Wide Broadband ASE Source based on Thulium-doped Fibre
for 2 μm Wavelength Region
M. A. Khamis and K. Ennser
College of Engineering, Swansea University, Swansea, U.K.
Keywords: Thulium-doped Fibre, Amplified Spontaneous Emission, Silica Glass Material, Numerical Modelling.
Abstract: This paper investigates the generation of the amplified spontaneous emission (ASE) from thulium-doped
silica fibre pumped at 1570 nm. The developed model provides the ASE spectral power at short and long
wavelength bands by using two different thulium doped fibre types with optimized fibre length. Shorter
wavelengths in the emission band can be accessed with a short thulium fibre, whereas longer wavelengths
can be obtained using a long thulium fibre. Our findings reveal that, in contrast to a 100 nm (1800nm-
1900nm) and 70 nm (1900nm-1970nm) broadband source at short and long wavelength bands, a broader
spectrum source can be achieved at about 170 nm (1800nm-1970nm) by a combined of the two ASE spectra
via a wideband 50:50 coupler. As a result, the proposed ASE source configuration doubles the bandwidth of
the conventional single fibre based light source.
1 INTRODUCTION
Over the last few years, broadband sources near 2
μm have attracted the attention of many researchers.
Hu et al. (2015) point out a broadband source at 2
μm have many useful characteristics, including high
output power, high light brightness, good beam
quality, compact structure and excellent spatial
coherence. These characteristics make broadband
sources at 2 μm suitable for use in a number of
significant applications, such as remote sensing (Li
et al., 2014), gas sensing (Hsu et al., 2008), medical
surgery (Morse et al. 1995), materials processing
(Jackson Sabella and Lancaster, 2007) and
atmospheric lidar measurement (Sugimoto et
al.,1990). In addition, according to Halder et al.
(2012) and Cheung et al. (2015), high power and
wideband sources are required in optical coherence
tomography and fibre optic gyroscopes.
One effective way to generate this broadband
source is by using the process of amplified
spontaneous emission between
3
F
4
-
3
H
6
transition in
thulium-doped fibre. High broadband source
efficiency can be obtained via diode pumping on the
transition
3
H
6
3
H
4
in combination with high
concentration of thulium-doped silica fibre in order
to take into account the cross-relaxation process
(Oh, 1994; Shen et al., 2008). Alternatively, the need
for high doping concentrations can be avoided by
using an in-band pumping scheme, which directly
excites the upper laser level on the transition
3
H
6
3
F
4
. Nevertheless, Tsang et al. (2005) explain that
high efficiencies can be achieved because of the
much lower quanta defect associated with this
pumping scheme. However, in spite of the progress
in the performance of thulium broadband sources the
efficiency and bandwidth are still below those
routinely provided from conventional thulium fibre
laser oscillators.
To better optimize the broadband source
performance near 2 μm. It is necessary to develop a
theoretical modeling and perform simulations. There
are relatively few theoretical studies on ASE sources
based on thulium-doped fibre (TDF) (Gorjan et al.,
2012; Yu et al., 2010). On the other hand, various
experimental configurations for broadening the
spectral bandwidth of ASE source have been
presented in the literature. Broader bandwidths up to
72 nm have been demonstrated using Tm: Ho-doped
silica fibre (Tsang et al., 2005). Up to 100 nm of
broadband spectra has been achieved using single
end operation (Shen et al., 2008). However, these
configurations have limited spectra bandwidth. This
paper proposes a new thulium ASE configuration
that doubles the bandwidth of the conventional
configuration.
In this paper, a broadening ASE source can be
generated from combining the ASE output source of
Khamis M. and Ennser K.
Wide Broadband ASE Source based on Thulium-doped Fibre for 2 Îijm Wavelength Region.
DOI: 10.5220/0006101801410146
In Proceedings of the 5th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2017), pages 141-146
ISBN: 978-989-758-223-3
Copyright
c
2017 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
141
TDF1
TDF2
1570 WDM
1570 WDM
1570 Pump
1570 Pump
50:50 Coupler
ISO
ASE O/P
two different TDFs as shown in fig.(1). The first
fibre TDF
1
is a commercial thulium fibre (TmDF200
from OFS) with short fibre length. Agger and
Povlsen (2006) demonstrated that the center
emission spectrum of this fibre is at the wavelength
1800 nm. The second fibre TDF
2
is a commercial
thulium fibre (SM-TSF-9/125 from Nufern) with
long fibre length. Jackson (2009) shows that this
fibre produces an emission spectrum with 1900 nm
center wavelength. Long TDF leads to shift the
output spectrum to ward long wavelength bands (Li
et al. 2013). Thus, TDF
1
generated ASE1 source
with short wavelength bands which is centered at
1840nm and TDF
2
produced ASE2 source with long
wavelength bands which is centered at 1950nm. The
two ASE sources were combined together into a
single ASE source via wideband 50:50 coupler. This
type of coupler is already applied to design a widely
tunable thulium laser (Stevens and Legg 2015).
