, Volume 13, Issue 2, pp 599–607 | Cite as

Arbitrary Multi-way Parallel Mathematical Operations Based on Planar Discrete Metamaterials

  • Yongle Wu
  • Zheng Zhuang
  • Li Deng
  • Yuanan Liu
  • Quan Xue
  • Zabih Ghassemlooy


Multi-way parallel mathematical operations along arbitrary transmission paths are constructed based on realizable planar discrete metamaterials in this paper. The introduced method of “computational metamaterials” is used to perform the desired mathematical operations. For producing high-efficiency devices, the function of multi-way parallel mathematical operations is indispensable in advanced analog computers. Therefore, in this paper, we propose the arbitrary transmission paths that can be implemented by the bending of the electromagnetic waves based on the finite embedded coordinate transformations, which has a strong potential to realize the function of multi-way parallel computation. Nevertheless, owing to the inherent inhomogeneous property, metamaterials are difficult to be achieved in nature currently. In order to make it possible for fabricating in practical applications, the planar discrete metamaterial is a promising medium due to its homogeneous property. Numerical simulations validate the novel and effective design method for parallel optical computation.


Multi-way Discrete metamaterials Mathematical operations Arbitrary transmission paths 



This work was supported in part by the National Natural Science Foundations of China (No.61422103, and No.61671084) and National Key Basic Research Program of China (973 Program) (No.2014CB339900).


  1. 1.
    Solla PD (1984) A history of calculating machines. IEEE Micro 4:22–52CrossRefGoogle Scholar
  2. 2.
    Clymer AB (1993) The mechanical analog computers of Hannibal Ford and William Newell. IEEE Ann Hist Comput 2:19–34CrossRefGoogle Scholar
  3. 3.
    Engheta N (2015) 150 years of Maxwell’s equations. Science 349:136–137CrossRefGoogle Scholar
  4. 4.
    Sihvola A (2014) Enabling optical analog computing with metamaterials. Science 343:144–145CrossRefGoogle Scholar
  5. 5.
    Zhu J, Song R (2009) Fast and stable computation of optical propagation in micro-waveguides with loss. Microelectron Reliab 49:1529–1536CrossRefGoogle Scholar
  6. 6.
    Bykov DA, Doskolovich LL, Bezus EA, Soifer VA (2014) Optical computation of the Laplace operator using phase-shifted Bragg grating. Opt Express 22:25084–25092CrossRefGoogle Scholar
  7. 7.
    Zhu J, Wang G (2015) High-precision computation of optical propagation in inhomogeneous waveguides. JOSA A 32:1653–1660CrossRefGoogle Scholar
  8. 8.
    Silva A, Monticone F, Castaldi G, Galdi V, Alù A, Engheta N (2014) Performing mathematical operations with metamaterials. Science 343:160–163CrossRefGoogle Scholar
  9. 9.
    AbdollahRamezani S, Arik K, Khavasi A, Kavehvash Z (2015) Analog computing using graphene-based metalines. Opt Lett 40:5239–5242CrossRefGoogle Scholar
  10. 10.
    Huang Y, Feng Y, Jiang T (2007) Electromagnetic cloaking by layered structure of homogeneous isotropic materials. Opt Express 15:11133–11141CrossRefGoogle Scholar
  11. 11.
    Gok G, Grbic A (2010) Tensor transmission-line metamaterials. IEEE Trans Antennas and Propagation 58:1559–1566CrossRefGoogle Scholar
  12. 12.
    Yi J, Burokur S N, Piau G P, Lustrac A D (2016) Coherent beam control with an all dielectric transformation optics based lens. Scientific Reports 6Google Scholar
  13. 13.
    Rahm M, Roberts DA, Pendry JB, Smith DR (2008) Transformation-optical design of adaptive beam bends and beam expanders. Opt Express 16:11555–11567CrossRefGoogle Scholar
  14. 14.
    Pendry JB, Schurig D, Smith DR (2006) Controlling electromagnetic fields. Science 312:1780–1782CrossRefGoogle Scholar
  15. 15.
    Jiang WX, Cui TJ, Zhou XY, Yang XM, Cheng Q (2008) Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials. Phys Rev E 78:066607CrossRefGoogle Scholar
  16. 16.
    Dougherty ER, Kim S, Chen Y (2000) Coefficient of determination in nonlinear signal processing. Signal Process 80:2219–2235CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Beijing Key Laboratory of Work Safety Intelligent Monitoring, School of Electronic EngineeringBeijing University of Posts and TelecommunicationsBeijingChina
  2. 2.Beijing Key Laboratory of Network System Architecture and Convergence, School of Information and Communication EngineeringBeijing University of Posts and TelecommunicationsBeijingChina
  3. 3.The State Key Laboratory of Millimeter Waves, Department of Electronic Engineering, CityU Shenzhen Research InstituteCity University of Hong KongKowloon TongHong Kong
  4. 4.Optical Communications Research Group, NCRLab, Faculty of Engineering and EnvironmentNorthumbria UniversityNewcastle upon TyneUK

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