20090912 - Iceaa2009 Themos Kallos
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School of Electronic Engineering and Computer Science
Simplified Directional Ground-Plane Cloaks by Christos Argyropoulos
Themos Kallos, Christos Argyropoulos, Yang Hao
Outline
Introduction to Cloaking Phenomena Simplified Directional Ground-Plane Cloaks Scattering Performance (FDTD) Bandwidth Performance (FDTD) 2
Cloaking Devices
Cloaking device: anisotropic and dispersive. Radially-dependent permittivity ε and permeability µ. The cloak is able to guide the electromagnetic waves around an object without any disturbances and reflections. The object placed inside the cloak becomes practically “invisible” to an exterior viewer.
Schurig et al., Opt. Expr., 2006.
3
[1]
Ground-Plane Cloaking • Cylindrical Cloak: Extreme bending Extreme materials • Leading to dispersive & narrowband response
[2]
• Ground-plane cloak has moderate material parameters, can be made all-dielectric [1] Argyropoulos et al., TAP 2009 [2] Li et al., PRL 2008
4
Experimental Results
[1]
[2]
• Microwave (2 cm) • Infrared (1.5 μm) [1] Liu et al., Science 2009 • Broadband [2] Valentine et al., Nat. Mat. 2009
5
Ground-Plane Cloak Challenges
Simpler design?
Free-Space operation?
Good Bandwidth Performance? 6
Ground-Plane Cloak # of cells [%]
Mirage Effect 30 (a) 20 10 0 60
80 100 Angle [Degrees]
y [µm]
(c)
120
Permitivity Map 4
0.5 0 1.5
2 1
0.5
0 x [ µm]
0.5
1
7
y [ µ
0 60
Cloak Design 80 100 Angle [Degrees]
4
0.5 0 1.5
2 1
y [ µm]
(b)
0.5
µm] y [ # of cells [%]
0.5
0 µ x [ m]
0.5
0 1.5
1
1
(b)t ij
(c)
4 1
1
1
1
0.5
4
g yy
0 0.5 x [µm]
1
2 1.5
1
1
20 (d) Approximate Permittivity Map
80 100 Angle [Degrees] 0.5 0 0.5 µ x [ m]
0.5
ij 1 1 ref det gij
30 (a)
10 0.5 0 60 0 1.5
0 µ x [ m]
g yx
0.5
Anisotropy Map
1
0.5
g ij
1.2
0 1.5
2
0 µ x [ m]
0.5
120
4
0.5
1
(d) Approximate Permittivity Map g xx g xy
Permitivity Map y [ µm]
y [ µm]
(c)
1.2
0 1.5
120
120 1.5
2
Li and Pendry, PRL 2008 Permitivity Map Kallos et al., PRA 2009
y [ µm]
# of cel
10
0.5
0.5 0 1.5
1
g
ij Anisotropy Map cos ij
det( gij ) 0.5
0 µ x [ m]
0.5
1
(d) Approximate Permittivity Map
g xy g yx g xx g yy
1.2 1
8
All Dielectric Cloak Design gii 1 µ = det( g) g ji
[ ] ij
gij g jj
The simplification is to make the meshes orthogonal, then gij and gji are going to be zero; if the meshes have equal sides, then gii=gjj, then g=gii*gjj=gii*gii;
[µ ] = [µ ]
ij −1
ij
g ii 1 = det( g ) g ji
1 ij −1 µij = µ = det( g )
[ ] [ ]
1 g ii = ( g ) 2 0 ii 1 0 = 0 1
0 g jj
g ii g ji
g ij g jj
g ij g jj
−1
−1
−1
9
NFDTD Run • 64x15 Nonorthogonal cells (cloak only) • Gaussian Pulse: f0 = 600 THz σt = 2.4 fs σx = 1.2 μm
• Ground Plane
• w/ object
• w/ cloak
10
Simplified Cloak Design µm] µµm] y [ y [ m] y [
λ=750 μm (Embedded in SiO2/εr =2.25) Original Grid Original Grid Original Grid
µm] µµm] y [ y [ m] y [
0.5 0.5 0.5 00 1.5 0 1.5 1.5
1 1 1
µm] µµm] y [y [ y [ m]
0.5 0.5 0.5 00 1.5 0 1.5 1.5
1 1 1
0.5 0.5 0.5 00 1.5 0 1.5 1.5
1.5 1.5 1.5
0.5 00 0.5 11 0.5 0.5 µ 0.5 x [ 0m] 1 x [µµ m] 0.5 x [ m] LowRes Sampled Grid LowRes Sampled Grid LowRes Sampled Grid
1.5 1.5 1.5
55 5 33 3 11 1 55 5 33 3 11 1