Notes that in our simulation, we choose couplers and
combiners have flatting coupling response over the
wavelengths range in order to allow broadband ASE
source.
Figure 1: A schematic diagram of proposed ASE source.
ISO is an optical isolator at 2μm, ASE o/p is the combined
ASE sources of TDF
1
and TDF
2
ASE output. Note that all
fibre ends are angle polished.
2 NUMERICAL MODEL OF ASE
A theoretical model of ASE generation are
presented. The investigation into ASE spectral
power is achieved by solving the rate and
propagation equations. The model takes into account
the wavelength-dependent absorption and emission
cross-sections. Based on Jackson and King (1999)
and including ASE, the rate equations of thulium
energy levels are established as follows:
22
12 1 21 2
2
21 2 12 1
(,) (,)
( , ) ( , )
pp
ss
dN N
w N zt w N zt
dt
w N zt w N zt
τ
=−
−+
(1)
12
(,) (,)
T
Nzt N Nzt=− (2)
Here N
T
is the Tm
3+
concentration and set to be a
constant. τ
2
is the spontaneous lifetime of the
3
F
4,
level N
1
and N
2
are the population densities of the
3
H
6
and
3
F
4
levels, respectively, w
p12
is the pumping
rate from
3
H
6
to
3
F
4
and w
p21
represents the de-
excitation of the
3
F
4
level; w
s21
is the stimulated
emission rate from
3
F
4
to
3
H
6
, and w
s12
is the
stimulated absorption rate from
3
H
6
to
3
F
4
. The
expressions of w
p12
, w
p21
, w
s21
and w
s12
can be
obtained from:
12
()(() ())
pp
pappp
core
wpzpz
hcA
λ
σλ
−+
Γ
=+
(3)
21
()(() ())
pp
peppp
core
wpzpz
hcA
λ
σλ
−+
Γ
=+
(4)
12
()[ () ()]
ss
sasfb
core
w ASE z ASE z
hcA
λ
σλ
Γ
=+
(5)
21
()[ () ()]
ss
sesfb
core
wASEzASEz
hcA
λ
σλ
Γ
=+
(6)
Here λ
p
is the wavelength of the pump light and λ
s
is
the signal light in vacuum; h is the Planck constant;
c is the light speed in vacuum; A
core
is the cross-
section area of the fibre core; σ
a
(λ
p
) and σ
a
(λ
s
) are
the absorption cross-sections of the pump light and
the signal light, respectively; σ
e
(λ
p
) and σ
e
(λ
s
) are the
emission cross-sections of the pump light and the
signal light, respectively; P
±
(z) is the pump
(corresponding to forward and backward) at position
z; and

() and

()are the forward and
backward amplified spontaneous emission powers at
position z; Γ
p
and Γ
s
are the confinement factors for
the pump and the signal, respectively which are
given by Eq. 7
(Whitley and Wyatt, 1993).
2
2
2
() 1 exp
a
w
λ

Γ=


(7)
Where w is the mode-width parameter of the fibre
and a is the radius of the fibre. The normalized
frequency V of the fibre is given by:
PHOTOPTICS 2017 - 5th International Conference on Photonics, Optics and Laser Technology
142
2.aNA
V
π
λ
=
(8)
As V>1.5the mode-width parameter w of a step-
index fibre can be determined by the normalized
frequency V of the fibre as:
3/2 6
0.632 1.478 4.76
w
VV
a
−−
=+ +
(9)
Meanwhile, the pump power distribution along
the fibre length can be expressed by the following
propagation equation:
21
()[ ( ( ) () ( ) ())
- ]
p
ppep ap
p
dp
p
zNzNz
dz
σλ σλ
α
±
±
Γ
(10)
The positive sign in (10) relates to the forward
direction and the negative sign to the reverse
direction. The distribution of the ASE forward and
backward powers along the fibre length can be
established as follows
(Hu et al., 2015; Yu et al., 2010):
21
2
2
3
()[ ( ( ) () ( ) ())
- ] 2 ( ) ( ) (11)
f
fses as
ses
s
dASE
A
SE z N z N z
dz
hc
Nz
σλ σλ
ασλ λ
λ
21
2
2
3
()[ ( ( ) () ( ) ())
- ] 2 ( ) ( ) (12)
b
bses as
ses
s
dASE
A
SE z N z N z
dz
hc
Nz
σλ σλ
ασλ λ
λ
=− Γ
−Δ
Where α
p
and α
s
are the intrinsic absorption at the
pump and signal wavelength for the Thulium-doped
fibre, respectively, ∆λ is the bandwidth of the
amplified spontaneous emission (ASE) around 2μm.
