Journal of Computational Electronics

, Volume 14, Issue 2, pp 574–581 | Cite as

Binary optimization of gold nano-rods for designing an optical modulator



An optical modulator with ultra small plasmonic nano rods that can filter the coherent optical frequency is developed. The performance of optical modulator based on dimmer metal nano rods on the top of silicon waveguides as coherent perfect absorber (CPA) is studied. In the proposed model, the optical modulator is excited by two monochromatic incident plan waves with the same frequencies and two polar angles “\(\uptheta =0\)” and “\(\uptheta =\Pi /2\)”. When the signal with \(\uptheta =0\) is applied to the modulator separately, the incident wave transmits from the first path and suppresses for the second one, while when both signals are applied to the modulator simultaneously, the CPA occurs for the first path and the ligthwave transmits from the second one. Therefore for two paths there are two states. “on” state when ligthwave transmitted from each path and “off” state when ligthwave suppressed. In this case two paths consist of different array of nano rods locations. Since the CPA efficiency depends strongly on the number of plasmonic nano rods and the nano rods location, a new efficient binary optimization method based the teaching–learning-based optimization (TLBO) algorithm is proposed to design an optimized array of the plasmonic nano-rods in order to achieve the maximum absorption coefficient in the ‘off’ state and the minimum absorption coefficient in the ‘on’ state. In Binary TLBO, a group of learner consists a matrix with binary entries, control the presence (‘1’) or the absence (‘0’) of nano rods in the array.


