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Modeling optical filters based on serially coupled microring resonators using radial basis function neural network

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Abstract

In this research for the first time by using radial basis function neural network (RBFNN), filters based on serially coupled microring resonators have been modeled. Also, signal flow graph (SFG) method based on Mason’s rule has been used to simulate filters. It has been represented when RBFNN has been learned, model can extract the outputs same as what was simulated by SFG method. It has been proved that RBFNN model can properly obtain results in several cases in which some parameters of filter like the order of filter; MRRs radius; coupling coefficients; and propagation loss have been changed. In these cases to design filter by an analytical method like the SFG, we need to obtain new transfer function. Obtaining novel transfer function would make filter designating complicated in terms of calculation and simulation time while the RBFNN can match with any change as fast as possible. The RBFNN has advantages of optimization ability, straightforward topological architecture, stable generalization ability, appropriate tolerance against input noise, online learning ability, accuracy in dynamically nonlinear approximation, predictability and fast and easy learning algorithms. These properties of RBFNN make it suitable to model pliable optical systems.

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References

  • Abonyi J, Feil B, Abraham A (2005) Computational intelligence in data mining. Informatica 29(1):59

    Google Scholar 

  • Ahmed MH, Hasan S, Ali A (2015) Learning Enhancement of Radial Basis Function Neural Network with Harmony Search Algorithm. Int J Adv Soft Comput Appl 7(1):98

    Google Scholar 

  • Amiri I, Ali J, Yupapin P (2012) Enhancement of FSR and finesse using add/drop filter and PANDA ring resonator systems. Int J Mod Phys B 26(04):1250034

    Google Scholar 

  • Barwicz T, Popovic MA, Rakich PT, Watts MR, Haus HA, Ippen EP, Smith HI (2004) Microring-resonator-based add-drop filters in SiN: fabrication and analysis. Opt Express 12(7):1437

    Google Scholar 

  • Boeck R (2011) Silicon ring resonator add-drop multiplexers. Series-coupled silicon racetrack resonators and the Vernier effect: theory and measurement, Ph.D. thesis, University of British Columbia

  • Boeck R, Jaeger NA, Rouger N, Chrostowski L (2010) Series-coupled silicon racetrack resonators and the Vernier effect: theory and measurement. Opt Express 18(24):25151

    Google Scholar 

  • Bona GL, Germann R, Offrein BJ (2003) SiON high-refractive-index waveguide and planar lightwave circuits. IBM J Res Dev 47(23):239

    Google Scholar 

  • Buzzi C, Grippo L, Sciandrone M (2001) Convergent decomposition techniques for training RBF neural networks. Neural Comput 13(8):1891

    MATH  Google Scholar 

  • Chaichuay C, Yupapin PP, Saeung P (2009) The serially coupled multiple ring resonator filters and Vernier effect. Optica Applicata 39(1):91

    Google Scholar 

  • Chandrasekaran M, Muralidhar M, Krishna CM, Dixit U (2010) Application of soft computing techniques in machining performance prediction and optimization: a literature review. Int J Adv Manuf Technol 46(5–8):445

    Google Scholar 

  • Chremmos I, Schwelb O, Uzunoglu N (2010) Photonic microresonator research and applications, vol 156. Springer, Berlin

    Google Scholar 

  • Dash CSK, Behera AK, Dehuri S, Cho SB (2016) Radial basis function neural networks: a topical state-of-the-art survey. Open Comput Sci 6(1):106

    Google Scholar 

  • Dhubkarya D, Nagaria D et al (2010) Implementation of a radial basis function using VHDL. Global J Comput Sci Technol 10(10):56

    Google Scholar 

  • Diaconiła I, Leon F (2011) A learning model for intelligent agents using radial basis function neural networks with adaptive training methods, Buletinul Institutului Politehnic Din IaŞI, pp 9–20

  • Dong P, Feng NN, Feng D, Qian W, Liang H, Lee DC, Luff B, Banwell T, Agarwal A, Toliver P et al (2010) GHz-bandwidth optical filters based on high-order silicon ring resonators. Opt Express 18(23):23784

