A novel system of multisoliton generation using nonlinear equations of the propagating signals is presented. This system uses a PANDA ring resonator incorporated with an add/drop filter system. Using resonant conditions, the intense optical fields known as multisolitons can be generated and propagated within a Kerr-type nonlinear medium. The present simulation results show that multisolitons can be controlled by using additional Gaussian pulses input into the add port of the PANDA system. For the soliton pulse in the microring device, a balance should be achieved between dispersion and nonlinear lengths. Chaotic output signals from the PANDA ring resonator are input into the add/drop filter system. Chaotic signals can be filtered by using the add/drop filter system, in which multi dark and bright solitons can be generated. In this work multi dark and bright solitons with an FWHM and an FSR of 425pm and 1.145 nm are generated, respectively, where the Gaussian pulse with a central wavelength of 1.55 μm and power of 600 mW is input into the system.

1. CHIN. PHYS. LETT. Vol. 28, No. 10 (2011) 104205
Simulation and Analysis of Multisoliton Generation Using a PANDA Ring
Resonator System
I. S. Amiri*
, A. Afroozeh, M. Bahadoran
Department of Physics, Science and Research Branch, Islamic Azad University, Tehran, Iran
(Received 8 July 2011)
A novel system of multisoliton generation using nonlinear equations of the propagating signals is presented. This
system uses a PANDA ring resonator incorporated with an add/drop filter system. Using resonant conditions,
the intense optical fields known as multisolitons can be generated and propagated within a Kerr-type nonlinear
medium. The present simulation results show that multisolitons can be controlled by using additional Gaussian
pulses input into the add port of the PANDA system. For the soliton pulse in the microring device, a balance
should be achieved between dispersion and nonlinear lengths. Chaotic output signals from the PANDA ring
resonator are input into the add/drop filter system. Chaotic signals can be filtered by using the add/drop filter
system, in which multi dark and bright solitons can be generated. In this work multi dark and bright solitons
with an FWHM and an FSR of 425 pm and 1.145 nm are generated, respectively, where the Gaussian pulse with
a central wavelength of 1.55 µm and power of 600 mW is input into the system.
PACS: 42.65.Tg DOI: 10.1088/0256-307X/28/10/104205
The generation of multisolitons becomes an inter-
esting subject when it is used to enlarge the capacity of
communication channels.[1]
The high optical output of
the ring resonator system is of benefit to long distance
communication links.[2]
Two techniques can be used to
generate soliton pulses. First, soliton pulses can be ob-
tained using a ring resonator system where large am-
plified signals are achieved. Second, a Gaussian soliton
can be generated in a simple system arrangement.[3]
This application becomes an attractive tool in the area
of photonics for soliton generation and investigation.
The advantage of using pumped solitons or Gaussian
solitons is that an intensive input light can be gener-
ated. There are many ways to achieve powerful light,
for instance, using a high-power light source or reduc-
ing the radius of the ring resonator.[4]
However, there are many research works report-
ing both theories and experiments using a common
Gaussian pulse for soliton studies.[5]
In practice, in-
tensive pulses can be obtained by using erbium-doped
fibers (EDFs) and semiconductor amplifiers incorpo-
rated with the experimental setup.[6]
A Gaussian pulse
is used to form a multi soliton using a ring resonator.[7]
In this work, a laser source such as a Gaussian
pulse with a central wavelength of 1.55 µm is used. A
nonlinear ring resonator system can be used to gen-
erate multiple soliton channels. We propose a mod-
ified add/drop optical filter called the PANDA sys-
tem, which consists of one centered ring resonator con-
nected to two smaller ring resonators on the right and
left sides.[8]
To form the multifunction operations of
the PANDA system, for instance, to control, tune and
amplify an additional Gaussian pulse is introduced
into the add port of the system. By controlling some
suitable parameters of the add optical pulse, the gen-
erated result within a ring resonator system can be
controlled. Therefore, a PANDA ring resonator can
be connected to an add/drop filter system in order to
filter noisy and chaotic signals. The nonlinear equa-
tions of the system due to the Kerr effect nonlinearity
type can be analyzed and simulated.