Plasmonic Modulator Finite Difference Time Domain Discrete Dipole Approximation Binary Optimization Plasmonic Device 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Vuckovic, J., Loncar, M., Scherer, A.: Surface plasmon enhanced light-emitting diode. IEEE J. Quantum Electron. 36, 1131–1144 (2000)CrossRefGoogle Scholar
  2. 2.
    Hobson, P.A., Wedge, S., Wasey, J.A.E., Sage, I., Barnes, W.L.: Surface plasmon mediated emission from organic light emitting diodes. Adv. Mater. 14, 1393–1396 (2002)CrossRefGoogle Scholar
  3. 3.
    Gontijo, I., Borodisky, M., Yablonvitch, E., Keller, S., Mishra, U.K., DenBaars, S.P.: Enhancement of spontaneous recombination rate in a quantum well by resonant surface plasmon coupling. Phys. Rev. B 60, 11564–11567 (1999)CrossRefGoogle Scholar
  4. 4.
    Okamoto, K., Niki, I., Shvartser, A., Narukawa, Y., Mukai, T., Scherer, A.: Surface-plasmon-enhanced light emitters based on InGaN quantum wells. Nat. Mater. 3, 601–605 (2004)CrossRefGoogle Scholar
  5. 5.
    Homeyer, E., Mattila, P., Oksanen, J., et al.: Enhanced light extraction from InGaN/GaN quantum wells with silver gratings. J Appl. Phys. Lett. 102, 081110 (2013)CrossRefGoogle Scholar
  6. 6.
    Maier, S.A.: Plasmonics: Fundamentals and Applications. Springer, New York (2007)Google Scholar
  7. 7.
    Barnes, W.L., Dereux, A., Ebbesen, T.W.: Surface plasmon subwavelength optics. Nature 424(6950), 824–830 (2003)CrossRefGoogle Scholar
  8. 8.
    Sorger, V.J., Zhang, X.: Physics. Spotlight on plasmon lasers. Science 333(6043), 709–710 (2011)CrossRefGoogle Scholar
  9. 9.
    Hill, M.T., Oei, Y.S., Smalbrugge, B., Zhu, Y., Vries, T.D., Veldhoven, P.J.V., Otten, F.W.M.V., Eijkemans, T.J., Turkiewicz, J.P., Waardt, H.D., Geluk, E.J., Kwon, S.H., Lee, Y.H., Notzel, R., Smit, M.K.: Lasing in metallic-coated nanocavities. Nat. Photonics 1(10), 589–594 (2007)CrossRefGoogle Scholar
  10. 10.
    Yu, K., Lakhani, A., Wu, M.C.: Subwavelength metal-optic semiconductor nanopatch lasers. Opt. Express 18(9), 8790–8799 (2010)CrossRefGoogle Scholar
  11. 11.
    Kwon, S.H., Kang, J.H., Seassal, C., Kim, S.K., Regreny, P., Lee, Y.H., Lieber, C.M., Park, H.G.: Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity. Nano Lett. 10(9), 3679–3683 (2010)CrossRefGoogle Scholar
  12. 12.
    Dionne, J.A., Diest, K., Sweatlock, L.A., Atwater, H.A.: PlasMOStor: a metal-oxide-Si field effect plasmonic modulator. Nano Lett. 9(2), 897–902 (2009)CrossRefGoogle Scholar
  13. 13.
    Lou, F., Dai, D., Wosinski, L.: Ultracompact polarization beam splitter based on a dielectric-hybrid plasmonic-dielectric coupler. Opt. Lett. 37(16), 3372–3374 (2012)CrossRefGoogle Scholar
  14. 14.
    Mauricio, O.G., Basurto, M., Arturo, O.P., Mario, P.C., Carlos, I.T.J., Gabriel, A.C.: Electro-optic modulator of polarization for the visible spectrum region liquid crystal materials, devices, and applications IX. In: Chien, L.-C. (ed.) Proceedings of the SPIE, Vol. 5003, pp. 175–178 (2003)Google Scholar
  15. 15.
    Barrios, C.A., Lipson, M.: Modeling and analysis of high-speed electro-optic modulation in high confinement silicon waveguides using metal-oxide-semiconductor configuration. J. Appl. Phys. 96, 6008–6015 (2004)CrossRefGoogle Scholar
  16. 16.
    Kekatpure, R.D., Brongersma, M.L.: CMOS compatible high-speed electro-optical modulator. In: Proceeding of SPIE 5926, paper G1 (2005)Google Scholar
  17. 17.
    Xu, Q., Schmidt, B., Pradhan, S., Lipson, M.: Micrometre-scale silicon electro-optic modulator. Nature 435, 325–327 (2005)CrossRefGoogle Scholar
  18. 18.
    Zhang, L., Yang, J.Y., Song, M., Li, Y., Zhang, B., Beausoleil, R.G., Willner, A.E.: Microring-based modulation and demodulation of DPSK signal. Opt. Express 15, 11564–11569 (2007)CrossRefGoogle Scholar
  19. 19.
    Dingel, B., Prescod, A., Madamopoulos, N., Madabhushi, R.: Performance of ring resonator-based linear optical modulator (IMPACC) under critical coupling (CC), over coupling (OC), and under coupling (UC) conditions. In: IEEE Photonics Conference (PHO), pp. 260–261 (2011)Google Scholar
  20. 20.
    Li, Y., Stewart, L.S., Dapkus, P.D.: High speed silicon microring modulator employing dynamic intracavity energy balance. Opt. Express. 7, 7404 (2012)CrossRefGoogle Scholar
  21. 21.
    Mock, A.: Low-power all-optical switch based on time-reversed microring laser. IEEE Photonics J 6, 2229–2235 (2012)CrossRefGoogle Scholar
  22. 22.
    Song, K., Mazmuder, P.: Active terahertz spoof surface plasmon polariton switch comprising the perfect conductor metamaterial. IEEE Trans. Electron. Dev. 56(11), 2792–2799 (2009)CrossRefGoogle Scholar
  23. 23.
    Xu, Z., Song, K., Mazumder, P.: Dynamic terahertz spoof surface plasmon-polariton switch based onresonance and absorption. IEEE Trans. Electron. Dev. 58(7), 2172–2176 (2011)CrossRefGoogle Scholar
  24. 24.
    Changjun, M., Wang, P., Chen, C., Deng, Y., Lu, Y., Ming, H., Ning, T., Zhou, Y., Yang, G.: All-optical switching in subwavelength metallic grating structure containing nonlinear optical materials. Opt. Lett. 33, 869–871 (2008)CrossRefGoogle Scholar
  25. 25.
