CHIN. PHYS. LETT. Vol. 28, No. 10 (2011) 104205
Simulation and Analysis of Multisoliton Generation Using a PANDA Ring
Reso...
CHIN. PHYS. LETT. Vol. 28, No. 10 (2011) 104205
soliton pulses while its temporal and spatial width in-
variances are reta...
CHIN. PHYS. LETT. Vol. 28, No. 10 (2011) 104205
the linear and nonlinear refractive indices of the sys-
tem are 𝑛0 = 3.34 ...
CHIN. PHYS. LETT. Vol. 28, No. 10 (2011) 104205
PANDA system can be controlled and tuned. Gener-
ated chaotic signals from...
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Simulation and Analysis of Multisoliton Generation Using a PANDA Ring Resonator System

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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.

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Simulation and Analysis of Multisoliton Generation Using a PANDA Ring Resonator System

  1. 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. 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. 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. 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. 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, Eyyuboˇgu 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 H F 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 and Chaiyasoonthorn S 2011 J. Nonlin. Opt. Phys. Mater. 20 85 [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) 104205-4

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