CHIN.PHYS. LETT. Vol. 28, No. 10 (2011) 104205

Simulation and Analysis of Multisoliton Generation Using a PANDA RingResonator System

I. S. Amiri*, A. Afroozeh, M. BahadoranDepartment 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. Thissystem 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 nonlinearmedium. The present simulation results show that multisolitons can be controlled by using additional Gaussianpulses input into the add port of the PANDA system. For the soliton pulse in the microring device, a balanceshould be achieved between dispersion and nonlinear lengths. Chaotic output signals from the PANDA ringresonator are input into the add/drop filter system. Chaotic signals can be filtered by using the add/drop filtersystem, in which multi dark and bright solitons can be generated. In this work multi dark and bright solitonswith an FWHM and an FSR of 425 pm and 1.145 nm are generated, respectively, where the Gaussian pulse witha central wavelength of 1.55µm 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 ofcommunication channels.[1] The high optical output ofthe ring resonator system is of benefit to long distancecommunication links.[2] Two techniques can be used togenerate soliton pulses. First, soliton pulses can be ob-tained using a ring resonator system where large am-plified signals are achieved. Second, a Gaussian solitoncan be generated in a simple system arrangement.[3]

This application becomes an attractive tool in the areaof photonics for soliton generation and investigation.The advantage of using pumped solitons or Gaussiansolitons 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 commonGaussian pulse for soliton studies.[5] In practice, in-tensive pulses can be obtained by using erbium-dopedfibers (EDFs) and semiconductor amplifiers incorpo-rated with the experimental setup.[6] A Gaussian pulseis used to form a multi soliton using a ring resonator.[7]

In this work, a laser source such as a Gaussianpulse with a central wavelength of 1.55µm is used. Anonlinear 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 andleft sides.[8] To form the multifunction operations ofthe PANDA system, for instance, to control, tune andamplify an additional Gaussian pulse is introducedinto 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 becontrolled. Therefore, a PANDA ring resonator canbe connected to an add/drop filter system in order tofilter noisy and chaotic signals. The nonlinear equa-tions of the system due to the Kerr effect nonlinearitytype can be analyzed and simulated.

The proposed system consists of a PANDA ringresonator connected to an add/drop filter system, asshown 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 effectcauses the refractive index 𝑛 of the medium, expressedby

𝑛 = 𝑛0 + 𝑛2𝐼 = 𝑛0 +𝑛2

𝐴eff𝑃, (1)

where 𝑛0 and 𝑛2 are the linear and nonlinear refractiveindexes, respectively. 𝐼 and 𝑃 are the optical intensityand the power, respectively. 𝐴eff is the effective modecore area of the device.[9] For an add/drop optical fil-ter design, the effective mode core areas range from0.50 to 0.10µm2. The parameters were obtained byusing 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 systemare given by[12]

𝐸𝑖1(𝑡) = 𝐸𝑖2(𝑡) = 𝐸𝑖0 exp[( 𝑧

2𝐿𝐷

)− 𝑖𝜔0𝑡

], (2)

where 𝐸𝑖0 and 𝑧 are the optical field amplitude andpropagation 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 ofthe signal is 𝜔0.[13] The nonlinear condition of themedium causes the gaussian beam to propagate as

*Corresponding author. Email: isafiz@yahoo.comc○ 2011 Chinese Physical Society and IOP Publishing Ltd

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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 calleda temporal and spatial soliton. Soliton pulses prop-agate within the microring device when the balancebetween the dispersion length (𝐿D) and the nonlin-ear length (𝐿NL = 1/Γ𝜑NL) is achieved. Therefore𝐿D = 𝐿NL, where Γ = 𝑛2 × 𝑘0 is the length scaleover which dispersive or nonlinear effects make thebeam become wider or narrower.[14] For the PANDAring resonator, the output signals inside the systemare given as follows:[15,16]

𝐸1 =√1− 𝛾1(

√1− 𝜅1𝐸4 + 𝑗

√𝜅1𝐸𝑖1), (3)

𝐸2 = 𝐸0𝐸1𝑒−𝛼

2𝐿2 −𝑗𝑘𝑛

𝐿2 , (4)

where 𝜅1, 𝛾1 and 𝛼 are the intensity coupling coeffi-cient, fractional coupler intensity loss and attenuationcoefficient, respectively, 𝑘𝑛 = 2𝜋