    Google Scholar 

  • Duliba KA (1991) Contrasting neural nets with regression in predicting performance in the transportation industry. In: Proceedings of the twenty-fourth annual Hawaii international conference on system sciences (IEEE), vol 4, pp 163–170

  • Fan H, Fu Z, Shao H, Wang X, Wang X (2017) Risk early warning and evaluation method for electric power SDH networks based on BP neural network algorithm. In: 2017 international conference on computer, information and telecommunication systems (CITS) (IEEE), pp 215–218

  • Gan M, Peng H, Chen L (2012) A global-local optimization approach to parameter estimation of RBF-type models. Inf Sci 197:144

    Google Scholar 

  • Goebuchi Y, Kato T, Kokubun Y (2016) Optimum arrangement of high-order series-coupled microring resonator for crosstalk reduction. Jpn J Appl Phys 45(7R):5769

    Google Scholar 

  • Guo SM, Lee CS, Hsu CY (2005) An intelligent image agent based on soft-computing techniques for color image processing. Expert Syst Appl 28(3):483

    Google Scholar 

  • Hagan MT, Demuth HB, Beale MH, De Jesús O (1996) Neural network design, vol 20. Pws Pub, Boston

    Google Scholar 

  • Hagness S, Rafizadeh D, Ho ST, Taflove A (1997) FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators. J Lightwave Technology 15(11):2154

  • Hamadneh N, Sathasivam S, Tilahun SL, Choon OH (2012) Learning logic programming in radial basis function network via genetic algorithm. J Appl Sci (Faisalabad) 12(9):840

    MATH  Google Scholar 

  • Haykin SS, Haykin SS, Haykin SS, Elektroingenieur K, Haykin SS (2009) Neural networks and learning machines. In: Neural networks and learning machines, vol 3, Pearson education: Upper Saddle River

  • Hidayat IS, Toyota Y, Torigoe O, Wada O, Koga R (2002) Application of transfer matrix method with signal flow-chart to analyze optical multi-path ring-resonator. Mem Faculty Eng Okayama Univ 36(2):73

    Google Scholar 

  • Huan HX, Hien DTT, Tue HH (2011) Efficient algorithm for training interpolation RBF networks with equally spaced nodes. IEEE Trans Neural Netw 22(6):982

    Google Scholar 

  • Ji X, Lu T, Cai W, Zhang P (2005) Discontinuous Galerkin time domain (DGTD) methods for the study of 2-D waveguide-coupled microring resonators. J Lightwave Technol 23(11):3864

    Google Scholar 

  • Karayiannis NB (1999) Reformulated radial basis neural networks trained by gradient descent. IEEE Trans Neural Netw 10(3):657

    Google Scholar 

  • Khai TQ, Ryoo YJ (2019) Design of adaptive kinematic controller using radial basis function neural network for trajectory tracking control of differential-drive mobile robot. Int J Fuzzy Logic Intell Syst 19(4):349

    Google Scholar 

  • Klein EJ (2007) Densely integrated microring-resonator based components for fiber-to-the-home applications, Ph.D. thesis, University of Twente

  • Lacey J, Payne F (1990) Radiation loss from planar waveguides with random wall imperfections. IEE Proc J Optoelectron 137(4):281

    Google Scholar 

  • Laleh MS, Razaghi M (2020) Simulation of reconfigurable double-input optical gates based on a microring flower-like structure. Part I. Basic gates. Appl Opt 59(15):4589

    Google Scholar 

  • Laleh MS, Razaghi M, Jafari O, Bevrani H (2019) Performance optimization of an optical filter based on serially coupled microring resonators using a fuzzy logic system. Opt Eng 58(2):026115

    Google Scholar 

  • Lee HS, Choi CH, Beom-Hoan O, Park DG, Kang BG, Kim SH, Lee SG, Lee EH (2004) A nonunitary transfer matrix method for practical analysis of racetrack microresonator waveguide. IEEE Photon Technol Lett 16(4):1086

