To calculate the maximum gain at different values of
temperature the approximate McCumber (1964)
procedure is often used to predict the emission crosssection spectrum of the 1.5 :m transition of Er-doped
glass fibers from the transition's measured absorption
spectrum at different values of
temperature
(Osam a, 2007).
A transcendental equation for the Maximu m G ain
(G max ) at Optimu m Length (L o p t) of single-channel Erbium
Doped Fiber A mplifiers (ED FA s) with fixed pump power
was arrived by R uhl (1992) and, independently, Lin and
Chi (1992). Desurvire (1994) also arrived to the same
equations in his first book (Desurvire, 1994). The
equivalent equations for Gmax and Lopt are Eqs. (10) and
(11) in (Ru hl, 199 2), (7) an d (10) in (Lin and C hi, 1992),
and (1.139) and (1.157) in (D esurvire, 1994 ),
respectively. Importantly, it was shown in (Rieznik and
MATERIALS AND METHODS
This theoretical work was done in 2008 at Faculty of
Scien ce, U niversity of A lexan dria, A lexan dria, Eg ypt.
M odel:
Calculation of maximum gain: The McCum ber (1964)
relation states that the absorption cross section F a (<) and
the emission cross section F e (<) spectra between a ground
state (manifold of eight sublevels of energy E1 j) and the
excited state (is a manifold of seven sublevels of energy
E 2 j) are related by (Gigonnet et al., 2002):
(1)
where; k is the B oltzmann constant, T the absolute
temperature, and < the optical frequency. The parameter
, (Gigonnet et al., 2002) is defined as:
(2)
381
Res. J. Appl. Sci. Eng. Technol., 2(3): 381-386, 2010
Table 1: Parameters for Mc-cumber cross section calculations
Fiber Core glass
R
)E 1 =7E 1
)E 2 =6E 2
(cmG 1 )
(cmG 1 )
1
Ge -Sio 2
1.35
361
450
2
NA
1.54
264
459
3
Ge /P-S io 2
1.27
304
374
4
Al/P -Sio 2
1.27
393
295
5
Fluorophosphates
0.99
415
325
6
Al-S io 3
1.08
231
467
7
Al-S io 2
1.65
554
458
8
Al-P -Sio 2
1.09
432
413
whe re E o = E 2 1 – E 1 1 is the energy difference between
the lowest energy levels of the two manifolds
(McCum ber, 1964) and Table 1.
If 0 p and 0 k are the ratio of the emission to the
absorption cross section for the pump and the signal,
respectively,
where;
(3)
Table 2: Th e optical parameters of Er-dope d fiberglass
Physical meaning
Symbol
Value
pum p w ave leng th
8p
980 nm
pum p inpu t pow er
P in
1 8 .4 d B m
sign al w ave leng th
8k
1550 nm
length of EDFA
L
27 m
core radius of EDFA
r
1.277 :m
core area of EDFA
A
5.1×10 - 1 2 m 2
overlap factor of EDFA
'
0.5
fluorescence time of EDFA
J
10.5 ms
ion density of EDFA
D
1.01×10 2 5 ions/m3
W e can neglect ESA also because it is absent for a
pump at 980 nm. For simplicity, we assum e that the gain
spectrum is homogeneously broadened. W ithin these
limits, the most fundamental limitation is due to the
energy conservation,
(4)
W here
and
integrations of the SCD m odel), but also that these fiber
parame ters are combin ed into just two easily-m easurable
constants per wavelength: the absorption constant " k and
the saturation power, at wavelength 8 k . To stress this fact,
we write the equations for G max and L o p t in terms of these
two spectral constants (Rieznik et al., 2006):
is the input power for the pump
and signal respectively, and 8 p , 8 k the pump and signal
wavelen gth.
In actual amplifiers, the absorption of pump photons
(and therefore gain) is lim ited by the finite numb er of rare
earth ions existing in the medium, the maximum signal
gain corresponding to a three-level laser medium of length
L is given by:
(7)
and
(8)
(5)
W here
,
In addition if we co nsider how many active ions are
available in the medium for certain pump, we have the
following expression:
(9)
with
(6)
and
" k ," p are the ab sorption and pum p coe fficients
respectively,
W here " k is the absorption coefficient for the signal, (for
pump at 980 nm 0 p = 0) (Yahya et al., 2004 ).
input signal pow er,
is input pump power and
is the
is the saturation power of the
pump and signal, respectively.
Calculation of optim um length at maximum gain: The
expression for G max derived from the TPE model is a
transcendental equation, while L o p t is explicitly given in
terms of the fibers intrinsic parameter and G max . W e stress
that the advantages in using the TP E model is not just to
have a simple transcendental equation for the gain as a
function of the input powe rs and fiber param eters
(avoiding the tedious and time-consuming numerical
RESULTS
The parameters used in calculations Mc-cumber cross
section is given in Tab le 1 (Gigonnet et al., 2002) and the
parame ters used in calculations the maximum gain and
optimum amplifier length also given in Table 2 and 3
(Osama et al., 2009).
