How to become invisible without a cloak
Fernando Guevara Vasquez
University of Utah
Science Day at the U
November 7 2009
Collaborators:
• Graeme W. Milton (University of Utah)
• Daniel Onofrei (University of Utah)
F. Guevara Vasquez, Science Day at the U
Cloaking
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What makes us visible?
Mostly reflections
Source
Object
Receiver
Wave
Sources
Light
Sun . . .
Radar
Antenna
Sonar
Shot
Ultrasound Transducers
Seismic
Shot
Examples from nature: bats,
(sonar) to find prey.
F. Guevara Vasquez, Science Day at the U
Receivers
Objects
Eyes
Wall . . .
Antenna
Plane
Microphone
Submarine
Transducers
Baby
Hydrophones Earth layers
dolphins, whales use echolocation
Cloaking
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Some reflections
F. Guevara Vasquez, Science Day at the U
Cloaking
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How to become invisible?
One way:
“Transformation based cloak”
Building cloak requires especially
designed materials with exotic
properties
(like bending light backwards!).
Sound, microwaves, light,. . .
F. Guevara Vasquez, Science Day at the U
Cloaking
4/10
How to become invisible?
One way:
“Transformation based cloak”
Building cloak requires especially
designed materials with exotic
properties
(like bending light backwards!).
Inconveniences:
• Blind Harry Potter
• Can only cloak a single
frequency (color),
i.e. it could cloak red light
but not blue.
Sound, microwaves, light,. . .
F. Guevara Vasquez, Science Day at the U
Cloaking
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Active exterior cloaking principle
ui
(incident)
F. Guevara Vasquez, Science Day at the U
Cloaking
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Active exterior cloaking principle
Now you see it. . .
ui
(incident)
us
(scattered)
F. Guevara Vasquez, Science Day at the U
Cloaking
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Active exterior cloaking principle
Device designed to:
• Cancel out ui inside
red disk
• Radiate very little
waves outside dotted
outline
ud
(device)
ud ≈ −ui
ud ≈ 0
F. Guevara Vasquez, Science Day at the U
Cloaking
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Active exterior cloaking principle
Now you don’t see it!
Objects can be hidden in
the “quiet” patch in red.
ui
(incident)
ud
(device)
F. Guevara Vasquez, Science Day at the U
Cloaking
5/10
Recipe for device (static case)
where p(z) = polynomial.
ud ≈ −ui , say near z = 1
ud ≈ 0 far away (|z| large)
F. Guevara Vasquez, Science Day at the U
Cloaking
6/10
Recipe for device (static case)
Taking the device to be:
ud (z) = −p(1/z)ui (z).
where p(z) = polynomial.
ud ≈ −ui , say near z = 1 ⇒ p(1) = 1
ud ≈ 0 far away (|z| large) ⇒ p(0) = 0
p(z)
p(1/z)
1
1
??
??
??
??
??
??
0
1
F. Guevara Vasquez, Science Day at the U
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Cloaking
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Some examples
ui (z) = z and p(z) = z give ud (z) = −p(1/z)ui (z) = −1.
p(z)
p(1/z)
−ud (z) = ui (z)p(1/z)
1.5
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1
1
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0
0
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1.5
2
−0.5
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−2
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2
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−0.5
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8
0
0
−6
−4
−2
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0
−1
−1
0
1
2
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−8
F. Guevara Vasquez, Science Day at the U
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Cloaking
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−8
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8
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Some examples
ui (z) = z and p(z) = z2 (−2z + 3) give ud (z) = z−1 (−2z−1 + 3)
p(z)
p(1/z)
−ud (z) = ui (z)p(1/z)
1.5
1.5
1.5
1
1
1
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0
0
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−0.5
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0
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−4
−2
0
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0
−1
−1
0
1
2
−8
−8
F. Guevara Vasquez, Science Day at the U
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Cloaking
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−8
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8
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Some examples
ui (z) = z
p(0) = 0, p(1) = 1 and 2 derivatives vanish at z = 0 and z = 1.
p(z)
p(1/z)
−ud (z) = ui (z)p(1/z)
1.5
1.5
1.5
1
1
1
0.5
0.5
0.5
0
0
0
−0.5
−1
−0.5
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0.5
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1.5
2
−0.5
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−4
−2
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2
4
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−0.5
−8
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8
0
0
−6
−4
−2
0
2
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1
0
−1
−1
0
1
2
−8
−8
F. Guevara Vasquez, Science Day at the U
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Cloaking
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−8
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8
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Some examples
ui (z) = z
p(0) = 0, p(1) = 1 and 3 derivatives vanish at z = 0 and z = 1.
p(z)
p(1/z)
−ud (z) = ui (z)p(1/z)
1.5
1.5
1.5
1
1
1
0.5
0.5
0.5
0
0
0
−0.5
−1
−0.5
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0.5
1
1.5
2
−0.5
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−6
−4
−2
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2
4
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−0.5
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8
0
0
−6
−4
−2
0
2
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1
0
−1
−1
0
1
2
−8
−8
F. Guevara Vasquez, Science Day at the U
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Cloaking
−8
−8
0
8
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Some examples
ui (z) = z
p(0) = 0, p(1) = 1 and 4 derivatives vanish at z = 0 and z = 1.
p(z)
p(1/z)
−ud (z) = ui (z)p(1/z)
1.5
1.5
1.5
1
1
1
0.5
0.5
0.5
0
0
0
−0.5
−1
−0.5
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0.5
1
1.5
2
−0.5
−8
−6
−4
−2
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2
4
6
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−0.5
−8
8
8
0
0
−6
−4
−2
0
2
4
6
8
1
0
−1
−1
0
1
2
−8
−8
F. Guevara Vasquez, Science Day at the U
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Cloaking
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−8
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Static device in action
Inactive device
Active device
10
10
0
0
−10
−10
0
F. Guevara Vasquez, Science Day at the U
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−10
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Cloaking
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8/10
Device for one single frequency (color of light)
Inactive devices
Active devices
20
20
0
0
−20
−20
0
F. Guevara Vasquez, Science Day at the U
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−20
−20
Cloaking
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20
9/10
Device for many frequencies (pulse)
F. Guevara Vasquez, Science Day at the U
Cloaking
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