    Google Scholar 

  • Liu C, Wang H, Yao P (2014) On terrain-aided navigation for unmanned aerial vehicle using b-spline neural network and extended Kalman filter. In: Proceedings of 2014 IEEE Chinese guidance, navigation and control conference (IEEE), pp 2258–2263

  • Makridakis S, Wheelwright SC, Hyndman RJ (2008) Forecasting: methods and applications. Wiley, New York

    Google Scholar 

  • Mario LY, Chin MK (2008) Optical buffer with higher delay-bandwidth product in a two-ring system. Opt Express 16(3):1796

    Google Scholar 

  • Mirjalili S, Mirjalili SM, Lewis A (2014) Let a biogeography-based optimizer train your multi-layer perceptron. Inf Sci 269:188

    MathSciNet  Google Scholar 

  • Montazer GA, Giveki D (2015) An improved radial basis function neural network for object image retrieval. Neurocomputing 168:221

    Google Scholar 

  • Mosavi M, Khishe M, Hatam Khani Y, Shabani M (2017) Training radial basis function neural network using stochastic fractal search algorithm to classify sonar dataset. Iran J Electr Electron Eng 13(1):100

    Google Scholar 

  • Narendra KS, Thathachar MA (2012) Learning automata: an introduction. Courier Corporation, London

    Google Scholar 

  • Ngo NQ, Luk SF et al (1993) Graphical representation and analysis of the Z-shaped double-coupler optical resonator. J Lightwave Technol 11(11):1782

    Google Scholar 

  • Nguyen LS, Frauendorfer D, Mast MS, Gatica-Perez D (2014) Hire me: computational inference of hirability in employment interviews based on nonverbal behavior. IEEE Trans Multimedia 16(4):1018

    Google Scholar 

  • Orr MJ et al (1996) Introduction to radial basis function networks

  • Osowski S, Herault J (1995) Signal flow graphs as an efficient tool for gradient and exact hessian determination. Complex Syst 9(1):29

    MATH  Google Scholar 

  • Poon JK, Scheuer J, Mookherjea S, Paloczi GT, Huang Y, Yariv A (2004) Matrix analysis of microring coupled-resonator optical waveguides. Opt Express 12(1):90

    Google Scholar 

  • Popovíc MA, Barwicz T, Watts MR, Rakich PT, Socci L, Ippen EP, Kärtner FX, Smith HI (2006) Multistage high-order microring-resonator add-drop filters. Opt Lett 31(17):2571

    Google Scholar 

  • Pv Tien (1971) Light waves in thin films and integrated optics. Appl Opt 10(11):2395

    Google Scholar 

  • Qasem SN, Shamsuddin SM (2011) Radial basis function network based on time variant multi-objective particle swarm optimization for medical diseases diagnosis. Appl Soft Comput 11(1):1427

    Google Scholar 

  • Rabus DG (2007) Integrated ring resonators. Springer, Berlin

    Google Scholar 

  • Razaghi M, Laleh MS (2016) Design and modeling of flower like microring resonator. Opt Commun 366:370

    Google Scholar 

  • Razaghi M, Ahmadi V, Connelly MJ (2009) Comprehensive finite-difference time-dependent beam propagation model of counterpropagating picosecond pulses in a semiconductor optical amplifier. J Lightwave Technol 27(15):3162

    Google Scholar 

  • Razaghi M, Gandomkar M, Ahmadi V, Das N, Connelly MJ (2012) Picosecond wavelength conversion using semiconductor optical amplifier integrated with microring resonator notch filter. Opt Quant Electron 44(3–5):255

    Google Scholar 

  • Schwelb O (2007) Microring resonator based photonic circuits: analysis and design. In: 2007 8th international conference on telecommunications in modern satellite, cable and broadcasting services (IEEE), pp 187–194

  • Schwenker F, Kestler HA, Palm G (2001) Three learning phases for radial- basis- function networks. Neural Netw 14(4–5):439

