Journal of Applied Sciences Research, 5(10): 1692-1697, 2009
© 2009, INSInet Publication
Corresponding Author: Osama Mahran, Faculty of Science, University of Alexandria, Alexandria, Egypt,
E-mail:o_mahran2003@yahoo.com
1692
2 3
Temperature Effect on the Emission Cross Section of Er in Al O Fiber Amplifier
3+
Osama Mahran, Mohammed Salah Helmy and Mourad Abd El Hai
Faculty of Science, University of Alexandria, Alexandria, Egypt
Abstract: The study of temperature dependent emission cross section, gain coefficient and gain of the Er-
2 3
doped Al O fiber amplifier in the range 290 to 310 K is carried out. McCumber procedure is used to
predict the emission cross-section spectrum of the 1.5 ì m transition of Er-doped glass fibers from the
transition's measured absorption spectrum. The gain coefficient and gain of the amplifier are calculated
using the transition rate equations at the pump wavelength 980 nm. It is found that emission cross section,
gain coefficient and the gain of the amplifier increase with temperature in the amplifier window 1.53 ì m.
Key words: Optical Amplifier, Temperature Effect, Erbium, Emission Cross Section.
INTRODUCTION
Accurate modeling of Er-doped fiber amplifiers
(EDFAs) and waveguide amplifiers for design and
performance analysis purposes requires the knowledge
of several parameters to a high accuracy, in particular,
the emission cross-section spectrum of Er in the host
under study . An understanding of the amplifier
[1]
temperature dependent characteristics is of a great
importance. Erbium-doped planar waveguides are being
studied because of their applications as integrated
optical amplifiers or lasers that operate at 1.5 ì m. The
rare earth ion Er has one of its intra-4f transitions
3+
around 1.53 ì m, coinciding with the low-loss window
of standard silica optical fibers. Optical amplifiers at
this wavelength are necessary to overcome losses in the
processing and distribution of optical signals, while
maintaining high bandwidth and low cross talk. The
use of planar amplifiers offers the important advantage
that they can be integrated together with other
waveguide devices on a single chip .
[2]
The performance of an Er-doped amplifier depends
on the magnitude and wavelength dependence of the
emission and absorption cross sections. Together with
the Er concentration profile, the optical intensity profile
and the waveguide loss, the knowledge of these
parameters enables a first-order estimate of the
2 3
potential optical gain. Al O waveguide films on silicon
wafers are interesting as a host material for Er because
waveguide fabrication technology is well developed for
this material .
[3]
One can theoretically analyze the temperature
dependent of both emission cross section and gain. The
approximate McCumber procedure is often used to
predict the emission cross-section spectrum of the 1.5-
ì m transition of Er-doped glass fibers from the
transition's measured absorption spectrum at different
values of temperature . The objective of this paper
[4]
is to calculate the emission cross section of the Er-
2 3
doped Al O waveguide from the absorption cross
section at different temperature values using McCumber
procedure, and then calculate the expected values of
gain coefficient at different population inversion factors
for different temperature values. Also, the gain of the
amplifier at different input power at different
temperature values is studied.
II-Theory
1. Calculation of the Emission Cross Section: The
McCumber relation states that the absorption cross
a e
section, ó ( í ), and the emission cross section, ó ( í ),
spectra between a ground state (a manifold of eight
1j
sublevels of energy E ) and the excited state (a
2j
manifold of seven sublevels of energy E ) are related
by
[5]
(1)
where k is the Boltzmann constant, T the absolute
temperature and í the optical frequency. The parameter
å is defined as
(2)
o 21 11
where E = E – E is the energy difference between
the lowest energy levels of the two manifolds.
Relation (1) can be written in the form
[5]
(3)