Theory:2-D LC Network Model
For interpretation of the reason why NRI is different from conventional TL.
“Planar Negative Refractive
Index Media Using
Periodically L–C Loaded
Transmission Lines”
George V. Eleftheriades, Senior
Member, IEEE, Ashwin K. Iyer,
Student Member, IEEE, and
Peter C. Kremer
Wave eq.:
Further extensions:
In conventional TL:
In NRI materials: Z=1/jωC, Y=1/jωL
Application of LHM
Phase shifter
 Overcome diffraction limit
Topic1:Phase shifter
Phase shifter seen in Fig. 1 offers some
significant advantages compared to
standard delayTLs: it is more compact in
size, it can achieve a positive or a
negative phase shift while occupying the
same short physical length and it
exhibits a linear, flatter phase response
with frequency,
leading to shorter group delays.
2-D cell periodic analysis
“Compact Linear Lead/Lag
Metamaterial Phase Shifters for
Broadband Applications”
Marco A. Antoniades, and
George V. Eleftheriades,IEEE
Unit cell with symmetric structure,
Bloch wave fcn: Product of phase factor and periodic fcn.
Mentioned before in Kenneth’s presentation.
Phase shift per unit cell(matched)
It can be simplified as:
Critical pt is intersection of +,-curve: f=0.9GHz
What if unmatched?
Stop band occurs!!! Where
Topic2:Diffraction limit
A conventional lens focuses only the
propagating waves, resulting in an imperfect
image of the object.
The evanescent waves with strong
attenuation , carries the details smaller than
wavelength of the object.
A light source lying along y-axis consists of a continuum of plane waves:
propagates at an angle with the optical z axis given by the direction cosine= kz/k.
Propagation wave with components s.t.
Evanescent waves has strong attenuation at path from the object to the image.
Minimum resolvable feature
(by Fourier transform)
Solution to overcome it.
With NRI materials, evanescent waves can be restored to a larger bandwidth:
(the diffraction limit) becomes smaller.