𝜆 is the wave propaga-tion number, 𝜆 is the input wavelength light field and𝐿 = 2𝜋𝑅PANDA where, 𝑅PANDA is the radius of thePANDA system, which is 300 nm. The electric field ofthe small ring at the right side of the PANDA ringsystem is given as

𝐸0 = 𝐸1

√(1− 𝛾)(1− 𝜅0) − (1− 𝛾)𝑒−

𝛼2 𝐿1−𝑗𝑘𝑛𝐿1

1−√1− 𝛾

√1− 𝜅0𝑒−

𝛼2 𝐿1−𝑗𝑘𝑛𝐿1

,

(5)where 𝐿1 = 2𝜋 𝑅𝑟 and 𝑅𝑟 is the radius of the rightring. The light fields of the left side of PANDA ringresonator can be expressed as

𝐸3 =√1− 𝛾2[

√1− 𝜅2𝐸2 + 𝑗

√𝜅2𝐸𝑖2], (6)

𝐸4 = 𝐸0𝐿𝐸3𝑒−𝛼

2𝐿2 −𝑗𝑘𝑛

𝐿2 , (7)

where,

𝐸0𝐿 = 𝐸3

√(1− 𝛾)(1− 𝜅3) − (1− 𝛾)𝑒−

𝛼2 𝐿2−𝑗𝑘𝑛𝐿2

1−√1− 𝛾

√1− 𝜅3𝑒−

𝛼2 𝐿2−𝑗𝑘𝑛𝐿2

,

(8)where 𝐿2 = 2𝜋𝑅𝐿 and 𝑅𝐿 is the left ring radius. Inorder to simplify these equations, the parameters of𝑥1, 𝑥2, 𝑦1 and 𝑦2 are defined as

𝑥1 = (1− 𝛾1)12 , 𝑥2 = (1− 𝛾2)

12 ,

𝑦1 = (1− 𝜅1)12 , 𝑦2 = (1− 𝜅2)

12 .

Therefore,

𝐸1 =𝑗𝑥1

√𝜅1𝐸𝑖1 + 𝑗𝑥1𝑥2𝑦1

√𝜅2𝐸0𝐿𝐸𝑖2𝑒

−𝛼2

𝐿2 −𝑗𝑘𝑛

𝐿2

1− 𝑥1𝑥2𝑦1𝑦2𝐸0𝐸0𝐿𝑒−𝛼2 𝐿−𝑗𝑘𝑛𝐿

,(9)

𝐸3 = 𝑥2𝑦2𝐸0𝐸1𝑒−𝛼

2𝐿2 −𝑗𝑘𝑛

𝐿2 + 𝑗𝑥2

√𝜅2𝐸𝑖2, (10)

𝐸4 = 𝑥2𝑦2𝐸0𝐸0𝐿𝐸1𝑒−𝛼

2 𝐿−𝑗𝑘𝑛𝐿

+ 𝑗𝑥2√𝜅2𝐸0𝐿𝐸𝑖2𝑒

−𝛼2

𝐿2 −𝑗𝑘𝑛

𝐿2 . (11)

Therefore, the output powers through and drop portsof the PANDA ring resonator can be expressed as

𝐸𝑡1and 𝐸𝑡2 and are given as

𝐸𝑡1 = 𝐴𝐸𝑖1 −𝐵𝐸𝑖2𝑒−𝛼

2𝐿2 −𝑗𝑘𝑛

𝐿2 [𝐶𝐸𝑖1𝐺

2 +𝐷𝐸𝑖2𝐺3

1− 𝐹𝐺2],

(12)

𝐸𝑡2 = 𝑥2𝑦2𝐸𝑖2[𝐴√𝜅1𝜅2𝐸0𝐸𝑖1𝐺+ 𝐷

𝑥1√𝜅1𝐸0𝐿

𝐸𝑖2𝐺2

1− 𝐹𝐺2],

(13)

where 𝐴 = 𝑥1𝑥2,𝐵 = 𝑥1𝑥2𝑦2√𝜅1𝐸0𝐿, 𝐶 =

𝑥21𝑥2𝜅1

√𝜅2𝐸0𝐸0𝐿, 𝐷 = (𝑥1𝑥2)

2𝑦1𝑦2√𝜅1𝜅2𝐸0𝐸

20𝐿,

𝐺 =(𝑒−

𝛼2

𝐿2 −𝑗𝑘𝑛

𝐿2

)and 𝐹 = 𝑥1𝑥2𝑦1𝑦2𝐸0𝐸0𝐿.

