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Tutorial
on
Saptarshi Ghosh
Thesis Supervisor: Dr. Kumar Vaibhav SrivastavaDepartment of Electrical Engineering
Indian Institute of Technology, Kanpur, India
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Presentation Outline
2
Introduction to Metamaterials
Overview of Metamaterial Absorbers
Modeling of Metamaterial Absorber Structure 1
PEC-PMC modes
Floquet Modes
Modeling of Other Metamaterial Absorber Structures
Conclusion
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Introduction to Metamaterials
3
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Overview of Metamaterial
4
Artificial composite materials consisting of structural units smaller thanthe wavelength (λ ) of the incident radiation.
Conventional material with atoms
Unit-cell driven metamaterial (size < λ /4)
Controllable electromagnetic properties(ε, µ, n,…) at desired frequency.
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Historical Overview
1968: Veselago [1] predicted the existence of LHM.
1996: Realization of negative permittivity practically [2] by Pendry.
1999: Experimental verification of negative permeability [3] by Pendry. 2000: First Experimental Demonstration of LHM [4] by Smith.
2001: First realization of Negative Refractive Index [5] by Shelby.
5
[1] V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of µ and ε,” Sov.
Phys. Uspekhi, Vol. 10, No. 4, pp. 509-514, 1968.
[2] J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic
microstructure,” Phys. Rev. Lett., Vol. 76, No. 25, pp. 4773-4776, June 1996.[3] J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced
nonlinear phenomena,” IEEE Trans. Micr. Theory. Tech., Vol. 47, No. 11, pp. 2075-2084, Nov. 1999.
[4] D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with
simultaneously negative permeability and permittivity,” Phys. Rev. Lett., Vol. 84, No. 18, pp. 4184-4187, 2000.
[5] R. A.Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,”
Science, Vol. 292, pp. 77-79, April 2001.
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Metamaterial Absorbers
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[6] P.Saville, “Review of Radar Absorbing Materials,” Defense R & D Canada-Atlantic, Jan. 2005.
Salisbury Screen
Conventional Absorbers [6]
Pyramidal Absorber
~λ
Wide bandwidth above 90%
absorption bandwidth
Disadvantage :
large thickness and fragile
Single-band absorber
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Metamaterial Absorber [7]
8
Structure is ultra-thin (λλλλ0 /35) compared to conventional absorbers.
Effective electromagnetic constitutive parameters (ε eff and µeff ) have
been tailored using unit cell design.
Absorbers can be made scalable- from microwave, terahertz,infrared, optical frequency range.
Structures can be easily fabricated using PCB technology.
First experimentally realized by Landy et. al. in 2008 [12].
[7] N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,”Phys. Rev. Lett., vol. 100, pp. 207402, May 2008.
a1 = 4.2 mm, a2 = 12 mm, W = 4 mm,
G = 0.6 mm, t = 0.6 mm, L = 1.7 mm,
H = 11.8 mmFR4 substrate thickness = 0.72 mm
Copper thickness = 0.017 mm
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Metamaterial Absorber
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When the reflected power (|S11|2) and transmitted power (|S21|
2) have
been minimized simultaneously, absorptivity (A) will be maximum.
2
21
2
11 ||||1 S S A −−=
|S11|2 = 0.01%
|S21|2 ~ 0.9%
A = 1-|S11|2-|S21|2 = 96%
At 11.65 GHz,
Simulated Absorptivity
What is the reason behind the absorptivity?
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Metamaterial Absorber [8]
10
When the reflected power (|S11|2) and transmitted power (|S21|
2)
have been minimized simultaneously, absorptivity (A) will be
maximum.
The design is made such a way that the input impedance is
matched exactly with the free space impedance.
Input impedance can be matched with free space impedance by
controlling the effective material parameters.
[8] D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from
inhomogeneous metamaterials,” Phys. Rev. E 71, pp. 036617, 2005.
2
21
2
11 ||||1 S S A −−=
ε ε
µ µ η
ε
µ η
ε ε
µ µ ω
′′+′
′′+′===
j
j Z
eff
eff
eff
eff
00
0
0)(
( )( ) 221
2
11
2
21
2
110
11)(
S S S S Z
−−−+=η ω
µ ε ′=′
ε ′′=′′
at absorption
frequency
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Effective Material Parameters [9]
11
[9] C. L. Holloway, E. F. Keuster, and A. Dienstfrey, “Characterizing metasurfaces /metafilms: the connection
between surface susceptibilities and effective material properties,” IEEE Antennas Wireless Propag. Lett., Vol.10, pp. 1507-1511, 2011.
µ ε ′≈′ µ ε ′′≈′′
++
−−+=
2111
2111
0 1
121
S S
S S
d k
jeff ε
+−
−++=
2111
2111
0 1
121
S S
S S
d k
jeff µ
Re(εeff ): 1.04; Re(µeff ): -1.12 Im(εeff ): 11.06; Im( µeff ): 8.86
At
11.65 GHz
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Metamaterial Absorber Structure 1
12
We are first going to design a single-band metamaterial absorber.
Metamaterial absorber structures are periodic structures Since metamaterial absorber structures are resonant structures, there must be
some equivalent capacitances (C) and inductances (L).
Inductance can be realized by any metallic patch
Capacitance can be realized by any gap between two metallic patches
depending on the direction of E-field.