The proposed system consists of a PANDA ring
resonator connected to an add/drop filter system, as
shown in Fig. 1. The laser Gaussian pulse input prop-
agates inside the ring resonator system, which is in-
troduced by the nonlinear Kerr effect. The Kerr effect
causes the refractive index 𝑛 of the medium, expressed
by
𝑛 = 𝑛0 + 𝑛2 𝐼 = 𝑛0 +
𝑛2
𝐴eff
𝑃, (1)
where 𝑛0 and 𝑛2 are the linear and nonlinear refractive
indexes, respectively. 𝐼 and 𝑃 are the optical intensity
and the power, respectively. 𝐴eff is the effective mode
core area of the device.[9]
For an add/drop optical fil-
ter design, the effective mode core areas range from
0.50 to 0.10 µm2
. The parameters were obtained by
using the practical parameters of the materials used
(InGaAsP/InP).[10,11]
Input optical fields of the Gaus-
sian pulses at the input and add ports of the system
are given by[12]
𝐸𝑖1(𝑡) = 𝐸𝑖2(𝑡) = 𝐸𝑖0 exp
[︁(︁ 𝑧
2𝐿 𝐷
)︁
− 𝑖𝜔0 𝑡
]︁
, (2)
where 𝐸𝑖0 and 𝑧 are the optical field amplitude and
propagation distance respectively. 𝐿D is the disper-
sion length of the soliton pulse, where 𝑡 is the soli-
ton phase shift time, and the carrier frequency of
the signal is 𝜔0.[13]
The nonlinear condition of the
medium causes the gaussian beam to propagate as
*Corresponding author. Email: isafiz@yahoo.com
c○ 2011 Chinese Physical Society and IOP Publishing Ltd
104205-1

2. CHIN. PHYS. LETT. Vol. 28, No. 10 (2011) 104205
soliton pulses while its temporal and spatial width in-
variances are retained, which explains why it is called
a temporal and spatial soliton. Soliton pulses prop-
agate within the microring device when the balance
between the dispersion length (𝐿D) and the nonlin-
ear length (𝐿NL = 1/Γ 𝜑NL) is achieved. Therefore
𝐿D = 𝐿NL, where Γ = 𝑛2 × 𝑘0 is the length scale
over which dispersive or nonlinear effects make the
beam become wider or narrower.[14]
For the PANDA
ring resonator, the output signals inside the system
are given as follows:[15,16]
𝐸1 =
√︀
1 − 𝛾1(
√
1 − 𝜅1 𝐸4 + 𝑗
√
𝜅1 𝐸𝑖1), (3)
𝐸2 = 𝐸0 𝐸1 𝑒− 𝛼
2
𝐿
2 −𝑗𝑘 𝑛
𝐿
2 , (4)
where 𝜅1, 𝛾1 and 𝛼 are the intensity coupling coeffi-
cient, fractional coupler intensity loss and attenuation
coefficient, respectively, 𝑘 𝑛 = 2𝜋
𝜆 is the wave propaga-
tion number, 𝜆 is the input wavelength light field and
𝐿 = 2𝜋𝑅PANDA where, 𝑅PANDA is the radius of the
PANDA system, which is 300 nm. The electric field of
the small ring at the right side of the PANDA ring
system is given as
𝐸0 = 𝐸1
√︀
(1 − 𝛾)(1 − 𝜅0) − (1 − 𝛾)𝑒− 𝛼
2 𝐿1−𝑗𝑘 𝑛 𝐿1
1 −
√
1 − 𝛾
√
1 − 𝜅0 𝑒− 𝛼
2 𝐿1−𝑗𝑘 𝑛 𝐿1
,
(5)
where 𝐿1 = 2𝜋 𝑅 𝑟 and 𝑅 𝑟 is the radius of the right
ring. The light fields of the left side of PANDA ring
resonator can be expressed as
𝐸3 =
√︀
1 − 𝛾2[
√
1 − 𝜅2 𝐸2 + 𝑗
√
𝜅2 𝐸𝑖2], (6)
𝐸4 = 𝐸0𝐿 𝐸3 𝑒− 𝛼
2
𝐿
2 −𝑗𝑘 𝑛
𝐿
2 , (7)
where,
𝐸0𝐿 = 𝐸3
√︀
(1 − 𝛾)(1 − 𝜅3) − (1 − 𝛾)𝑒− 𝛼
2 𝐿2−𝑗𝑘 𝑛 𝐿2
1 −
√
1 − 𝛾
√
1 − 𝜅3 𝑒− 𝛼
2 𝐿2−𝑗𝑘 𝑛 𝐿2
,
(8)
where 𝐿2 = 2𝜋𝑅 𝐿 and 𝑅 𝐿 is the left ring radius. In
order to simplify these equations, the parameters of
𝑥1, 𝑥2, 𝑦1 and 𝑦2 are defined as
𝑥1 = (1 − 𝛾1)
1
2 , 𝑥2 = (1 − 𝛾2)
1
2 ,
𝑦1 = (1 − 𝜅1)
1
2 , 𝑦2 = (1 − 𝜅2)
1
2 .