    Díaz, J.S.G., Carrier, J.P.: Graphene-based plasmonic switches at near infrared frequencies. Opt. Express 21, 15490–15504 (2013)CrossRefGoogle Scholar
  26. 26.
    Krasavin, A.V., Zheludev, N.: Active plasmonics: Controlling signals in Au/Ga waveguide using nanoscale structural transformations. Appl. Phys. Lett. 84(8), 1416–1418 (2004)CrossRefGoogle Scholar
  27. 27.
    MacDoland, K.F., Samson, Z.L., Stockman, M.I., Zheludev, N.I.: Ultrafast active plasmonics. Nat. Photonics 3(1), 55–58 (2009)CrossRefGoogle Scholar
  28. 28.
    Gomez Rivas, J., Sanchez-Gil, J.A., Kuttge, M., Bolivar, P.H., Kurz, H.: Optically switchable mirrors for surface plasmon polaritons propagating on semiconductor surfaces. Phys. Rev. B 74(24), 245324 (2006)CrossRefGoogle Scholar
  29. 29.
    Sanchez-Gil, J.A., Rivas, J.G.: Thermal switching of the scattering coefficients of terahertz surface plasmon polaritons impinging on a finite array of subwavelength grooves on semiconductor surfaces. Phys. Rev. B 73(20), 205410 (2006)CrossRefGoogle Scholar
  30. 30.
    Kalousek, R., Dub, P., Břínek, L., ŠikolaD, T.: Response of plasmonic resonant nanorods: an analytical approach to optical antennas. Opt. Express 20(16), 17916–17927 (2012)CrossRefGoogle Scholar
  31. 31.
    Hormozi-Nezhad, M.R., Karami, P., Robatjazi, H.: A simple shape-controlled synthesis of gold nanoparticles using nonionic surfactants. RSC Adv. 3, 7726–7732 (2013)CrossRefGoogle Scholar
  32. 32.
    Kawamura, G., Nogami, M., Matsuda, A.: Shape-controlled metal nanoparticles and their assemblies with optical functionalities. J. Nanomat. 2013, 631350 (2013)Google Scholar
  33. 33.
    Choi, Charles J., Semancik, Steve: Effect of interdome spacing on the resonance properties of plasmonic nanodome arrays for label-free optical sensing. Opt. Express 21, 28304–28313 (2013)CrossRefGoogle Scholar
  34. 34.
    Dühring, B.M., Sigmund, O.: Optimization of extraordinary optical absorption in plasmonic and dielectric structures. J. Opt. Soc. Am. B 30, 1154–1160 (2013)CrossRefGoogle Scholar
  35. 35.
    Becker, J., Trügler, A., Jakab, A.: The optimal aspect ratio of gold nanorods for plasmonic bio-sensing. Plasmonics J 5, 161–167 (2010)CrossRefGoogle Scholar
  36. 36.
    Taflove, A., Brodwin, M.E.: Numerical solution of steady state electromagnetic scattering problems using the time dependent Maxwell’s equations. IEEE Trans. Microw. Theory Tech. 23(8), 623–630 (1975)CrossRefGoogle Scholar
  37. 37.
    Weiland, T.: A discretization method for the solution of Maxwell’s equations for six-component fields. Arch. Elektron. Übertragungstech. 31, 116–120 (1977)Google Scholar
  38. 38.
    Harrington, R.F.: Field Computation by Moment Method. IEEE Press, Piscataway (1993)CrossRefGoogle Scholar
  39. 39.
    Kern, A.M., Martin, O.J.F.: Surface integral formulation for 3D simulations of plasmonic and high permittivity nanostructures. J. Opt. Soc. Am. A 26(4), 732–740 (2009)CrossRefMathSciNetGoogle Scholar
  40. 40.
    Gallinet, B., Kern, A.M., Martin, O.J.F.: Accurate and versatile modeling of electromagnetic scattering on periodic nanostructures with a surface integral approach. J. Opt. Soc. Am. A 27(10), 2261–2271 (2010)CrossRefGoogle Scholar
  41. 41.
    Taboada, J.M., Rivero, J., Obelleiro, F., Araújo, M.G., Landesa, L.: Method-of-moments formulation for the analysis of plasmonic nano-optical antennas. J. Opt. Soc. Am. A 28(7), 1341–1348 (2011)CrossRefGoogle Scholar
  42. 42.
    Taflove, A., Hagness, S.C.: Computational Electrodynamics: The Finite Difference Time Domain Method, 2nd edn. Artech House, Norwood (2000)Google Scholar
  43. 43.
    Jin, J.M.: The Finite Element Method in Electromagnetics, 2nd edn. John Wiley & Sons, New York (2002)MATHGoogle Scholar
  44. 44.
    Draine, B.T., Flatau, P.J.: Discrete-dipole approximation for scattering calculations. J. Opt. Soc. Am. A. 11, 1491–1499 (1994)CrossRefGoogle Scholar
  45. 45.
    Forestiere, C., Miano, G., Boriskina, S.V., Negro, L.D.: The role of nanoparticle shapes and deterministic aperiodicity for the design of nanoplasmonic arrays. Opt. Express 17, 9648–9661 (2009)CrossRefGoogle Scholar
  46. 46.
    Loke, Vincent L.Y., Mengüç, M.Pinar, Nieminen, Timo A.: Discrete dipole approximation with surface interaction: Computational toolbox for MATLAB. JQSRT 27(10), 2293–2303 (2010)Google Scholar
  47. 47.
    Le Ru, E.C., Etchegoin, P.G.: Principles of Surface-Enhanced Raman Spectroscopy and Related Plasmonic Effects, 1st edn. Elsevier, Amsterdam (2009)Google Scholar
  48. 48.
    Roa, R.V., Savsani, V.J., Vakharia, D.P.: Teacher-learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput. Aided Des. 43, 303–315 (2011)Google Scholar
  49. 49.
    Akhlaghi, M., Emami, F., Nozhat, N.: Binary TLBO algorithm assisted for designing plasmonic nano bi-pyramids-based absorption coefficient. Mod. Opt. 61(13), 1092–1096 (2014)CrossRefGoogle Scholar
  50. 50.
    Ma, Y.W., Zhang, J., Zhang, L.H., Jian, C.S., Wu, S.F.: Theoretical analysis the optical properties of multi-coupled silver nano shell particles. Plasmonics J. 6, 705–713 (2011)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Opto ElectronicShiraz University of TechnologyShirazIran

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