Points to remember:
LC f
2
2
1
π ≈
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Metamaterial Absorber Structure 1
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8 x 8 Array Front View of Unit Cell Side View
Perspective
View
a = 10 mm, w = 0.4 mm,
l = 6.5 mm, g = 0.2 mm
Copper thickness = 0.035 mm,FR4 thickness = 1 mm
(εr =4.25 & tanδ =0.02)
t
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HFSS →Insert the Design → Draw a 3-D rectangular box
Metamaterial Absorber Structure 1
3D box
Properties window
Project manager
Progress windowMessage manager
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Project Variables
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Project variables are applicable
to a particular project
Prefixed with “$” sign
Project variable is applied to all
the designs inside a project
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Design Variables
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Design variables are applicable
to a particular design
Independent from one design to
another design
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Square Metal Ground Plane
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Positional coordinates : 0,0,0
X-size: 10 mm; Y-size: 10 mm; Z-size: 0.035 mm
Assign material: copper
FR-4 Dielectric Substrate
Positional coordinates : 0,0,0
X-size: 10 mm; Y-size: 10 mm; Z-size: 0.035 mm
Assign material: copper
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Top Metallic Patch
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First draw a square box
Then, draw a middle line and add it to the square loop
Lastly, subtract a small gap from the middle line
Assign material: copper
Air Box
An air box needs to be provided for providing boundary condition
Assign material: vacuum
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PEC/PMC Boundary condition
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Opposite Current : PEC
PEC: Opposite CurrentSame Current : PMC
Same Current : PMC
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PEC/PMC Boundary condition
PEC boundary PMC boundary
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Assigning Wave ports
21
Since back side is full metal plane, transmission (S 21) is zero
No need to put wave port 2 at the back
Deembedding is not necessary, as we are interested in magnitude of
reflection coefficient (|S 11|2
) only.
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Analysis
Solution Frequency: 6 GHz
Maximum delta S (∆S): 0.02
Frequency range: 2 GHz – 10 GHz
Sweep type : Fast/ Interpolating/ Discrete
Sweep type Solution time Comments
Fast 7 min 10 sec Quickest, but most inaccurate
Interpolating 10 min 12 sec Not the quickest, not the most accurate
Discrete ∼∼∼∼16 hours Slowest, but most accurate
It is the difference in
error between two
consecutive passes
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Since only 1 port, only 1 S-parameter is available
Reflection coefficient: S(1,1) in dB or in mag
Reflection coefficient : -24 dB at 6.07 GHz
Absorptivity: {1- (mag(S(1,1))2)}*100
Results
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Surface Current Distributions
Top surface Bottom surface
Current is flowing in circulating loop around the incident magnetic field
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What if the PEC/PMC boundary conditions will be interchanged ?
Some Common Questions
PEC boundary PMC boundary
Reflection dip will change to 7.42 GHz instead of 6.07 GHz
Reflection coefficient (S 11) will decrease to -9.03 dB instead of -24 dB
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Will this PEC/PMC boundary condition be valid if the structure is
complicated ?
Will this PEC/PMC boundary condition work when the current flow
will not be as simple as this ?How to measure the oblique incidence measurement ?
How to measure the reflectivity when the structure is rotated ?
Some Common Questions
Solution Use Floquet Ports
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Used exclusively with planar periodic structures
Example : Planar phased array, frequency selective surface (FSS)
Floquet Ports
The analysis of the infinite structure is then accomplished by analyzing a
single unit cell by providing periodic boundary conditions (PBC).
PBC
PBC
P B C P
B C
Periodic in x-y plane
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Master/ Slave Boundary Condition
Master 1
Master 2Slave 1
Slave 2
No change in reflection coefficient or reflection dip under normal
incidence even if there is reversal of master 2 and slave 2 directions
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Assigning Floquet ports
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No need to put floquet port 2 at the back
Deembedding is not necessary, as we are interested in magnitude of
reflection coefficient (|S 11|2) only.
We have to provide lattice vectors “a” and “b” to define theperiodicity in x- y plane
Periodic in x-direction
Periodic in y-direction
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Fast sweep is not available in lower versions of HFSS (upto HFSS 13)
Result remains almost same
Absorptivity: {1- (mag(S(1,1))2)}*100
Analysis and Results
Any Other advantage ?
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There is a phase delay between the Master and Slave boundary
The default value is zero
Assign some variables in place of scan angles
Angle variation
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When phi scan angle is varied from 0o to 90o, the incident wave is
polarized keeping the incident wave propagation direction constant
Since the structure is asymmetrical, reflection dip will change
Polarization Angle variation
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Floquet port has the extra advantage of modal decomposition
During assigning “floquet port”, the default number of modes is : 2
These number of modes and type of modes can be manually controlled
Oblique Incidence
TE mode TM mode
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Variation of theta scan angle (θ) from 0o to 90o
TE Polarization TM Polarization
When mode is TE (0,0) When mode is TM (0,0)
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Some Other Examples
C L f
2
1
2
1
×≈
π
Resonant frequency will decrease to 4 GHz whereas the early
presented structure has a reflection dip at 6 GHz
However, the structure is still asymmetrical w.r.t. field vector directions
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Some Other Examples (contd.)
Structure is symmetrical w.r.t.
incident field vector directions.
The structure exhibits reflection dip at close to 6 GHz
Small deviation in frequency from the initial proposed structure is due
to difference in gap (g) value
Structure is four-fold symmetrical
Structure is polarization-insensitive
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Conclusion
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A brief introduction about metamaterial and metamaterial absorber has been
discussed.
A single-band metamaterial absorber structure has been studied in detail.
Different boundary conditions and modes have been investigated to analyze the
structure.
Some other examples have also been discussed.
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Thank You
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