Therefore,
𝐸1 =
𝑗𝑥1
√
𝜅1 𝐸𝑖1 + 𝑗𝑥1 𝑥2 𝑦1
√
𝜅2 𝐸0𝐿 𝐸𝑖2 𝑒− 𝛼
2
𝐿
2 −𝑗𝑘 𝑛
𝐿
2
1 − 𝑥1 𝑥2 𝑦1 𝑦2 𝐸0 𝐸0𝐿 𝑒− 𝛼
2 𝐿−𝑗𝑘 𝑛 𝐿
,
(9)
𝐸3 = 𝑥2 𝑦2 𝐸0 𝐸1 𝑒− 𝛼
2
𝐿
2 −𝑗𝑘 𝑛
𝐿
2 + 𝑗𝑥2
√
𝜅2 𝐸𝑖2, (10)
𝐸4 = 𝑥2 𝑦2 𝐸0 𝐸0𝐿 𝐸1 𝑒− 𝛼
2 𝐿−𝑗𝑘 𝑛 𝐿
+ 𝑗𝑥2
√
𝜅2 𝐸0𝐿 𝐸𝑖2 𝑒− 𝛼
2
𝐿
2 −𝑗𝑘 𝑛
𝐿
2 . (11)
Therefore, the output powers through and drop ports
of the PANDA ring resonator can be expressed as
𝐸 𝑡1and 𝐸 𝑡2 and are given as
𝐸 𝑡1 = 𝐴𝐸𝑖1 − 𝐵𝐸𝑖2 𝑒− 𝛼
2
𝐿
2 −𝑗𝑘 𝑛
𝐿
2 [
𝐶𝐸𝑖1 𝐺2
+ 𝐷𝐸𝑖2 𝐺3
1 − 𝐹 𝐺2
],
(12)
𝐸 𝑡2 = 𝑥2 𝑦2 𝐸𝑖2[
𝐴
√
𝜅1 𝜅2 𝐸0 𝐸𝑖1 𝐺 + 𝐷
𝑥1
√
𝜅1 𝐸0𝐿
𝐸𝑖2 𝐺2
1 − 𝐹 𝐺2
],
(13)
where 𝐴 = 𝑥1 𝑥2,𝐵 = 𝑥1 𝑥2 𝑦2
√
𝜅1 𝐸0 𝐿, 𝐶 =
𝑥2
1 𝑥2 𝜅1
√
𝜅2 𝐸0 𝐸0 𝐿, 𝐷 = (𝑥1 𝑥2)2
𝑦1 𝑦2
√
𝜅1 𝜅2 𝐸0 𝐸2
0 𝐿,
𝐺 =
(︁
𝑒− 𝛼
2
𝐿
2 −𝑗𝑘 𝑛
𝐿
2
)︁
and 𝐹 = 𝑥1 𝑥2 𝑦1 𝑦2 𝐸0 𝐸0 𝐿.