    MATH  Google Scholar 

  • Semouchkina E, Cao W, Mittra R (2000) Modeling of microwave ring resonators using the finite-difference time-domain method (FDTD). Microwave Opt Technol Lett 24(6):392

    Google Scholar 

  • Simon D (2002) Training radial basis neural networks with the extended Kalman filter. Neurocomputing 48(1–4):455

    MATH  Google Scholar 

  • Thandar AM, Khine MK (2012) Radial basis function (RBF) neural network classification based on consistency evaluation measure. Int J Comput Appl 54(15):69

    Google Scholar 

  • Tikk D, Kóczy LT, Gedeon TD (2003) A survey on universal approximation and its limits in soft computing techniques. Int J Approx Reason 33(2):185

    MathSciNet  MATH  Google Scholar 

  • Urbonas D, Balčytis A, Gabalis M, Vaškevičius K, Naujokaitė G, Juodkazis S, Petruškevičius R (2015) Ultra-wide free spectral range, enhanced sensitivity, and removed mode splitting SOI optical ring resonator with dispersive metal nanodisks. Opt Lett 40(13):2977

    Google Scholar 

  • Vachkov G, Stoyanov V, Christova N (2015) Growing RBF network models for solving nonlinear approximation and classification problems. In: ECMS, pp 481–487

  • Van Laarhoven PJ, Aarts EH (1987) Simulated annealing. In: Simulated annealing: theory and applications, Springer, pp 7–15

  • Van V, Absil PP, Hryniewicz J, Ho PT (2001) Propagation loss in single-mode GaAs-AlGaAs microring resonators: measurement and model. J Lightwave Technol 19(11):1734

    Google Scholar 

  • Van V, Ibrahim T, Absil P, Johnson F, Grover R, Ho PT (2002) Optical signal processing using nonlinear semiconductor microring resonators. IEEE J Sel Top Quantum Electron 8(3):705

    Google Scholar 

  • Venghaus H (2006) Wavelength filters in fibre optics, vol 123. Springer, Berlin

    Google Scholar 

  • Xiong K, Xiao X, Li X, Hu Y, Li Z, Chu T, Yu Y, Yu J (2012) CMOS-compatible reconfigurable microring demultiplexer with doped silicon slab heater. Opt Commun 285(21–22):4368

    Google Scholar 

  • Yariv A (2002) Critical coupling and its control in optical waveguide-ring resonator systems. IEEE Photon Technol Lett 14(4):483

    Google Scholar 

  • Yu J, Duan H (2013) Artificial bee colony approach to information granulation-based fuzzy radial basis function neural networks for image fusion. Opt Int J Light Electron Opt 124(17):3103

    Google Scholar 

  • Yu H, Reiner PD, Xie T, Bartczak T, Wilamowski BM (2014) An incremental design of radial basis function networks. IEEE Trans Neural Netw Learn Syst 25(10):1793

    Google Scholar 

  • Yu B, He X (2006) Training radial basis function networks with differential evolution. In: Proceedings of IEEE international conference on granular computing, Citeseer, pp 369–372

  • Yupapin P, Teeka C, Ali J (2012) Nanoscale nonlinear Panda ring resonator. CRC Press, New York

    Google Scholar 

  • Zhang Q, Li B (2014) A low-cost GPS/INS integration based on UKF and BP neural network. In: Fifth international conference on intelligent control and information processing (IEEE), pp 100–107

  • Zhang W, Luo Q, Zhou Y (2009) A method for training RBF neural networks based on population migration algorithm. In: 2009 international conference on artificial intelligence and computational intelligence (IEEE), vol 1, pp 165–169

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Correspondence to Mohammad Razaghi.

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Seifi Laleh, M., Razaghi, M. & Bevrani, H. Modeling optical filters based on serially coupled microring resonators using radial basis function neural network. Soft Comput 25, 585–598 (2021). https://doi.org/10.1007/s00500-020-05170-6

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