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School of Electronic Engineering and Computer Science
Saul Wiggin, Wenxuan Tang, Yang Hao and Ian Youngs
101
A dieletric approach using
transformation electromagnetics
for optical systems
2
Outline
• An introduction to the theory of transformation
optics and significant innovations: invisibility
cloaks, carpet cloaks and flat lenses.
• A model of a Cooke Triplet is calculated as an
example of a conventional optical system.
• The results from an FDTD simulation are
presented
• Discussion and conclusions
3
Outline
• An introduction to the theory of transformation
optics and significant innovations: invisibility
cloaks, carpet cloaks and flat lenses.
• A model of a Cooke Triplet is used as an example
of a conventional optical system.
• The results from an FDTD simulation are
presented
• Discussion and conclusion
4
Invisibility cloak
“Harry potter” style
invisibility cloak reported
limitations : singular
values, narrow bandwidth
and losses.
“Controlling electromagnetic fields” J. Pendry, Schurig
and Smith Science vol 312, 1780 (June 2006)
5
Transformation Optics
Maxwell’s equations are
invariant in different
coordinate systems
“Controlling electromagnetic fields” J. Pendry, Schurig and Smith Science vol 312, 1780 (June 2006)
6
Carpet cloak
•Transform a plane
rather than a point
•Broadband
•Lossless
“Hiding under a carpet: a new strategy for
cloaking” Li and Pendry
Phys rev lett, vol 101, 20 (2008)
7
Simplifying Cloak Design λ=750 μm
• 64x15 Non-Orthogonal Blocks
• 80x20 Orthogonal Blocks
37.5 nm x 37.5 nm
• 6x2 Orthogonal Blocks
482.5 nm x 375 nm
“Manipulating the loss in electromagnetic cloaks for perfect
wave absorption,”Kallos, ARGYROPOULOS and HAO, PRA
2009
x [m]
y [
m]
Original Grid
-1.5 -1 -0.5 0 0.5 1 1.50
0.5
1
3
5
x [m]
y [m
]
High-Res Sampled Grid
-1.5 -1 -0.5 0 0.5 1 1.50
0.5
1
3
5
x [m]
y [m
]
Low-Res Sampled Grid
-1.5 -1 -0.5 0 0.5 1 1.50
0.5
1
3
5
x [m]
y [m
]
High-Res Sampled Grid (Free Space)
-1.5 -1 -0.5 0 0.5 1 1.50
0.5
1
1.5
2
x [m]
y [
m]
Low-Res Sampled Grid (Free Space)
-1.5 -1 -0.5 0 0.5 1 1.50
0.5
1
1.5
2
x [m]
y [
m]
Original Grid
-1.5 -1 -0.5 0 0.5 1 1.50
0.5
1
3
5
x [m]
y [m
]
High-Res Sampled Grid
-1.5 -1 -0.5 0 0.5 1 1.50
0.5
1
3
5
x [m]
y [m
]
Low-Res Sampled Grid
-1.5 -1 -0.5 0 0.5 1 1.50
0.5
1
3
5
x [m]
y [m
]
High-Res Sampled Grid (Free Space)
-1.5 -1 -0.5 0 0.5 1 1.50
0.5
1
1.5
2
x [m]
y [
m]
Low-Res Sampled Grid (Free Space)
-1.5 -1 -0.5 0 0.5 1 1.50
0.5
1
1.5
2
x [m]
y [
m]
Original Grid
-1.5 -1 -0.5 0 0.5 1 1.50
0.5
1
3
5
x [m]
y [m
]
High-Res Sampled Grid
-1.5 -1 -0.5 0 0.5 1 1.50
0.5
1
3
5
x [m]
y [m
]
Low-Res Sampled Grid
-1.5 -1 -0.5 0 0.5 1 1.50
0.5
1
3
5
x [m]
y [m
]
High-Res Sampled Grid (Free Space)
-1.5 -1 -0.5 0 0.5 1 1.50
0.5
1
1.5
2
x [m]
y [
m]
Low-Res Sampled Grid (Free Space)
-1.5 -1 -0.5 0 0.5 1 1.50
0.5
1
1.5
2
8
Flat lens
“Discrete coordinate transformation for designing all-dieletric flat antennas” Tang et al
IEEE Transactions on antenna and propagation vol 58, no 12 (Dec 2010)
• Compression of virtual
space means that it is
an all-dieletric device
• A low resolution flat
lens could be
constructed with only
7 different blocks with
permittivity's within
naturally occurring
materials
9
Outline
• An introduction to the theory of transformation
optics used to design invisibility cloaks, carpet
cloaks and flat lenses.
• A model of a Cooke Triplet is used as an example
of a conventional optical system.
• The results from an FDTD simulation are
presented
• Discussion and conclusion
11
Optical Design
Y(mm)
1000
500
0
500 1000 1500 2000 x(mm)
Y(mm)
1000
500
0
500 1000 1500 2000 x(mm)
• The Cooke triplet is
defined by ray tracing
• Structured grid
generation is carried out
• Each ray acts as a
boundary for the
orthogonal mesh
generated
• The grid is made as
orthogonal as possible
by using the Laplace
smoothing function
12
Permittivity map
• The device is only
a function of
permittivity
• The permittivity is
calculated from
the metric tensor
• The map in FDTD
is generated by
symmetry by being
reflected in the X
axis
13
Outline
• An introduction to the theory of transformation
optics used to design invisibility cloaks, carpet
cloaks and flat lenses.
• A model of a Cooke Triplet is used as an example
of a conventional optical system.
• The results from an FDTD simulation are
presented
• Discussion and conclusion
16
Outline
• An introduction to the theory of transformation optics used
to design invisibility cloaks, carpet cloaks and flat lenses.
• A model of a Cooke Triplet is used as an example of a
conventional optical system.
• The results from an FDTD simulation are presented
• Discussion and conclusion
17
Siedel aberrations • All aberrations in an
image classified by
Siedel
• Third order
aberrations are:
spherical, coma,
astigmatism, field
curvature and
distortion.
• In addition there is
chromatic aberration
due to dispersion in
the material
18
L Spherical aberration Focus Long SA
Conventional 4483mm 1510mm
MTM 4954mm 560mm
Reduced 4125mm 2910mm
Conventional
MTM
Reduced
19
T Spherical aberration Trans SA
Conventional 80mm
MTM 50mm
Reduced 100mm
Cooke triplet
MTM Triplet
Reduced map
21
Sources of error
• curved
boundary's are
represented with a
staircase
approximation
• Discrete method
of transformation
results in
reflections between
blocks
Lambda/10 Lamba/20 true
Conventional
lens
4483mm 5375mm 5020mm
22
Further work: fabrication and measurements
“All-dielectric invisibility
cloaks made of BaTiO3-
loaded polyurethane foam”
Bao et al, New journal of
physics, 13, 103023
(2011)
23
Conclusion
• Transformation optics has been used to
design a Cooke’s triplet
• Transformation optics can be used to design
general optical systems
• This can result in improvements in size,
weight, complexity and adaptability which
are important for applications in science,
defence and industry