𝐸 𝑡1 output from the PANDA system can be input
into the add/drop filter system which is made of a ring
resonator coupled to two fiber waveguides with proper
parameters.[17]
The light fields inside the add/drop fil-
ter system are given as
𝐸 𝑎 =
𝐸 𝑡1 𝑗
√
𝜅4
1 −
√
1 − 𝜅4
√
1 − 𝜅5 𝑒
−𝛼
2 𝐿 𝑎𝑑−𝑗𝑘 𝑛 𝐿 𝑎𝑑
,
(14)
𝐸 𝑏 =
𝐸 𝑡1 𝑗
√
𝜅4
1 −
√
1 − 𝜅4
√
1 − 𝜅5 𝑒
−𝛼
2 𝐿 𝑎𝑑−𝑗𝑘 𝑛 𝐿 𝑎𝑑
·
√
1 − 𝜅5 𝑒
−𝛼
2
𝐿 𝑎𝑑
2 −𝑗𝑘 𝑛
𝐿 𝑎𝑑
2 , (15)
where 𝜅4 and 𝜅5 are the coupling coefficients of the
add/drop filter system, 𝐿 𝑎𝑑 = 2𝜋 𝑅 𝑎𝑑 and 𝑅 𝑎𝑑 is the
radius of the add/drop system. The output powers
from the add/drop filter system are given by Eqs. (16)
and (17), where 𝐸 𝑡3 and 𝐸 𝑡4 are the electric field out-
puts of the through and drop ports of the system,
respectively.
𝐼 𝑡3
𝐼 𝑡1
=
⃒
⃒
⃒
⃒
𝐸 𝑡3
𝐸 𝑡1
⃒
⃒
⃒
⃒
2
=
[︁
1 − 𝜅4 − 2
√
1 − 𝜅4
√
1 − 𝜅5 𝑒
−𝛼
2 𝐿 𝑎𝑑
cos(𝑘 𝑛 𝐿 𝑎𝑑)
+ (1 − 𝜅5)𝑒−𝛼𝐿 𝑎𝑑
1 + (1 − 𝜅4)(1 − 𝜅5)𝑒−𝛼𝐿 𝑎𝑑
− 2
√
1 − 𝜅4
√
1 − 𝜅5 𝑒
−𝛼
2 𝐿 𝑎𝑑
cos(𝑘 𝑛 𝐿 𝑎𝑑)
]︁−1
,
(16)
𝐼 𝑡4
𝐼 𝑡1
=
⃒
⃒
⃒
⃒
𝐸 𝑡4
𝐸 𝑡1
⃒
⃒
⃒
⃒
2
=
[︁
𝜅4 𝜅5 𝑒
−𝛼
2 𝐿 𝑎𝑑
1 + (1 − 𝜅4)(1 − 𝜅5)𝑒−𝛼𝐿 𝑎𝑑
− 2
√
1 − 𝜅4
√
1 − 𝜅5 𝑒
−𝛼
2 𝐿 𝑎𝑑
cos(𝑘 𝑛 𝐿 𝑎𝑑)
]︁
.
(17)
These nonlinear equations of the output powers can be
simulated in which the dark and bright multisolitons
can be generated.[18]
Gaussian beams with central wavelength of
1.55 µm and power of 600 mW are introduced into the
add and input ports of the PANDA ring resonator.
The simulated result, based on solution of the nonlin-
ear equations for the input power, propagating inside
the fiber system has been shown in Fig. 2. The fiber
system has nonlinearity of the Kerr effect type, where
104205-2

3. CHIN. PHYS. LETT. Vol. 28, No. 10 (2011) 104205
the linear and nonlinear refractive indices of the sys-
tem are 𝑛0 = 3.34 and 𝑛2 = 3.2 × 10−17
, respectively.
In Fig. 2, the coupling coefficients of the PANDA ring
resonator are given as 𝜅0=0.2, 𝜅1=0.35, 𝜅2=0.1 and
𝜅3=0.95, respectively, and 𝛾 = 𝛾1 = 𝛾2 = 0.1. The
radius of the centered ring of the PANDA system
has been chosen as 𝑅PANDA = 300 nm, where the
radii of the right and left rings are 𝑅 𝑟 = 180 nm and
𝑅 𝐿 = 200 nm, respectively. The output soliton sig-
nals are amplified and tuned using the add port of
the system. Figures 2(a) and 2(b) show the powers in
the form of chaotic signals before entering the right
ring of the PANDA system and the amplification of
signals during propagation of light inside right ring,
respectively, where Figs. 2(c) and 2(d) show the pow-
ers before entering the left ring and the amplification
of signals within the right ring, respectively. We find
that the signals are stable and seen within the system
where the chaotic signals are generated at the through
port shown in Fig. 2(e).