3 RESULTS AND DISCUSSION
To solve the thulium rate equations for the ASE
model in steady state condition, the time derivatives
of eq. (1) to (2) for in-band pumping are set to zero.
The fourth-order Runge-Kutta method is applied to
solve the differential equations of the pump and the
amplified spontaneous emission ASE signals. Table
1 and 2 summarizes all parameters values used in the
numerical simulations of the TDF
1
(Agger and
Povlsen 2006) and TDF
2
(Jackson 2009),
respectively. Initially, the entire population is
assumed to be at the ground level
3
H
6
in the
numerical calculations.
Table 1: Values of numerical parameters for TDF
1.
Symbol Quantity Value
N
T
Thulium concentration 8.4×10
25
m
-3
τ
2
Lifetime of level
3
F
4
650µs
λ
p
In-band pump wavelength
1570nm
σ
a
(λ
p
) Laser absorption cross
section at 1570nm.
2.1×10
-25
m
2
σ
e
(λ
p
) Laser emission cross section
at 1570nm.
0
σ
a
(λ
s
) Laser absorption cross
section at signal wavelength
See (Agger and
Povlsen, 2006)
σ
e
(λ
s
)
Laser emission cross section
at signal wavelength
See (Agger and
Povlsen, 2006)
NA Numerical aperture 0.26
A Area cross section of the core 3.1×10
-11
m
-2
α
p
Intrinsic absorption at the
pump wavelength
1.07×10
-3
m
-1
α
s
Intrinsic absorption at the
signal wavelength
1.15×10
-2
m
-1
Table 2: Values of numerical parameters for TDF2.
Symbol Quantity Value
N
T
Thulium concentration 1.37×10
25
m
-3
τ
2
Lifetime of level
3
F
4
250µs
λ
p
In-band pump wavelength
1570nm
σ
a
(λ
p
) Laser absorption cross
section at 1570nm.
2×10
-25
m
2
σ
e
(λ
p
) Laser emission cross section
at 1570nm.
0
σ
a
(λ
s
) Laser absorption cross
section at signal wavelength
See (Jackson
2009)
σ
e
(λ
s
)
Laser emission cross section
at signal wavelength
See (Jackson
2009)
NA Numerical aperture 0.15
A Area cross section of the
core
6.36×10
-11
m
-2
α
p
Intrinsic absorption at the
pump wavelength
1.07×10
-3
m
-1
α
s
Intrinsic absorption at the
signal wavelength
1.15×10
-2
m
-1
Table 3 explains the initial conditions for the
pump power and the ASE spectrum in forward and
backward directions. The thulium-doped fibre with
length L is divided into N segments along the z-
direction. The solution is applied for the pump and
the ASE power propagating in the first segment
(segment 0) by using the initial conditions in Table
3. For the following segments (segment 1 to N-1),
the power for the pump and the ASE at one end of a
segment is applied as the input for the next segment.
Relaxation method is used to solve the differential
equations of the pump and the ASE powers (Emami
2011). Using the data of Table 1, 2 and the values of
the emission and the absorption cross-section, we
solve numerically the rate equations of the pump and
ASE power distribution.
Wide Broadband ASE Source based on Thulium-doped Fibre for 2 Îijm Wavelength Region
143
Table 3: Initial conditions.
Initial condition Explanation
P
+
p
(z=0) = Forward
launched pumppower
Initial condition for 1558nm
and 793nm pumps at z=0.
P
-
p
(z=L) =Backward
launched pump power
Initial condition for 1558nm
and 793nm pumps at z=L.
P
s
(z=0)= seed power
Initial condition for seed power
at z=0.
ASE
f
(z=0)=0
Initial condition for forward
amplified spontaneous
emission at z=0.
ASE
b
( z=L)=0
Initial condition for backward
amplified spontaneous
emission at z=L.
