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

10

A Cooke Triplet

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

14

Results

• Sinusoidal

wave:

f0 = 8 GHz

∆x = ∆y = λ/20

15

Reflection coefficient for MTM triplet

• Very few reflections

• broadband

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

20

Coma Conventional

MTM

Reduced

Coma

Conventional 400mm

MTM 200mm

Reduced 200mm

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

24

Thank you