Abstract
Determination of accurate modeling parameters of optical materials prior to defining the materials in the simulation model is fundamentally important to obtain simulation results close to the experimental ones. However, extracting modeling parameters of optical materials is inherently difficult because it involves fitting both real and imaginary parts of the relative permittivity using a single set of parameters. In this paper, an evolutionary algorithm called differential evolution (DE) has been utilized to extract the optical modeling parameters of graphene oxide. The performance of DE to find the optimal results has been analyzed by using different objective functions and boundary values. Two objective functions are used out of which one is proposed by us. Root-means-square (RMS) deviation, a measure of accuracy of the numerically obtained results has been determined for each case. From the obtained results it has been found that the DE algorithm extracted the optical modeling parameters successfully with very small RMS deviation for both real and imaginary parts of the complex relative permittivity.
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Smith DR, Pendry JB, Wiltshire MC (2004) Metamaterials and negative refractive index. Science 305(5685):788–792
Shalaev VM (2007) Optical negative-index metamaterials. Nat photonics 1(1):41–48
Shalaev VM, Cai W, Chettiar UK, Yuan H-K, Sarychev AK, Drachev VP, Kildishev AV (2005) Negative index of refraction in optical metamaterials. Opt Lett 30(24):3356–3358
West PR, Ishii S, Naik GV, Emani NK, Shalaev VM, Boltasseva A (2010) Searching for better plasmonic materials. Laser Photonics Rev 4(6):795–808
Aspnes DE, Studna AA (1983) Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV. Phys Rev B 27(2):985–1009
Boltasseva A, Shalaev VM (2008) Fabrication of optical negative-index metamaterials: Recent advances and outlook. Metamaterials 2(1):1–17
Coroama VC, Hilty LM, Heiri E, Horn FM (2013) The direct energy demand of internet data flows. J Ind Ecol 17(5):680–688
Chen Y-K (2012) Challenges and opportunities of internet of things. In: 17th Asia and South Pacific design automation conference (ASP-DAC), 2012. IEEE, pp 383–388
Gubbi J, Buyya R, Marusic S, Palaniswami M (2013) Internet of things (IoT): a vision, architectural elements, and future directions. Futur Gener Comput Syst 29(7):1645–1660
Bangerter B, Talwar S, Arefi R, Stewart K (2014) Networks and devices for the 5G era. IEEE Commun Mag 52(2):90–96
Miorandi D, Sicari S, De Pellegrini F, Chlamtac I (2012) Internet of things: Vision, applications and research challenges. Ad Hoc Netw 10(7):1497–1516
Saber MG, Sagor RH (2015) Design and study of nano-plasmonic couplers using aluminium arsenide and alumina. IET Optoelectron 9(3):125–130
Saber MG, Sagor RH (2014) Design and analysis of a gallium lanthanum sulfide based nanoplasmonic coupler yielding 67 % efficiency. Optik-Int J Light Electron Opt 125(18):5374–5377
Sagor RH, Amin MR, Saber MG (2014) Design of a simple integrated coupler for SPP excitation in a dielectric coated Ag thin film. Chin Phys Lett 31(6):064201
Rakic AD, Djurišic AB, Elazar JM, Majewski ML (1998) Optical properties of metallic films for vertical-cavity optoelectronic devices. Appl Opt 37(22):5271–5283
Pernice WHP, Payne FP, Gallagher DFG (2007) A general framework for the finite-difference time-domain simulation of real metals. IEEE Trans Antennas Propag 55(3):916–923
Clegg J, Robinson M (2012) A genetic algorithm for optimizing multi-pole Debye models of tissue dielectric properties. Phys Med Biol 57(19):6227