0.5 00 0.5 11 1.5 0.5 0.5 1.5 µ 0.5 x [ 0 m] 0.5 1 1.5 µ x [ m] x [µm] HighRes Sampled Grid (Free Space) HighRes Sampled Grid (Free Space) Kallos et al., PRA 2009 22 HighRes Sampled Grid (Free Space) 2 0.5 0.5 1.5
µ ]m] [µm]
1 1 1
0.5 00 0.5 11 0.5 0.5 0.5 x [µµ 0m] 0.5 1 x [µm] x [ m] HighRes Sampled Grid HighRes Sampled Grid HighRes Sampled Grid
55 5 33 3 11 1
• 64x15 Non-Orthogonal Blocks
• 80x20 Orthogonal Blocks 37.5 nm x 37.5 nm
• 6x2 Orthogonal Blocks 482.5 nm x 375 nm
11
Simplified Cloak Design Embedded in Air y [ µm]
LowRes Sampled Grid
2
0.5 0 1.5
1
0.5
0 0.5 µ x [ m]
1
1.5
y [ µm]
HighRes Sampled Grid (Free Space) 0.5 0 1.5
2
• Ignore dispersive regions
1.5 1
0.5
0 0.5 µ x [ m]
1
1.5
LowRes Sampled Grid (Free Space) y [ µm]
1
• Dispersive min(ε)=0.8
1.5
2
0.5 0 1.5
1
• 4x2 Orthogonal Blocks
1.5 1
0.5
0 0.5 x [ µm]
1
1.5
1
Kallos et al., PRA 2009
12
Simplified Cloaks Comparisons Approximations: • Ignore anisotropy • Ignore dispersive values • Simplified blocks • Simplified cloaks (8x2, 4x2) work very well in free space without dispersive values Kallos et al., PRA 2009
13
1
0.5 0 0
Spectral Amplitude [a.u.] Energy [a.u.] Spectral Amplitude [a.u.]
Spectral Amplitude [a.u.]
Energy [a.u.]
1 Optical Bandwidth
Energy [a.u.]
Quantitative Performance 0.5
Ground Plane No Cloak 80x20 Cloak 0 0 30 80x20 Cloak (dispersive) 60 90 1 1 (a)Angle [deg] (c) 4x2 Cloak
30 60 1 90 Angle [deg] 0.5
187 nm ~ x / 12
Ground Plane No Cloak 80x20 Cloak 80x20 Cloak (dispersive) 4x2 Cloak
0.5 0 0 0
1
1 0.5
0.5
0 30 60 90 0 30 60 0.5 0.5 0 Angle [deg] Angle [deg] • High-res cloaks are slightly 1400 1600 1800 400 600 800 1 Frequency [THz] 1Frequency [THz] better (b) (d) 0 0 1400 1600 1800 400 600 800 Frequency [THz]0.5 • Visible spectrum is Frequency [THz] 0.5
restored
• Dispersive sections do not significantly affect spectrum
0
• Differences appear after Kallos et al., PRA 2009 1600 THz
400 600 800 Frequency [THz]
0
90
1400 1600 1800 Frequency [THz]
14
Quantitative Performance Optical Bandwidth
Ground Plane No Cloak 80x20 Cloak 80x20 Cloak (dispersive) 4x2 Cloak
• Tradeoff between bandwidth and design complexity • Bandwidth deteriorates slightly with increased frequency (electrically larger objects) • Critical at nano-scale optical devices
15
Free-Space Directional Cloak Single angle of operation
(a)
(b)
Rotationally symmetric device - Top view
Kallos et al., PRA 2009
16
Free-Space Directional Cloak Energy Distribution
Spectral Distribution
(b)
17
Free-Space Directional Cloak Practical Application: reduce coupling between GPS antenna and VHF whip antenna No Cloak
A C C A
B D
B D
PE D C D B B
A C C A
4x4 Directional Cloak
Relative Permittivity values A = 1.20 B = 1.32 C = 1.07 D = 1.47 18
Conclusions
Ground-plane cloaks have less demanding nondispersive material parameters. Simplified designs work for electrically small elements (dx~λ). Bandwidth vs. Complexity trade-off. The energy transmitted behind the directional free-space cloak is improved by one order of magnitude compared to a non-cloaked object. The proposed device has broadband performance and preserves the frequency spectrum over the most of the visible range.
