Journal of Computer and Communications, 2013, 1, 54-58
Published Online December 2013 (http://www.scirp.org/journal/jcc)
http://dx.doi.org/10.4236/jcc.2013.17013
Open Access JCC
The λ-Characteristics of the Ring Laser Based on
Non-Uniform SOA
Zhi Wang, Limei Zhang, Yingfeng Liu, Lanlan Liu
Institute of Optical Information, Beijing Jiaotong University, Beijing 100044 Key Laboratory of Luminescence and Optical Informa-
tion, Ministry of Education, China.
Received October 2013
ABSTRACT
Semiconductor optical amplifier -based ring cavity laser (SOA -RL), which has been widely used in optical communica-
tions, optical fiber sensing, and bio-photonics fields, can be tuned at an ultra high speed up to Mega Hertz over 100 nm
bandwidth r ange with high SNR and flatness output. A steady-state model and segmentation algorithms are employed to
investigate the gain spectra of four kinds of non-uniform SOA and the lasing wavelength of the SOA-RL. It shows that
the dependence of the lasing wavelength on the average width is stronger when the light propagates from narrower to
wider end than conversely, and there are some particular structures to show ultra high stability lasing wavelength. It is
supposed that the main reason could be the carrier density distribution along the propagation.
Keywords: Semiconductor Optical Amplifier; Non-Uniform; Ring Laser; Gain
1. Introduction
Ring laser based on semiconductor optical amplifier
(SOA-RL) [1,2] can be conveniently tuned as wave-
length swept laser or Fourier domain mode locked laser
[3], and employed in many fields, such as the characte-
ristic test for optical fiber communication system [4],
optical coherence tomography (OCT) [5], ultra high res-
olution distributed optical fiber sensors, optical power
equilibrium [6] and all optical packet switching [7]. The
SOA-RL shows us some properties of both the ring cav-
ity and external cavity lasers, and can operate at some
different regimes with some in-line devices, such as the
filter, fiber coupler, isolator and polarization controller
[8]. It is more easily to oscillate with single longitudinal
mode and output narrow pulse sequence at high repeat
rate with the structure of ring cavity [9]. SOA-RL has
good compatibility with optical fiber systems, which can
reduce kinds of connection loss and disturbance, such as
the refraction loss, back scattering loss, and suppress the
effect of the backward light into the SOA [10]. The flex-
ibility and fiber-compatibility of the SOA-RL itself em-
phasize its importance in the future photonic devices and
next generation optical telecommunications.
There are only a few literatures about the mechanism
of the SOA-RL while lots of applications reports. The
SOA shows particular prop erties with non-uniform injec-
tion [11], but there is no literature to discuss the SOA-RL
with non-uniform injection. In fact, the non-uniform in-
jection can be only realized for the SOA with non-uni-
form active layer, so the non-uniform SOA, instead of
the non-uniform injection, will be investigated in this
manuscript with segmentation method.
The gain properties of a few kinds of non-uniform
SOAs are simulated and followed by the output of the
SOA-RLs with the corresponding non-uniform SOAs.
2. Model and Algorithm
Figure 1 is the basic structure of the SOA-RL, in which
the SOA (InPhenix Inc.) is the gain medium, the tunable
filter (@1550 nm, FFP-TF2，Micron Optics Inc.) is dri-
ven by external signal (sawtooth or sinusoidal), the coup-
ler is for feedback and output, isolators (ISO), polariza-
Isolator
Tunable Filter
SOA
Coupler
Isolator
Output
Figure 1. The basic scheme of the SOA-RL.

The λ-Characteristics of the Ring Laser Based on Non-Uniform SOA
Open Access JCC
55
tion control (PC), and dispersion management fibers are
also included in the cavity.
The cavity length of the SOA-RL is about tens of me-
ters or kilometers, the ro undtrip time of light in the cavity
is about hundreds of ns or μs. The experiments show that
tens of roundtrips is necessary to build up the laser from
ASE with the amplifications by the SOA, and it will cost
about a few μs or ms, which is much longer than the gain
recovery time of bulk SOAs (about hundreds of ps and
dominated by the carrier recovery time), so the SOA can
be regarded to operate at steady state.
The SOA is split into sections, and carrier density and
photon density are regarded as constant in every section.
The gain is wavelength (frequency) dependent, and the
ASE band width is over 100 nm, so the ASE photons is
assumed to exist only at some discrete frequencies cor-
responding to integer multiples of cavity resonances, and
the gain properties at other frequencies are obtained by
fitting and interpolation.
For non-uniform SOA, the height h(z) and the width
W(z) of the active layer will be z-dependent, so the rate
equation of the carrier density N at z can be written as
Equation (1) refer to Ref.[12].
( )
( )( )
( )
( )( )( )
( )
( )( )
( )
( )( )( )
( )
( )( )
( )
1
1
1
,
2,
s
m
N
m ksksk
k
N
mjj jj
j
dN zIRNz
dteF z
g NzNzNz
hzWz
gNz KNzNz
hzWz
ν
ν
+−
=
−+−
=
= −
 Γ
−+