Kelley DF, Destan TJ, Luebbers RJ (2007) Debye function expansions of complex permittivity using a hybrid particle swarm-least squares optimization approach. IEEE Trans Antennas Propag 55(7):1999–2005
Kildishev AV, Chettiar UK, Liu Z, Shalaev VM, Kwon D-H, Bayraktar Z, Werner DH (2007) Stochastic optimization of low-loss optical negative-index metamaterial. JOSA B 24(10):A34–A39
Saber MG, Sagor RH, Ahmed A (2015) A genetic algorithm based approach for the extraction of optical parameters. Silicon:1–6
Saber MG, Sagor RH (2014) Optimization of the optical properties of cuprous oxide and silicon-germanium alloy using the Lorentz and Debye models. Electron Mater Lett 10(1):267–269
Saber MG, Sagor RH (2013) Extraction of optimized parameters for Si0. 6Ge0. 4 material and SPP mode propagation through Si0. 6Ge0. 4/Ag/Si0. 6Ge0. 4 waveguide. Optoelectron Lett 9(6):454–457
Sagor RH, Saber MG, Al-Amin MT, Al Noor A (2013) An optimization method for parameter extraction of metals using modified Debye model. SpringerPlus 2(1):1–5
Deinega A, John S (2012) Effective optical response of silicon to sunlight in the finite-difference time-domain method. Opt Lett 37(1):112–114
Sagor RH, Shahriar KA, Saber MG, Amin MR (2015) Extraction of modeling parameters for low-loss alternative plasmonic material. Procedia-Social Behav Sci 195:2061–2066
Shahriar KA, Sohel IH, Joy A, Mahamudun M, Sagor RH, Saber MG (2014) Extraction of lorentz model parameters for dielectrics and their application in nanoplasmonics. In: International conference on electrical and computer engineering (ICECE), 2014. IEEE, pp 238–241
Novoselov KS, Geim AK, Morozov S, Jiang D, Zhang Y, Dubonos SA, Grigorieva I, Firsov A (2004) Electric field effect in atomically thin carbon films. Science 306(5696):666–669
Jung I, Vaupel M, Pelton M, Piner R, Dikin DA, Stankovich S, An J, Ruoff RS (2008) Characterization of thermally reduced graphene oxide by imaging ellipsometry. J Phys Chem C 112(23):8499–8506
Storn R (1996) Differential evolution design of an IIR-filter. In: Proceedings of IEEE international conference on evolutionary computation, 1996. IEEE, pp 268–273
Storn R (1999) System design by constraint adaptation and differential evolution. IEEE Trans Evol Comput 3(1):22–34
Liu J, Lampinen J (2005) A fuzzy adaptive differential evolution algorithm. Soft Comput 9(6):448–462
Rocca P, Oliveri G, Massa A (2011) Differential evolution as applied to electromagnetics. IEEE Antennas Propag Mag 53(1):38–49
Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359
Mallipeddi R, Suganthan PN, Pan Q-K, Tasgetiren MF (2011) Differential evolution algorithm with ensemble of parameters and mutation strategies. Appl Soft Comput 11(2):1679–1696
Liu J, Qiao S (2015) A image segmentation algorithm based on differential evolution particle swarm optimization fuzzy c-means clustering. Comput Sci Inf Syst 12(2):873–893
Lei B, Tan E-L, Chen S, Ni D, Wang T, Lei H (2014) Reversible watermarking scheme for medical image based on differential evolution. Expert Syst Appl 41(7):3178–3188
Iliya S, Neri F, Menzies D, Cornelius P, Picinali L (2014) Differential evolution schemes for speech segmentation: a comparative study. In: IEEE symposium on differential evolution (SDE), 2014. IEEE, pp 1–8
Qing A, Lee CK (2010) Differential evolution in electromagnetics. Springer
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Saber, M.G., Ahmed, A. & Sagor, R.H. Performance Analysis of a Differential Evolution Algorithm in Modeling Parameter Extraction of Optical Material. Silicon 9, 723–731 (2017). https://doi.org/10.1007/s12633-016-9422-z
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DOI: https://doi.org/10.1007/s12633-016-9422-z