19
Thank you! [email protected]
[email protected]
20
Simplified Directional Ground-Plane Cloaks by Christos Argyropoulos
Themos Kallos, Christos Argyropoulos, Yang Hao
Outline
Introduction to Cloaking Phenomena Simplified Directional Ground-Plane Cloaks Scattering Performance (FDTD) Bandwidth Performance (FDTD) 2
Cloaking Devices
Cloaking device: anisotropic and dispersive. Radially-dependent permittivity ε and permeability µ. The cloak is able to guide the electromagnetic waves around an object without any disturbances and reflections. The object placed inside the cloak becomes practically “invisible” to an exterior viewer.
Schurig et al., Opt. Expr., 2006.
3
[1]
Ground-Plane Cloaking • Cylindrical Cloak: Extreme bending Extreme materials • Leading to dispersive & narrowband response
[2]
• Ground-plane cloak has moderate material parameters, can be made all-dielectric [1] Argyropoulos et al., TAP 2009 [2] Li et al., PRL 2008
4
Experimental Results
[1]
[2]
• Microwave (2 cm) • Infrared (1.5 μm) [1] Liu et al., Science 2009 • Broadband [2] Valentine et al., Nat. Mat. 2009
5
Ground-Plane Cloak Challenges
Simpler design?
Free-Space operation?
Good Bandwidth Performance? 6
Ground-Plane Cloak # of cells [%]
Mirage Effect 30 (a) 20 10 0 60
80 100 Angle [Degrees]
y [µm]
(c)
120
Permitivity Map 4
0.5 0 1.5
2 1
0.5
0 x [ µm]
0.5
1
7
y [ µ
0 60
Cloak Design 80 100 Angle [Degrees]
4
0.5 0 1.5
2 1
y [ µm]
(b)
0.5
µm] y [ # of cells [%]
0.5
0 µ x [ m]
0.5
0 1.5
1
1
(b)t ij
(c)
4 1
1
1
1
0.5
4
g yy
0 0.5 x [µm]
1
2 1.5
1
1
20 (d) Approximate Permittivity Map
80 100 Angle [Degrees] 0.5 0 0.5 µ x [ m]
0.5
ij 1 1 ref det gij
30 (a)
10 0.5 0 60 0 1.5
0 µ x [ m]
g yx
0.5
Anisotropy Map
1
0.5
g ij
1.2
0 1.5
2
0 µ x [ m]
0.5
120
4
0.5
1
(d) Approximate Permittivity Map g xx g xy
Permitivity Map y [ µm]
y [ µm]
(c)
1.2
0 1.5
120
120 1.5
2
Li and Pendry, PRL 2008 Permitivity Map Kallos et al., PRA 2009
y [ µm]
# of cel
10
0.5
0.5 0 1.5
1
g
ij Anisotropy Map cos ij
det( gij ) 0.5
0 µ x [ m]
0.5
1
(d) Approximate Permittivity Map
g xy g yx g xx g yy
1.2 1
8
All Dielectric Cloak Design gii 1 µ = det( g) g ji
[ ] ij
gij g jj
The simplification is to make the meshes orthogonal, then gij and gji are going to be zero; if the meshes have equal sides, then gii=gjj, then g=gii*gjj=gii*gii;
[µ ] = [µ ]
ij −1
ij
g ii 1 = det( g ) g ji
1 ij −1 µij = µ = det( g )
[ ] [ ]
1 g ii = ( g ) 2 0 ii 1 0 = 0 1
0 g jj
g ii g ji
g ij g jj
g ij g jj
−1
−1
−1
9
NFDTD Run • 64x15 Nonorthogonal cells (cloak only) • Gaussian Pulse: f0 = 600 THz σt = 2.4 fs σx = 1.2 μm
• Ground Plane
• w/ object
• w/ cloak
10
Simplified Cloak Design µm] µµm] y [ y [ m] y [
λ=750 μm (Embedded in SiO2/εr =2.25) Original Grid Original Grid Original Grid
µm] µµm] y [ y [ m] y [
0.5 0.5 0.5 00 1.5 0 1.5 1.5
1 1 1
µm] µµm] y [y [ y [ m]
0.5 0.5 0.5 00 1.5 0 1.5 1.5
1 1 1
0.5 0.5 0.5 00 1.5 0 1.5 1.5
1.5 1.5 1.5
0.5 00 0.5 11 0.5 0.5 µ 0.5 x [ 0m] 1 x [µµ m] 0.5 x [ m] LowRes Sampled Grid LowRes Sampled Grid LowRes Sampled Grid
1.5 1.5 1.5
55 5 33 3 11 1 55 5 33 3 11 1