Γ
−+


∑
∑
,
(1)
where I is the amplifier bias current, e is the electron
charge, L is the length of the active region, Γ is the frac-
tion of amplified photons resides in the active region, gm
is the material gain coefficient. The bias current is as-
sumed to pass through the active region only and have a
uniform distribution across the active region width. The
first term on the right hand side represents the addition of
carriers to the active region from the bias current. These
injected carriers are then depleted by various mechan-
isms occurring within the amplifier. R(N) is the recom-
bination rate term including both radiative and nonradia-
tive carrier recombination rates. The third and fourth
terms represent radiative recombination of carriers due to
the amplified signal (νk) and amplified spontaneous
emission (ASE, νj), superscript “+” or “−” means forw ard
or backward propagation light.
In Equation (1),
( )( )( )( )
2
0
/d
L
Fzh zWzhz z=
∫
, could
be called as volume factor. For the uniform SOA, the F(z)
is exactly the same as the volume of the active area, and
even for the non-uniform SOA, when the height is uni-
form, F(z) is also exactly the volume of the active area.
Considering the ring structure of the SOA-RL, the al-
gorithm segmentation method for the quasi-steady state
SOA comes from M. J. Connelly [12], we will not dis-
cuss the algorithm itself.
3. Non-Uniform SOA
In this manuscript, the non-uniform SOA has only the
width of the active area z-dependent, which is shown in
Figure 2. The SOA is segmented into 40 subsections for
the whole length 700 micron, all the parameters, such as
the size of the active area, the photon density, the carrier
density, are considered as uniform in every particular
section.
Equations (2a) to (2d)express the dependence of the
width W(z) on the position z, which are linear, triangular,
exponential, and quadratic, where Nz is the total section
number, Wave is the average width along the propagation,
a and b are parameters for different functions.
( )
00 0000
1
,2
ave z
Wzazb WaNb=+=+
, (2a)
( )
11
11 11
11
1
,4
ave z
z
az b
WWaN b
aNz b
+

== +
−+
, (2b)
( )
2
2
222 22
exp( ),1
z
aN
ave z
b
Wbaz We
aN
==− , (2c)
22
3 33333
1
,3
ave z
WazbWaNb=+=+
. (2d)
Figure 3(a) shows the dependence of the width on the
position for Wave = 500 nm and b = 0.2 Wave. In order to
check the gain property of the non-uniform SOA, the cw
light inject from the narrower end and propagate to the
wider end, or from the wider end to the narrower end.
Figure 3(b) is the gain spectra for different non-uniform
SOA when the input power is −20 dBm, the legend with
“−c” means light propagating conversely from wider end
to narrower end. It is very interesting that the gain with
“−c” is a little greater than that without “−c”, which
means that the gain is higher when the light propagates
from wider to narrower end, and the gain for uniform
SOA is just the edge between the gain of light propagat-
ing from wider to narrower and from narrower to wider.
Δ z
W
1
Δ z
W
2
Δ z
W
3
Δ z
W
N-2
Δ z
W
N-1
Δ z
W
N
Figure 2. The segmentation model of the non-uniform SOA.

