Microsoft PowerPoint - Meta_2009_patterned_screens_color [Compatibility Mode]DYNAMIC AND CIRCUIT THEORY DYNAMIC AND CIRCUIT THEORY MODELS FOR THE ANALYSIS OF SUBMODELS FOR THE ANALYSIS OF SUB--
WAVELENGTH TRANSMISSION WAVELENGTH TRANSMISSION THROUGH PATTERNED SCREENSTHROUGH PATTERNED SCREENS
A B Yakovlev C S R Kaipa Y R Padooru A. B. Yakovlev, C. S. R. Kaipa, Y. R. Padooru, F. Medina, and F. Mesa
Third International Congress on Advanced Third International Congress on Advanced Electromagnetic Materials in Microwaves and Optics
London, United Kingdom 30 August 4 September 200930 August – 4 September, 2009
Introduction Introduction Analytical modeling of sub-wavelengthAnalytical modeling of sub-wavelength multilayered FSS grids
Homogenization of grid impedance in terms of Homogenization of grid impedance in terms of effective circuit parameters
Transfer matrix approach
Circuit theory model of sub-wavelength multilayered FSS grids
Transmission line network formalism in terms of grid and slab admittance (impedance)
Even and odd excitations for multilayered symmetric grids
2
Analysis of Fabry-Perot type resonances in relation to sub-wavelength complete transmission
H
Incident wave
Layer N+1
d Layer 1
TE Polarization TE Polarization
xjkz dγ l
MMMM dzxMdzMx
Transfer matrix across the plane of grid












5










1 01
.....Nl 2,1
TM Polarization TM Polarization
ll l










.....Nl Y
Q l
.....Nl 2,1
D
w
h
Grid impedance D = 2 mm, w = 0.2 mm, h = 1 mm
dielectric permittivity: 10.2
2 effk
effk D w D
Luukkonen et al., IEEE Trans. Antennas Propagat., 56, June 2008
Circuit Theory Model Circuit Theory Model S
Port 1 Port 20Y
n+1 = even m = (n+1)/2
mh 1h nh
Even Excitation: Open Circuit (Magnetic Wall)


cosθηη 00 θsinεηη r00 m


9Tretyakov, Artech House, 2003
Medina, Mesa, Marques, IEEE Trans. Microw. Theory Tech. 56, Dec. 2008
Even ExcitationEven Excitation Even Excitation: Open Circuit (Magnetic Wall)Even Excitation: Open Circuit (Magnetic Wall)
PMCPort 1 0Y 1Y Y
1gY 2gY
1h 2




in TE/TM
g TE/TM
10 TE/TM
P TE/TM
1gY 2gY
transmission line
TE TM TE TM P
Y Y S


multilayered structure
Y YY Y
1gY 1ngY
ngY 2gY 2
Y Y
Y gTE/TM m
Odd Excitation: Short Circuit (Electric Wall)
TE/TM
of grid and PEC
zIncident wave
Reflected wave
0 0
|S21| - Analytical 0
|S21| - Analytical 30
|S21| - Analytical 60
8 9 10 11 12 13 14 15 16 1717 -30
-25
|S11| - HFSS 0
|S11| - HFSS 30
|S11| - HFSS 60
8 9 10 11 12 13 14 15 16 1717 -30
-25
14
0 0
|S21| - Analytical 0
|S21| - Analytical 30
|S21| - Analytical 60
8 9 10 11 12 13 14 15 16 1717 -30
-25
|S11| - HFSS 0
|S11| - HFSS 30
|S11| - HFSS 60
8 9 10 11 12 13 14 15 16 1717 -30
-25
15
Paired Screens of FishnetsPaired Screens of Fishnets H
H
z
0 0
|S11| - Analytical 0
|S11| - Analytical 30
|S11| - Analytical 60
10 11 12 13 14 15 16 17 18 19 2020 -30
-25
|S21| - HFSS 30
|S21| - HFSS 60
10 11 12 13 14 15 16 17 18 19 2020 -30
-25
17
Reflection and Transmission Magnitude Reflection and Transmission Magnitude TM PolarizationTM Polarization
0 0
|S21| - Analytical 0
|S21| - Analytical 30
|S21| - Analytical 60
10 11 12 13 14 15 16 17 18 19 2020 -30
-25
|S11| - HFSS 0
|S11| - HFSS 30
|S11| - HFSS 60
10 11 12 13 14 15 16 17 18 19 2020 -30
-25
18
Multilayer SubMultilayer Sub--Wavelength Patch GridsWavelength Patch Grids Transmission Magnitude, TE polarization
5
0
0.9
Transmission Magnitude, TE polarization 45-degree incidence
15
-10
-5
-25
0
0.1
0.
D
Period D = 2 mm Gap w = 0.2 mm
rε h Increasing the number of grids • creates pass bands and stop bands • sharp transition between bands
19
• increases the pass band
0
-10
-5
dB
-25
-20
Period D = 2 mm 0 5 10 15 20 25 30
-30
Frequency(GHz)
Period D = 2 mm Gap w = 0.2 mm Thickness h = 2 mm Permittivity: 10.2
20
Y YY Port 2Port 1
h
h
2 tan 0g
Y Y C

1 0


Total Transmission Total Transmission
Excess length associated with edge capacitance
TE/TM r
θε Ccη
h 2
(GHz) E l h
10
15
h = 1 mm h = 2 mm h = 4 mm(mm) Calculated Excess length
1 17.2105 13.0606
5
( 1h)
h 4 mm h = 6 mm h = 8 mm h = 10 mm
4 7.279 7.1182 6 5.458 5.4616 8 4.392 4.4304 -10
-5
H (
22
-15
for two-sided fishnet structure
TE/TM r
(mm) Calculated Excess length
TT
0
5
10
1h)
h = 4 mm h = 6 mm h = 8 mm h = 10 mm
4 9.165 9.0589 6 6.566 6.5359 8 5.124 5.1121 -10
-5
H (
23
-15
Analytical and circuit theory models are developed for rapid and efficient analysis of reflection/transmission properties ofy p p multilayered sub-wavelength patterned screens
The observed resonances of total transmission at low frequencies in multilayered sub-wavelength grids correspond to Fabry-Perot type resonances of a dielectric slab loaded with effective grid admittances
Analytical formulas for frequencies of total transmission are obtained for two-sided patch arrays and wire grids in terms of an excess length associated with effective edge capacitance andexcess length associated with effective edge capacitance and inductance
24