𝐸𝑡1 output from the PANDA system can be inputinto the add/drop filter system which is made of a ringresonator coupled to two fiber waveguides with properparameters.[17] The light fields inside the add/drop fil-ter system are given as

𝐸𝑎 =𝐸𝑡1𝑗

√𝜅4

1−√1− 𝜅4

√1− 𝜅5𝑒

−𝛼2 𝐿𝑎𝑑−𝑗𝑘𝑛𝐿𝑎𝑑

,(14)

𝐸𝑏 =𝐸𝑡1𝑗

√𝜅4

1−√1− 𝜅4

√1− 𝜅5𝑒

−𝛼2 𝐿𝑎𝑑−𝑗𝑘𝑛𝐿𝑎𝑑

·√1− 𝜅5𝑒

−𝛼2

𝐿𝑎𝑑2 −𝑗𝑘𝑛

𝐿𝑎𝑑2 , (15)

where 𝜅4 and 𝜅5 are the coupling coefficients of theadd/drop filter system, 𝐿𝑎𝑑 = 2𝜋 𝑅𝑎𝑑 and 𝑅𝑎𝑑 is theradius of the add/drop system. The output powersfrom the add/drop filter system are given by Eqs. (16)and (17), where 𝐸𝑡3 and 𝐸𝑡4 are the electric field out-puts of the through and drop ports of the system,respectively.

𝐼𝑡3𝐼𝑡1

=

𝐸𝑡3

𝐸𝑡1

2=[1− 𝜅4 − 2

√1− 𝜅4

√1− 𝜅5𝑒

−𝛼2 𝐿𝑎𝑑 cos(𝑘𝑛𝐿𝑎𝑑)

+ (1− 𝜅5)𝑒−𝛼𝐿𝑎𝑑1 + (1− 𝜅4)(1− 𝜅5)𝑒

−𝛼𝐿𝑎𝑑

− 2√1− 𝜅4

√1− 𝜅5𝑒

−𝛼2 𝐿𝑎𝑑 cos(𝑘𝑛𝐿𝑎𝑑)

]−1

,(16)

𝐼𝑡4𝐼𝑡1

=

𝐸𝑡4

𝐸𝑡1

2=

[𝜅4𝜅5𝑒

−𝛼2 𝐿𝑎𝑑1 + (1− 𝜅4)(1− 𝜅5)𝑒

−𝛼𝐿𝑎𝑑

− 2√1− 𝜅4

√1− 𝜅5𝑒

−𝛼2 𝐿𝑎𝑑 cos(𝑘𝑛𝐿𝑎𝑑)

].

(17)

These nonlinear equations of the output powers can besimulated in which the dark and bright multisolitonscan be generated.[18]

Gaussian beams with central wavelength of1.55µm and power of 600 mW are introduced into theadd and input ports of the PANDA ring resonator.The simulated result, based on solution of the nonlin-ear equations for the input power, propagating insidethe fiber system has been shown in Fig. 2. The fibersystem has nonlinearity of the Kerr effect type, where

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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 ringresonator are given as 𝜅0=0.2, 𝜅1=0.35, 𝜅2=0.1 and𝜅3=0.95, respectively, and 𝛾 = 𝛾1 = 𝛾2 = 0.1. Theradius of the centered ring of the PANDA systemhas been chosen as 𝑅PANDA = 300nm, where theradii of the right and left rings are 𝑅𝑟 = 180 nm and𝑅𝐿 = 200nm, respectively. The output soliton sig-nals are amplified and tuned using the add port ofthe system. Figures 2(a) and 2(b) show the powers inthe form of chaotic signals before entering the rightring of the PANDA system and the amplification ofsignals 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 amplificationof signals within the right ring, respectively. We findthat the signals are stable and seen within the systemwhere the chaotic signals are generated at the throughport shown in Fig. 2(e).

Add-drop filter

RLRr

PANDA

Et1

ELEa

Eb

Multi Soliton, Et3

Input Gaussian Beam, Ei1 at input port

Input Gaussian beam, Ei2at addport

E1E0

E2E3

E4K4K1

K3K0

K2

K5Et2 (Output)

Et4 (Output)

Right ringLeft ring

Fig. 1. Schematic diagram of a PANDA ring resonatorconnected to an add/drop filter system.