The λ-Characteristics of the Ring Laser Based on Non-Uniform SOA
Open Access JCC
56
(a) width
(b) Gain spectra
Figure 3. The width and the gain spectra of the non-uni-
form SOA for Wave = 500 nm and b = 0.2 Wave.
The peak gain wavelength shows some dependence on
the structure of the non-uniform SOA, and of course it
also depends on some other parameters, such as injection
current, the temperature. Table 1 shows the parameters
in the simulations [13].
4. Lasing Wavelength of the SOA-RL
For the ring laser based on the non-uniform SOA, the
lasing wavelength ( λ
L) will be the peak gain wavelength
due to the competition in the resonator, so the lasing wa-
velength heavily depends on the SOA’s structure and the
injection current. In order to only check the effect of the
non-uniform width of the active region of the SOA on
the lasing wavelength ( λ
L), other parameters are set as
constant, include the length, the height of the active area,
the injection current, the confinement factor, the carrier
lifetime, etc.. Figures 4-7 show the lasing wavelength
( λ
L) of the SOA-RL for the non-uniform width of linear,
Table 1. Some parameters in the simulations.
Parameter Symbol Value in SIU
Molar fraction of Arsenide in the active region y 0.892
Bandgap energy quadratic coefficient a 1.35
Bandgap energy quadratic coefficient b −0.775
Bandgap energy quadratic coefficient c 0.149
Effective mass of electron in the CB me 4.10 × 10−32
Effective mass of heavy hole in the VB mhh 4.19 × 10−31
Effective mass of light hole in the VB mlh 5.06 × 10−31
Auger recombination coefficient Caug 3.0 × 10−41
Leakage recombination coefficient Dleak 0. 00 × 1048
Linear radiative recombination coefficient Arad 1 × 107
Bimolecular radiative
recombination coefficient Brad 5.6 × 10−16
Linear nonradiative
recombination coefficient due to traps Anrad 3.5 × 108
Bimolecular nonradiative
recombination coefficient Bnrad 0.00 × 10−16
Length L 700 micr on
Height d 400 nm
Light velocity in vacuum c 3 × 108
Active region refractive index n1 3.22
Optical confinement factor Γ 0.45
triangular, exponential and quadratic function with the
position.
Figure 4(a) shows the relationships between the lasing
wavelength and the linearly non-uniform width for pa-
rameters b0/Wave being 0.2, 0.4, 0.6 and 0.8, the
λ
L of
both directional propagating are illustrated together with
the uniform SOA. It is interesting that the dependence of
the lasing wavelength on the average width is a bit
stronger when the light propagates from narrower to
wider end than conversely. The lasing wavelength of
“0.8−c” shows almost independent on the average width.
In order to check it accurately, Figure 4(b) shows the
lasing wavelength for b0/Wave from 0.7 to 0.92 (spacing
0.02) propagating from wider to narrower end. The
maximum wavelength difference for “0.8−c” is less than
6 pm within the average width range from 0.3 to 0.8 mi-
crons.
Figure 5(a) shows the relationships between the lasing
wavelength and the triangularly non-uniform width for
parameters b1/Wave between 0.1 and 1.8 (spacing 0.1).
When b1/Wave is less than 1, the active area becomes
wider from both end to the middle, and becomes narrow-
er from both end to the middle when it is greater than 1,
and uniform when b1/Wave = 1. The
λ
L increases with the
average width for all cases, the lines are closer for greater
b1/Wave than smaller. It means that the lasing wavelength
is stable at a particular average width when the slope is in
some range. Figure 5(b) shows the dependence of
λ
L on
b1/Wave for different average width, the maximum wave-
0510 1520 2530 3540
0
500
1000
1500
s ecti on num ber
widt h nm
linear
t riangul ar
exponentail
quadrat ic
uniform
1520 1530 1540 1550 1560 1570 1580 1590 1600 1610
0
10
20
30
40
50
60
λ (nm )
Gain
li near
li near-c
t ri angular
ex ponentail
ex ponential-c
quadratic
quadratic-c
uniform

