Metamaterial Lens of Specifiable Frequency-Dependent Focus and Adjustable Aperture for Electron Cyclotron Emission in the DIII-D Tokamak

  • K. C. Hammond
  • S. D. Massidda
  • W. J. Capecchi
  • F. A. Volpe


Electron Cyclotron Emission (ECE) of different frequencies originates at different locations in non-uniformly magnetized plasmas. For simultaneous observation of multiple ECE frequencies from the outside edge of a toroidal plasma confinement device (e.g. a tokamak), the focal length of the collecting optics should increase with the frequency to maximize the resolution on a line of sight along the magnetic field gradient. Here we present the design and numerical study of a zoned metamaterial lens with such characteristics, for possible deployment with the 83–130 GHz ECE radiometer in the DIII-D tokamak. The lens consists of a concentric array of miniaturized element phase-shifters. These were reverse-engineered starting from the desired Gaussian beam waist locations and further optimized to account for diffraction and finite-aperture effects that tend to displace the waist. At the same time we imposed high and uniform transmittance, averaged over all phase-shifters. The focal length is shown to increase from 1.32 m to 2.08 m over the frequency range of interest, as desired for low-field DIII-D discharges (B = −1.57 T). Retracting the lens to receded positions rigidly moves the waists accordingly, resulting in a good match—within a fraction of the Rayleigh length—of the EC-emitting layer positions at higher fields (up to B= −2.00 T). Further, it is shown how varying the lens aperture might move the waists “non-rigidly” to better match the non-rigid movement of the EC-emitting layers with the magnetic field. The numerical method presented is very general and can be used to engineer any dependence of the focal length on the frequency, including zero or minimal chromatic aberration.


Metamaterial lens Electron cyclotron emission (ECE) Chromatic aberration 


  1. 1.
    M. Bornatici, R. Cano, O. de Barbieri, F. Engelmann, Nuclear Fusion 23(9), 1153 (1983)CrossRefGoogle Scholar
  2. 2.
    W.H.M. Clark, Plasma Physics 25(12), 1501 (1983)CrossRefGoogle Scholar
  3. 3.
    J.L. Luxon, Nuclear Fusion 42, 614 (2002)CrossRefGoogle Scholar
  4. 4.
    R.F. Ellis, M.E. Austin, D. Taussig, in Proceedings of the 14th Joint Workshop on Electron Cyclotron Emission and Electron Cyclotron Resonance Heating (EC 14) (2006)Google Scholar
  5. 5.
    M. Born, E. Wolf, Principles of Optics, 6th edn. (Cambridge University Press, 2006)Google Scholar
  6. 6.
    D.R. Smith, J.J. Mock, A.F. Starr, D. Schurig, Physical Review E 71 (2005)Google Scholar
  7. 7.
    R.B. Greegor, C.G. Parazzoli, J.A. Nielsen, M.A. Thompson, M.H. Tanielian, D.R. Smith, Applied Physics Letters 87 (2005)Google Scholar
  8. 8.
    T. Driscoll, D.N. Basov, A.F. Starr, P.M. Rye, S. Nemat-Nasser, D. Schurig, D.R. Smith, Applied Physics Letters 88 (2006)Google Scholar
  9. 9.
    H.F. Ma, X. Chen, H.S. Xu, X.M. Yang, W.X. Jiang, T.J. Cui, Applied Physics Letters 95 (2009)Google Scholar
  10. 10.
    K. Sarabandi, N. Behdad, IEEE Transactions on Antennas and Propagation 55(5), 1239 (2007)CrossRefGoogle Scholar
  11. 11.
    L. Zhang, G. Yang, Q. Wu, J. Hua, IEEE Transactions on Magnetics 48(11), 4534 (2012)CrossRefGoogle Scholar
  12. 12.
    W.J. Capecchi, N. Behdad, F.A. Volpe, Optics Express 20(8), 8761 (2012)CrossRefGoogle Scholar
  13. 13.
    M.G. Silveirinha, Physical Review Letters 102(19), 193903 (2009)CrossRefGoogle Scholar
  14. 14.
    M.A. Al-Joumayly, N. Behdad, IEEE Transactions on Antennas and Propagation 59(12), 4542 (2011)CrossRefGoogle Scholar
  15. 15.
    M.A. Al-Joumayly, N. Behdad, IEEE Transactions on Antennas and Propagation 58(12), 4033 (2010)CrossRefGoogle Scholar
  16. 16.
    P.F. Goldsmith, Quasioptical Systems: Gaussian Beam Quasioptical Propagation and its Applications (IEEE Press, 1998)Google Scholar
  17. 17.
    J.P. Tetienne, R. Blanchard, N. Yu, P. Genevet, M.A. Kats, J.A. Fan, T. Edamura, S. Furuta, M. Yamanishi, F. Capasso, New Journal of Physics 13, 053057 (2011)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • K. C. Hammond
    • 1
  • S. D. Massidda
    • 1
  • W. J. Capecchi
    • 2
  • F. A. Volpe
    • 1
  1. 1.Department of Applied Physics and Applied MathematicsColumbia UniversityNew YorkUSA
  2. 2.Department of PhysicsUniversity of Wisconsin-MadisonMadisonUSA

Personalised recommendations