0

0.5

1

1.5

|E1|2

(W

)|E

3|2

(W

)

|E2|2

(W

)|E

4|2

(W

)

0

1

2

3

4

5

1.5 1.52 1.54 1.56 1.58 1.60

0.5

1

1.5

1.5 1.52 1.54 1.56 1.58 1.60

0.5

1

1.5

2

2.5

1.53 1.535 1.54 1.545 1.55 1.555 1.56 1.565 1.570

1

2

3

4

5

Wavelength (mm)

Thro

ughput |E

t1|2

(W

)

(c) (d)

(b)(a)

(e)

Fig. 2. Multisoliton signal generation using the PANDAring resonator system, where (a), (b), (c) and (d) are pow-ers inside the PANDA system and (e) is the output powerfrom 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 fromthe chaotic signals, an add/drop filter system is used.This system filters the chaotic signals and generatesa multi-optical soliton, which is used to improve thecapacity of the system, making it applicable to longdistance communication. In order to generate a multi-optical soliton, the chaotic signals from the PANDAring 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, whereFigs. 3(c) and 3(d) represent multisolitons in the formof bright solitons and the expansion of the drop portsignals, respectively. The coupling coefficients of theadd/drop filter system are given as 𝜅4 = 0.9, 𝜅5 = 0.5,where the radius of the ring is 𝑅𝑎𝑑 = 100µm.

(a) (b)

(c) (d)

0.2

0.3

0.4

0.5

0.6

0.7

0.8E

thro

ugh (

W)

ED

rop (

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 anadd/drop filter system: (a) dark soliton at the throughport, (b) expansion of a multi dark soliton, (c) brightsoliton at tge drop port, and (d) expansion of a multibright soliton with an FWHM and an FSR of 425 pm and1.145 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 ofa personnel wavelength (network) is practical for thelarge 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 forsoliton 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 beformed by using a PANDA ring resonator system. Thissystem is connected to an add/drop filter system inorder to generate a multi optical soliton. Gaussianbeams with central wavelength of 1.55µm are intro-duced into the input and add ports of the PANDAsystem, which are sufficient to generate a high ca-pacity soliton. In this case, the interior signals of the

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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 beinput into the add/drop filter system. The add/dropsystem will filter the chaotic signals in which a multi-soliton with FWHM and FSR of 425 pm and 1.145 nmcan be generated.

The authors would like to thank KMITL, Thai-land and UTM for providing the research facilities.The authors acknowledge the IDF financial supportfrom UTM.

References[1] Jukgoljun B, Pipatsart S, Jalil M A, Yupapin P P and Ali

J 2011 Optik 122 1492[2] Yuan Y, Cai Y, Qu J, Eyyubogu H T, Baykal Y and Ko-

rotkova O 2009 Opt. Express 17 17344[3] Pornsuwancharoen N, Fujii Y, Srinuanjan K and Yupapin

P P 2010 Optik 121 1863[4] Jiang H B 1991 Appl. Phys. B Photophys. Laser Chem. 53

(5-6) 347[5] Deng D and Guo Q 2007 Opt. Lett. 32 3206

[6] Liaw S K, Hsieh Y S, Cheng W L, Chang C L and Ting HF 2008 J. Opt. Network. 7 662

[7] Yupapin P P and Vanishkorn B 2011 Appl. Math. Model.35 1729

[8] Mitatha S, Piyatamrong B, Yupapin P P, Knobnob B andChaiyasoonthorn S 2011 J. Nonlin. Opt. Phys. Mater. 2085

[9] Su Y, Liu F and Li Q 2007 Proc. SPIE 6783 68732P[10] Fietz C and Shvets G 2007 Opt Lett. 32 1683[11] Kokubun Y, Hatakeyama Y, Ogata M, Suzuki S and Zaizen

N 2007 IEEE J. Sel. Top. Quantum Electron. 11 4[12] Jukgoljun B, Suwanpayak N, Teeka C and Yupapin P P

2010 Opt. Engin. 49 12[13] Agarwal G P 2007 Nonlinear Fiber Optics 4th edn (New

York: Academic)[14] Tasakorn M, Teeka C, Jomtarak R and Yupapin P P 2010

Opt. Engin. 49 075002[15] Uomwech K, Sarapat K and Yupapin P P 2010 Microwave

Opt. Technol. Lett. 52 1818[16] Phatharaworamet T, Teeka C, Jomtarak R, Mitatha S and

Yupapin P P 2010 J. Lightwave Technol. 28 2804[17] Phattaraworamet T, Jomtarak R, Mitatha S and Yupapin

P P 2011 Microwave Opt. Technol. Lett. 53 516[18] Srinuanjan K, Kamoldilok S, Tipaphong W and Yupapin P

P 2011 Optik (in press)

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