A MATLAB program is developed to evaluate
the optimum thulium-doped fibre length for each of
the two TDFs of fig. 1. Note that in our simulation
the feedbacks of ends’ reflection are set to zero and
it is only applied forward pump configuration.
Figure2 and 3 illustrate the theoretical prediction of
the output ASE forward power and the residual
pump power for TDF
1
and TDF
2
, respectively. The
launched pump power is equal 27dBm (0.55 W) at
case TDF
1
and 31.7dBm (1.5W) at TDF2. We
clearly notice that the optimum fibre length of TDF1
is 1.2 m at 1840nm output ASE as shown in fig. 2.
In contrast to TDF2, the optimum fibre length is 5m
at 1950nm output ASE as illustrated in fig. 3. In our
configuration, 1.2m of TDF
1
is a suitable length to
obtain short wavelength bands of ASE source which
is centred at 1840nm, whereas 8m of TDF
2
is more
suitable to access long wavelength bands which is
centred at 1950nm.
The next step is to investigate the output power
spectra of ASE at short and long wavelength bands.
Figure 4 shows the ASE spectrum of TDF
1
at 1.2m
Figure 2: Pump power distribution along TDF
1
length and
the forward ASE at 1840nm when the launched pump
power is 0.55W.
Figure 3: Pump power distribution along TDF
2
length and
the forward ASE at 1950nm when the launched pump
power is 1.5W.
fibre length and 27dBm launched pump power. The
bandwidths of forward ASE has full-width half
maximums (FWHM) of approximately 100 nm
between 1800nm and 1900nm compared to only
68nm and 88nm in forward and backward ASE
obtained by
Gorjan et al. (2012). The discrepancies are
due to the difference in thulium fibre characteristics.
Fig. 5 shows the ASE spectrum of TDF
2
at 8m fibre
length and 31.7dBm is the launched pump power.
The bandwidth of forward ASE at FWHM is
approximately 70 nm between 1900nm and 1970nm.
Finally, fig. 6 illustrates the combined ASE spectra
of the TDF
1
and TDF
2
spectra. Notes that a wide
50:50 coupler is used and assumed to be flat over the
range (1800nm-2000nm). It is clearly seen that the
combined ASE provides approximately 170 nm
bandwidth at FWHM between 1800nm and 1970nm.
Thus, this is the first time to our knowledge that over
170nm bandwidth ASE source based only on
thulium-doped fibre is reported.
Figure 4: Power spectrum of the forward ASE at 1.2m of
TDF
1
when 27dBm is the total input pump power.
0 0.2 0.4 0.6 0.8 1 1.2 1.4
0
0.05
Fiber length (m)
ASE Power (W)
0 0.2 0.4 0.6 0.8 1 1.2 1.4
0
0.5
1
Pump power (W)
0 1 2 3 4 5 6 7
0
0.05
0.1
Fiber length (m)
ASE Power (W)
0 1 2 3 4 5 6 7
0
1
2
Pump power (W)
1650 1700 1750 1800 1850 1900 1950 2000 2050
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Wavelength (nm)
ASE peak power (W)
PHOTOPTICS 2017 - 5th International Conference on Photonics, Optics and Laser Technology
144
Figure 5: Power spectrum of the forward ASE at 8m of
TDF
2
when 31.7dBm is the total input pump power.
Figure 6: Combined power spectrum of the TDF
1
and
TDF
2
ASE spectra by using flat wide 50:50 coupler.
4 CONCLUSION
A theoretical model of ASE generation around 2µm
is built up by solving a set of rate and propagation
equations. A MATLAB program is developed using
the Runge-Kutta method to investigate the behaviour
of the ASE generation at 2µm from two different
thulium fibres types at 1570nm.
We chose two different fibre characteristics with
optimised fibre length in order to generate ASE
source for short and long wavelength bands. Wide
band ASE source can be generated by combining the
two wavelength bands. Thus, the main scope of this
study is to generate broad band ASE source at 2 µm
for applications that require broader ASE bandwidth
such as optical coherence tomography.
Our simulation results show that short wavelength
bands (1800nm-1900nm) with 100nm FWHM
bandwidth can be generated from the TDF
1
. In
contrast to long wavelength bands (1900nm-
1970nm) with 70nm FWHM bandwidth can be
generated from TDF
2
. More than 170nm (1800nm-
1970nm) should be produced from combining the
two above ASE spectra. Note that we choose
couplers and combiners have flatting coupling
response over the wavelengths range in order to
allow broadband ASE source. Hence, our suggested
configuration is a suitable arrangement to obtain
over 170nm wider broadband source at 2 μm from
thulium doped fibre.
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