0.5 00 0.5 11 1.5 0.5 0.5 1.5 µ 0.5 x [ 0 m] 0.5 1 1.5 µ x [ m] x [µm] HighRes Sampled Grid (Free Space) HighRes Sampled Grid (Free Space) Kallos et al., PRA 2009 22 HighRes Sampled Grid (Free Space) 2 0.5 0.5 1.5
µ ]m] [µm]
1 1 1
0.5 00 0.5 11 0.5 0.5 0.5 x [µµ 0m] 0.5 1 x [µm] x [ m] HighRes Sampled Grid HighRes Sampled Grid HighRes Sampled Grid
55 5 33 3 11 1
• 64x15 Non-Orthogonal Blocks
• 80x20 Orthogonal Blocks 37.5 nm x 37.5 nm
• 6x2 Orthogonal Blocks 482.5 nm x 375 nm
11
Simplified Cloak Design Embedded in Air y [ µm]
LowRes Sampled Grid
2
0.5 0 1.5
1
0.5
0 0.5 µ x [ m]
1
1.5
y [ µm]
HighRes Sampled Grid (Free Space) 0.5 0 1.5
2
• Ignore dispersive regions
1.5 1
0.5
0 0.5 µ x [ m]
1
1.5
LowRes Sampled Grid (Free Space) y [ µm]
1
• Dispersive min(ε)=0.8
1.5
2
0.5 0 1.5
1
• 4x2 Orthogonal Blocks
1.5 1
0.5
0 0.5 x [ µm]
1
1.5
1
Kallos et al., PRA 2009
12
Simplified Cloaks Comparisons Approximations: • Ignore anisotropy • Ignore dispersive values • Simplified blocks • Simplified cloaks (8x2, 4x2) work very well in free space without dispersive values Kallos et al., PRA 2009
13
1
0.5 0 0
Spectral Amplitude [a.u.] Energy [a.u.] Spectral Amplitude [a.u.]
Spectral Amplitude [a.u.]
Energy [a.u.]
1 Optical Bandwidth
Energy [a.u.]
Quantitative Performance 0.5
Ground Plane No Cloak 80x20 Cloak 0 0 30 80x20 Cloak (dispersive) 60 90 1 1 (a)Angle [deg] (c) 4x2 Cloak
30 60 1 90 Angle [deg] 0.5
187 nm ~ x / 12
Ground Plane No Cloak 80x20 Cloak 80x20 Cloak (dispersive) 4x2 Cloak
0.5 0 0 0
1
1 0.5
0.5
0 30 60 90 0 30 60 0.5 0.5 0 Angle [deg] Angle [deg] • High-res cloaks are slightly 1400 1600 1800 400 600 800 1 Frequency [THz] 1Frequency [THz] better (b) (d) 0 0 1400 1600 1800 400 600 800 Frequency [THz]0.5 • Visible spectrum is Frequency [THz] 0.5
restored
• Dispersive sections do not significantly affect spectrum
0
• Differences appear after Kallos et al., PRA 2009 1600 THz
400 600 800 Frequency [THz]
0
90
1400 1600 1800 Frequency [THz]
14
Quantitative Performance Optical Bandwidth
Ground Plane No Cloak 80x20 Cloak 80x20 Cloak (dispersive) 4x2 Cloak
• Tradeoff between bandwidth and design complexity • Bandwidth deteriorates slightly with increased frequency (electrically larger objects) • Critical at nano-scale optical devices
15
Free-Space Directional Cloak Single angle of operation
(a)
(b)
Rotationally symmetric device - Top view
Kallos et al., PRA 2009
16
Free-Space Directional Cloak Energy Distribution
Spectral Distribution
(b)
17
Free-Space Directional Cloak Practical Application: reduce coupling between GPS antenna and VHF whip antenna No Cloak
A C C A
B D
B D
PE D C D B B
A C C A
4x4 Directional Cloak
Relative Permittivity values A = 1.20 B = 1.32 C = 1.07 D = 1.47 18
Conclusions
Ground-plane cloaks have less demanding nondispersive material parameters. Simplified designs work for electrically small elements (dx~λ). Bandwidth vs. Complexity trade-off. The energy transmitted behind the directional free-space cloak is improved by one order of magnitude compared to a non-cloaked object. The proposed device has broadband performance and preserves the frequency spectrum over the most of the visible range.
19
Thank you! [email protected]
[email protected]
20
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