382
Res. J. Appl. Sci. Eng. Technol., 2(3): 381-386, 2010
Maximum gain
Tab le 3: T he p aram eters u sed in this calcu lation of o ptim um leng th
Parameter
Value
0.2 mG 1
"s
"p
0.1 mG 1
0.02 mW
0.01 mW
64 mW
20 mW
McCumber emission cross section
Fig. 3: The maximum gain for erbium doped alumino-germanosilicate glass fiber amplifier, calculated for different
values of maximum wavelength at room temperature
The norm alized expe rimen tal values of the absorption
cross section and the McCumber (1964) theory
calculation for the erbium doped alumino-germanosilicate
glass fiber amplifier at temperature range 290-310ºK is
represented in Fig. 1. This figure shows that as the
temperature slightly increases the emission cross section
increases but the wavelength at max imum gain not shifted
with temperature changes. So that the window at which
the signal is amplified not affect by slightly temperature
changes.
The maximum gain values in dB for the erbium
doped alumino-germanosilicate glass fiber amplifier are
plotted against wavelength range from 1530 to 1560 nm
at input power 64 mw at temperature ran ge 290-310 ºK as
shown in Fig. 2. Also the gain is plotted with length at
different values of wavelength in Fig. 3, where the
relation is found to be linear between the gain and the
length. The Optim um length for the erbium doped
alum ino-germa nosilica te glass fiber amplifier is
calculated for fixed pu mp p ower and the maximum g ain
of the amplifier studied before. Since the max imum gain
studied at differen t values of tempera ture, also the
optimum length is studied at different values of
temperature in Fig. 4.
Fig. 5 and 9 represents the normalized values of the
emission cross section of Er-doped Al2 O 3 fiber amplifier
and yttria-Alu mina -Silicate Erbium Doped Fiber
Amplifier as calculated using McC umber (1964) theory at
different temperatures, from 290 to 310ºK respectively. It
is clear that, the emission cross-section increases w ith
temperature. The m aximum gain values in dB for the E rdoped Al2 O 3 fiber am plifier and yttria-A lumina-Silicate
Fig. 1: Emission spectrum with the experimental absorption
cross section for erbium doped alumino-germanosilicate
glass fiber a mplifier, calculated for different values of
temperature
Maximum gain
Fig. 2: The maximum gain spectrum for erbium doped
alumino-germano-silicate glass fiber amplifier,
calculated for different values of temperatures
383
Res. J. Appl. Sci. Eng. Technol., 2(3): 381-386, 2010
Maximum gain
Optimum length
Fig. 6: The maximum gain spectrum for erbium doped Al2O3
glass fiber amplifier, calculated for different values of
temperatures
Fig. 4: The Optimum length variation for erbium doped
alumino-germano-silicate glass fiber amplifier,
calculated for different values of temperature at
maximum gain of the amplifier
Gain
McCumber emission cross section
Fig. 7: The maximum gain erbium doped Al2O3 glass fiber
amplifier, calculated for different values of maximum
wavelength at room temperature
Fig. 5: The normalized values of the emission cross section of
Er-doped Al2O3 fiber Amplifier as calculated using Mc
Cumber theory at different temperatures
at different values of wavelength in Fig. 7 and 11, where
the relation is found to be linear between the gain and the
length. The Optimum length for the Er-doped Al2 O 3 fiber
amplifier and yttria-Alumina-Silicate Erbium Doped Fiber
Amplifier is calculated for fixed pump power and the
maximum gain of the amplifier studied before. Since the
maximum gain studied at different values of temperature,
also the optimum length is studied at different values of
temperature in Fig. 8 and 12, respectively.
Erbium Doped Fiber Amp lifier are plotted against
wavelen gth range from 1530 to 1560 nm at input power
64 mw at temperature range 290-310ºK respectively as
shown in Fig. 6 and 1 0. Also the gain for the Er-doped
Al2 O 3 fiber amplifier and yttria-Alumina-Silicate Erbium
Doped Fiber Am plifier resp ectively is plotted with length
384
Res. J. Appl. Sci. Eng. Technol., 2(3): 381-386, 2010
Optimum length
Maximum gain
Fig. 8: The Optimum length variation for erbium doped Al2O3
glass fiber amplifier, calculated for different values of
temperature at maximum gain of the amplifier
McCumber emission cross section
Fig. 10: The maximum gain spectrum for yttria-AluminaSilicate Erbium Doped Fiber Amplifier, calculated for
different values of amplifier length at room
temperature
Gain
Fig. 9: The normalized values of the emission cross section of
yttria-Alumina-Silicate Erbium Doped Fiber Amplifier
as calculated using Mc Cumber theory at different
temperatures
Fig. 11: The maximum gain for yttria-Alumina-Silicate Erbium
Doped Fiber Amplifier, calculated for different values
of maximum wavelength at room temperature
Tab le 4: F eatu res o f the E DF A w ith thre e diff eren t hos ts
Host
8 o (nm)
Alu min o-g rma nos ilicate
A l2 O 3
yttria-A lum ina-S ilicate
1560
1537
1550
G max ( dB )
---------------------------------------------------------------------------------------------------T (º K )
290
294
298
300
305
310
2.48
3.82
5.81
7.13
11 .8
19
2.11
3.27
5.01
6.17
10 .3
16 .8
1.45
2.24
3.41
4.2
6.96
11 .3
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Res. J. Appl. Sci. Eng. Technol., 2(3): 381-386, 2010
Tab le 5: F eatu res o f the E DF A w ith thre e diff eren t hos ts
Host
8 o (nm)
Alu min o-g rma nos ilicate
A l2 O 3
yttria-A lum ina-S ilicate
1560
1537
1550
L o p t (m)
---------------------------------------------------------------------------------------------------T (º K )
290
294
298
300
305
310
9
11 .6
15 .5
18 .1
27 .1
41 .4
8
10 .1
13 .2
15 .3
22 .7
34 .4
6.8
8.2
10 .3
11 .8
16 .7
24 .6
Optimum length
and temperature 300ºK relative to erbium doped
aluminum-oxide fiber amplifier which exhibits a value of
gain 15.3 at center wavelength 1537 nm and temperature
300ºK and for erbium doped yattria-silicate fiber amplifier
which exhibits a value of gain 11.8 at center wavelen gth
1550 nm and temperature 300ºK.