Add-drop filter
RL
Rr
PANDA
Et1
EL
Ea
Eb
Multi Soliton, Et3
Input Gaussian
Beam, Ei1 at input port
Input Gaussian beam, Ei2
at addport
E1
E0
E2E3
E4
K4K1
K3
K0
K2
K5
Et2 (Output)
Et4 (Output)
Right ringLeft ring
Fig. 1. Schematic diagram of a PANDA ring resonator
connected to an add/drop filter system.
0
0.5
1
1.5
|E1|2(W)|E3|2(W)
|E2|2(W)|E4|2(W)
0
1
2
3
4
5
1.5 1.52 1.54 1.56 1.58 1.6
0
0.5
1
1.5
1.5 1.52 1.54 1.56 1.58 1.6
0
0.5
1
1.5
2
2.5
1.53 1.535 1.54 1.545 1.55 1.555 1.56 1.565 1.57
0
1
2
3
4
5
Wavelength (mm)
Throughput|Et1|2(W)
(c) (d)
(b)(a)
(e)
Fig. 2. Multisoliton signal generation using the PANDA
ring resonator system, where (a), (b), (c) and (d) are pow-
ers inside the PANDA system and (e) is the output power
from the throughput.
Chaotic signals can be used in secured optical com-
munication in which the information is input into
the signals. In order to retrieve the information from
the chaotic signals, an add/drop filter system is used.
This system filters the chaotic signals and generates
a multi-optical soliton, which is used to improve the
capacity of the system, making it applicable to long
distance communication. In order to generate a multi-
optical soliton, the chaotic signals from the PANDA
ring resonator are input into the add/drop filter sys-
tem. Therefore the proposed system is suitable to en-
hance both the security and the capacity of optical sig-
nals. Figures 3(a) and 3(b) show the generation of mul-
tisolitons in the form of dark solitons and the expan-
sion of the through port signals, respectively, where
Figs. 3(c) and 3(d) represent multisolitons in the form
of bright solitons and the expansion of the drop port
signals, respectively. The coupling coefficients of the
add/drop filter system are given as 𝜅4 = 0.9, 𝜅5 = 0.5,
where the radius of the ring is 𝑅 𝑎𝑑 = 100 µm.
(a) (b)
(c) (d)
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Ethrough(W)EDrop(W)
1.5 1.52 1.54 1.56 1.58 1.6
0.4
0.5
0.6
0.7
0.8
Wavelength (mm)
1.547 1.549 1.551 1.553
Wavelength (mm)
FWHM=425 pm
FSR=1.145 nm
Fig. 3. Output multisoliton signal generation using an
add/drop filter system: (a) dark soliton at the through
port, (b) expansion of a multi dark soliton, (c) bright
soliton at tge drop port, and (d) expansion of a multi
bright soliton with an FWHM and an FSR of 425 pm and
1.145 nm, respectively.
Increases in the communication channel and net-
work capacity can be achieved by using different soli-
ton bands or central wavelengths, as shown in Fig. 3.
Apart from communication applications, the idea of
a personnel wavelength (network) is practical for the
large demand user due to un-limited wavelength dis-
crepancy, whereas a specific soliton band can be gener-
ated using the proposed system. There is potential for
soliton bands to be generated and used in many appli-
cations, such as multi color holography, medical tools,
security imaging and transparent holography and de-
tection.
In conclusion, extensive chaotic signals can be
formed by using a PANDA ring resonator system. This
system is connected to an add/drop filter system in
order to generate a multi optical soliton. Gaussian
beams with central wavelength of 1.55 µm are intro-
duced into the input and add ports of the PANDA
system, which are sufficient to generate a high ca-
pacity soliton. In this case, the interior signals of the
104205-3

4. CHIN. PHYS. LETT. Vol. 28, No. 10 (2011) 104205
PANDA system can be controlled and tuned. Gener-
ated chaotic signals from the PANDA system can be
input into the add/drop filter system. The add/drop
system will filter the chaotic signals in which a multi-
soliton with FWHM and FSR of 425 pm and 1.145 nm
can be generated.
The authors would like to thank KMITL, Thai-
land and UTM for providing the research facilities.
The authors acknowledge the IDF financial support
from UTM.
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