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
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
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
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
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
Bona GL, Germann R, Offrein BJ (2003) SiON high-refractive-index waveguide and planar lightwave circuits. IBM J Res Dev 47(23):239
Buzzi C, Grippo L, Sciandrone M (2001) Convergent decomposition techniques for training RBF neural networks. Neural Comput 13(8):1891
Chaichuay C, Yupapin PP, Saeung P (2009) The serially coupled multiple ring resonator filters and Vernier effect. Optica Applicata 39(1):91
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
Chremmos I, Schwelb O, Uzunoglu N (2010) Photonic microresonator research and applications, vol 156. Springer, Berlin
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
Dhubkarya D, Nagaria D et al (2010) Implementation of a radial basis function using VHDL. Global J Comput Sci Technol 10(10):56
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
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
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
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
Hagan MT, Demuth HB, Beale MH, De Jesús O (1996) Neural network design, vol 20. Pws Pub, Boston
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
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
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
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
Karayiannis NB (1999) Reformulated radial basis neural networks trained by gradient descent. IEEE Trans Neural Netw 10(3):657
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
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
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
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
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
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
Mario LY, Chin MK (2008) Optical buffer with higher delay-bandwidth product in a two-ring system. Opt Express 16(3):1796
Mirjalili S, Mirjalili SM, Lewis A (2014) Let a biogeography-based optimizer train your multi-layer perceptron. Inf Sci 269:188
Montazer GA, Giveki D (2015) An improved radial basis function neural network for object image retrieval. Neurocomputing 168:221
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
Narendra KS, Thathachar MA (2012) Learning automata: an introduction. Courier Corporation, London
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
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
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
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
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
Pv Tien (1971) Light waves in thin films and integrated optics. Appl Opt 10(11):2395
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
Rabus DG (2007) Integrated ring resonators. Springer, Berlin
Razaghi M, Laleh MS (2016) Design and modeling of flower like microring resonator. Opt Commun 366:370
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
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
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
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
Simon D (2002) Training radial basis neural networks with the extended Kalman filter. Neurocomputing 48(1–4):455
Thandar AM, Khine MK (2012) Radial basis function (RBF) neural network classification based on consistency evaluation measure. Int J Comput Appl 54(15):69
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
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
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
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
Venghaus H (2006) Wavelength filters in fibre optics, vol 123. Springer, Berlin
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
Yariv A (2002) Critical coupling and its control in optical waveguide-ring resonator systems. IEEE Photon Technol Lett 14(4):483
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
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
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
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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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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DOI: https://doi.org/10.1007/s00500-020-05170-6