REFERENCES
Cheng, C. and X. Min, 2005. Optimization of an erbiumdoped fiber amplifier with radial effects. O pt.
Comm., Science Direct, 254: 215-222.
Desurvire, E., 1994, Erbium Doped Fiber Amplifiers:
Principles and Applications. Wiley, New Y ork.
Gerlas, N.H ., J.A. Elsken, P. Albert, C.V. D am, K.W.M.
Uffelen and M .K. Smit, 1997. Absorption and
emission cross section of Er3 + in Al2 O 3 waveguides.
Appl. Opt., 36: 3338-3341.
Gigonnet,
M .J.F.,
E.
Murphy-Chutorian
and
D.G. Falquier, 2002. Fundamental limitations of the
McC umber relation applied to er-doped silica and
other amo rphous- ho st lasers. IE EE J. Quantum
Electron., 38(12): 1629-1637.
Lin, M.C. and S. Chi, 1992. IEEE photon. Technol. Lett.,
4: 354.
McC umber, D.E., 1964. Theory of phononterminated
optical masers. Phys. Rev., 134(2A): A299-A306.
Osama, M., 2007. Yttria-alumina-silicate erbium doped
fiber amplifier characteristics at 1540 nm . Int. J. Pure
Appl. Phy., 3(1): 83-90.
Osama, M., M.S. Helmy, et al. 2009. Temperature effect
on the emission cross section of Er3 + in Al2 O 3 fiber
amplifier. J. Appl. Sci. Res., 5(10): 1692-1697.
Rieznik, A.A. and W.A. Arellano, 2003. ED FA s gain and
NF dependence o n the Wber length: comparison
between L and C bands. Proceedings of the IEEE
Microwave and Optoelectronics Conference paper
SaD -3, Foz de Iguazu , Brazil.
Rieznik, A.A., H.L. Fragnito, M .B. Costa e Silva and
J.P. Von der W eid, 2006. Study o n optimum fiber
length for maximum gain in C- and L-band ED FAs.
Opt. Comm., Science Direct, 266: 546-551.
Ruhl, F.F., 1992. A ccurate ana lytical formulas for gainoptimised EDFAs. Electron. Lett., 28: 312.
Yahya, M.Z., M . Osama and M .Z. Yahya, et al., 2004.
Erbium doped fiber amplifier performance using
different host materials in the band 1450-1650 nm: A
comparative study. IIUM Eng. J., 5(2): 53-64.
Fig. 12: The Optimum length variation for yttria-AluminaSilicate Erbium Doped Fiber Amplifier, calculated for
different values of temperature at maximum gain of the
amplifier
CONCLUSION
W e can summarize the features of the erbium doped
with the three different hosts material at temperature
range 290 to 310ºK and the optimum length of the
amplifier to improve the performance of the optical
amplifier where the results given in the Table 4 and 5.
It is found that the erbium doped aluminogerm anosilicate fiber am plifier exh ibits large value of
gain 7.13 dB at center wavelength 1560 nm and
temperature 300ºK relative to erbium doped aluminumoxide fiber amplifier which exhibits a value of gain 6.17
at center wavelength 1537 nm and temperature 300ºK and
for erbium doped yattria-silicate fiber amplifier which
exhibits a value of gain 4.2 at center wavelength 1550 nm
and temperature 300ºK.
Also it is found that the erbium doped aluminogerm anosilicate fiber amplifier exhibits a mo re
broadening in the gain curve (= 40 nm). The broadening
in gain is required in amplification of the signal at large
range of w avelengths.
For the optimum fiber length it is found that the
erbium doped alumino-germano silicate fiber amplifier
exhibits value of 18.1 m at ce nter w avelength 1560 nm
386