The λ-Characteristics of the Ring Laser Based on Non-Uniform SOA
Open Access JCC
57
(a)
(b)
Figure 4. The lasing wavelength of the SOA-RL for the li-
near non-uniform width.
(a)
(b)
Figure 5. The lasing wavelength of the SOA-RL for the tri-
angular non-uniform width.
length difference is about 7 pm for Wave = 0.75 μm when
b1/Wave is greater than 1, and about 4 pm for Wave = 0.55
μm when b1/Wave is greater than 1.3.
Figure 6(a) shows the relationships between the lasing
wavelength and the exponentially non-uniform width for
parameters b2/Wave from 0.1 to 0.9 with the spacing 0.1,
the
λ
L of both directional propagating are illustrated to-
gether. It is also interesting that the dependence of the
lasing wavelength on the average width is a bit stronger
when the light propagates from narrower to wider end
than conversely. The lasing wavelength of “0.8−c” shows
almost independent on the average width. In order to
check it clearly, Figure 6(b) shows the lasing wave-
length for b2/Wave from 0.71 to 0.9 (spacing 0.01) propa-
gating from wider to narrower end. The maximum wa-
velength difference for “0. 8−c” is less than 4.5 pm within
the average width range from 0.3 to 0.8 microns.
Figure 7(a) shows the relationships between the lasing
wavelength and the quadratically non-uniform width for
parameters b3/Wave from 0.1 to 0.9 with the spacing 0.1,
the
λ
L of both directional propagating are illustrated to-
gether. It also shows that the dependence of the lasing
wavelength on the average width is stronger when the
light propagates from narrower to wider end than con-
versely. The lasing wavelength of “0.9−c” shows almost
independent on the average width. In order to check it
(a)
(b)
Figure 6. The lasing wavelength of the SOA-RL for the ex-
ponential non -uniform width.
0.3 0.4 0.5 0.6 0.7 0.8
1571.5
1571.6
1571.7
1571.8
1571.9
1572
1572.1
1572.2
1572.3
Wave ( µ m)
λ
L (nm)
0.2
0.4
0.6
0.8
uniform
0.8-c
0.6-c
0.4-c
0.2-c
0.3 0.4 0.5 0.6 0.7 0.8
1571.7
1571.72
1571.74
1571.76
1571.78
1571.8
λ
L
(nm)
W
ave
( µ m)
0.92-c
0.7-c
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8
1571.76
1571.78
1571.8
1571.82
1571.84
1571.86
1571.88
W
ave
( µ m)
λ
L
(nm)
1.8
0.1
00.2 0.4 0.6 0.811.2 1.4 1.61.8
1571.76
1571.78
1571.8
1571.82
1571.84
1571.86
1571.88
b
1
/W
ave
λ
L
(nm)
0.8 µ m
0.3 µ m
0.30.35 0.4 0.450.5 0.550.6 0.650.7 0.75 0.8
1571
1571.2
1571.4
1571.6
1571.8
1572
1572.2
1572.4
1572.6
1572.8
W
ave
( µ m)
λ
L
(nm)
0.1-c
0.1
0.9 0.9-c
0.30.35 0.4 0.45 0.50.55 0.60.65 0.70.750.8
1571.64
1571.66
1571.68
1571.7
1571.72
1571.74
1571.76
1571.78
1571.8
1571.82
W
ave
( µ m)
λ
L
(nm)
0.71-c
0.9-c

The λ-Characteristics of the Ring Laser Based on Non-Uniform SOA
Open Access JCC
58
(a)
(b)
Figure 7. The lasing wavelength of the SOA-RL for the qu-
adratic non-uniform width.
clearly, Figure 7(b) shows the lasing wavelength for
b3/Wave from 0.8 to 0.95 (spacing 0.01) propagating from
wider to narrower end. The maximum wavelength dif-
ference for “0.8−c” is less than 6.8 pm within the average
width range from 0.3 to 0.8 microns.
5. Discussion and Conclusion
The gain property for a fe w kind of non-uniform SOA is
simulated, and the lasing wavelength of the ring cavity
laser with the non-uniform SOA is investigated with the
dependence on the active area width and the non-uni-
formity. It shows that the dependence of the lasing wave-
length on the average width is stronger when the light
propagates from narrower to wider end than conversely.
It is supposed that the main reason could be the carrier
density distribution along the propagation.
6. Acknowledgements
This work was supported in part by the National Natural
Science Foundation of China under grant 61077048, Bei-
jing Natural Science Foundation under grant 4132035,
Specialized Research Fund for the Doctoral Program of
Higher Education under grant 20120009110032, and by
Beijing Ji a otong University under grant 2012J B M103.
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0.30.35 0.40.45 0.50.55 0.60.65 0.70.75 0.8
1571
1571.2
1571.4
1571.6
1571.8
1572
1572.2
1572.4
1572.6
1572.8
W
ave
( µ m)
λ
L
(nm)
0.9 0.9-c
0.1
0.1-c
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0. 8
1571.68
1571.7
1571.72
1571.74
1571.76
1571.78
1571.8
W
ave
( µ m)
λ
L
(nm)
0.95-c
0.8-c