644 CHINESE OPTICS LETTERS / Vol. 6, No. 9 / S eptember 10, 2008
Analysis of erbium doped holey fiber using
fundamental space filling mode
Faramarz E. Seraji
1
and Mohammad D. Talebzadeh
2
1
Iran Telecomm Research Center, Tehran, Iran
2
Vali-Asr University and International Center of Science and High Technology and Environmental Science, Kerman, Iran
Received March 25, 2008
Erbium-doped holey fiber with hexagonal lattice was modeled by using effective index method . In order to
calculate the equivalent step index of the periodic structure of the cladding holey optical fiber, all-vectorial
fundamental space filling mode approach was utilized. By using EH
11
mode, we have numerically solved
the rate equ ations of a three-level pumping scheme for a fiber laser. The obtained results have shown a
good agreement with the oth er experimental results, recently. The results have predicted amplifiers with
gain efficiencies as high as 10 dB/mW.
OCIS codes: 060.2310, 060.2410, 060.2320, 140.3500, 140.4480.
doi: 10.3788/COL20080609.0644.
In erbium doped fiber amplifie rs (EDFAs), to obtain high
gain efficiency one needs to use fiber s with high numer-
ical aperture (NA) to achieve the maximum population
inversion of the erbium ions. It is useful to confine the
erbium ions to the central part of the core to enforce the
pumping light propagating with the fundamental HE
11
mode
[1,2]
. Germanium-doping, which is used in the core
of high NA fiber, reduces the emission bandwidth of
the Er
3+
ions and limits its concentrations. This results
in narrower gain bandwidths and increases the device
lengths
[1,3]
.
Recently, holey o ptical fibers (HOFs) with high NA
have become popular in ma king EDFAs with hig h gain
efficiency
[4]
. The stacking procedure used to fabricate
HOFs makes it possible to locate the rare-earth ions ac-
curately in the central region of the fiber, where has the
maximum intensity of fundamental modes for pumping
and signal fields
[1]
. For amplification investigation in
HOFs, the fundamental modes of core and cladding are
to be known, which have been investigated by different
analytical and numerical methods
[5−10]
.
The electromagnetic field profile of the propagating
modes of an Er-doped holey fiber (EDHF) was car-
ried out by a finite element method solver
[4]
. The
amplification properties of different HOFs have been
studied by a full vector finite-element modal formula-
tion combined with a po pulation and propagation rate
equation solver
[11]
. The angular emission pa ttern was
compared with the results of a multiple scattering sim-
ulation to study the emission of 532-nm light through
the photonic crystal cladding of an optica lly pumped
Er-doped silica-air HO F in Ref. [12]. In spite of these
reports, the number of articles reporting the modeling
of EDHF is rather small. Combining previous models of
EDFAs
[13]
and of HOFs
[10]
, in this paper , we presented
a simple hybrid model which can predict the behavior of
EDHFs. This model, unlike the FEM analysis, is easy
to use for single-mode EDHFs and needs lesser time for
computations.
In an infinitely self-similar hex agonal lattice, the exact
solutions of Maxwell’s eq uations exhibit either an odd
or an even parity with respect to planes marked either
with S
1
or S
2
as in Fig. 1. The electromagnetic fields
are unaffected whenever the symmetry planes S
1
or S
2
(dashed lines) are replaced either by a perfect electric or
by a perfect magnetic conductor
[10]
.
The effective index of the cladding mode is stro ngly
affected by the radius R of the hexago nal cell in HOFs,
as shown in Fig. 2. In cylindrical coordinates (r, φ, z),
the electric and magnetic fields at point P in Fig. 2 on
Fig. 1. S chematic of the infinitely self-similar hexagonal lat-
tice. d: air-hole diameter; Λ: air-hole spacing.
Fig. 2. Equivalent circular unit cell of a hexagonal cell with
a radius of R.
1671-7694/2008/090644-04
c
2008 Chinese Optics Letters