Office of Technology Transfer – University of Michigan

Tensor Transmission-Line Metamaterials

Technology #4528

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Anthony Grbic
Managed By
Joohee Kim
Licensing Specialist, Physical Sciences & Engineering 734-764-8202
Patent Protection
US Patent Pending

Transmission-Line Meta-materials

Transmission-line (TL) meta-materials are artificially structured media with unusual electromagnetic properties, which are found of great interest with numerous applications. Particularly, the ability of TL meta-materials to control the electromagnetic field along a surface/radiating aperture allows immediate applications in antenna design. TL meta-materials possessing effective material parameters that are diagonal in the Cartesian basis have been extensively studied in the past. A research group in EECS of University of Michigan has, however, developed TL meta-materials with arbitrary tensors that could potentially provide unprecedented control of the electromagnetic field, and thus allow one to synthesize arbitrary surface current distributions (namely arbitrary antenna aperture illuminations).

Two-dimensional Tensor Transmission-Line Network

The research group demonstrates that the material parameter distributions of transformation-designed electromagnetic devices can be directly mapped to two-dimensional transmission-line networks. The proposed tensor TL meta-materials combine microwave network circuits with transformation optics (used as a circuit synthesis method), and promise broad bandwidths of operation and low losses due to their travelling-wave structures. As a result, the proposed tensor TL meta-materials allow the synthesis of arbitrary surface current distributions, and then naturally allow the synthesis of planar antennas with fixed, arbitrary far-field radiation patterns. The inclusion of tunable reactive elements, such as varactors (diode-based or MEMs-based), into the tensor TL meta-materials will further enable arbitrarily configurable antenna apertures. The proposed tensor TL meta-materials have been both analytically studied and experimentally verified. In addition to application to antennas, this technology could be also useful in the design of antenna feeds, beamforming network, multiplexers, power divider and couplers. Finally, combing the spatial field manipulation offered by transformation circuits with traditional filter concepts will lead to wireless devices that provided both focusing/collimating and filtering functionality.

Applications and Advantages


  • Antenna design.
  • Beam forming Network, Power divider and Couplers.
  • Focusing and Filtering Wireless Devices.


  • Transmission-line Meta-materials with arbitrary tensors.
  • Synthesis of arbitrary surface current distribution.