super-resolution properties of the maxwell fish-eye · 2011-12-01 · • super-resolution...

COMSOL Conference Stuttgart, October 26-28, 2011

Super-resolution Properties of the Maxwell Fish-Eye

D. Grabovičkić , J. C. González, J. C. Miñano, P. Benítez

Cedint, Universidad Politécnica de Madrid, Spain


Outline

1. Introduction

2. Spherical Geodesic Waveguide 3. Simulations in COMSOL Multiphysics

4. Conclusions


Maxwell fish-eye

2

2( )

1 ( / )n

a

2 2 2x y

x

y

J.C. Maxwell 1854

All Geometrical Optics rays from P are perfectly imaged on Q in Geometrical Optics P (x0, 0)

Q (-a2/x0, 0)

circle =a ray


Maxwell fish-eye

x

y

P

Q

circle =a ray

Q’

Mirror

2

2( )

1 ( / )n

a

, ( ) 1a n


Maxwell fish-eye

U. Leonhardt 2009

What happens in Wave Optics?

[Ulf Leonhardt, New Journal of Physics 11 (2009)]

cos cos

4sin( )

iP e PE

z 2

0( 1) ( )ak


Experimental demonstration of l/5 super-resolution

[Yungui Ma, Singapore]

Super-resolution stands for the capacity of an optical system to resolve bellow by the diffraction limit


Outline

1. Introduction

2. Spherical Geodesic Waveguide

3. Simulations in COMSOL Multiphysics

4. Conclusions


Spherical Geodesic Waveguide

x' y'

z'

x

y

z

Cylindrical 3D MFE lens

Material with spherical symmetry

2 2 2

( )

' ' '

an r

r

r x y z

2

2( )

1 ( / )n

a

Each z=constant plane is mapped on a different sphere via stereographic projections

[J.C. Miñano, P. Benítez, J.C. González, NJP, 12 (2010)]

E E


Spherical Geodesic Waveguide

10 mm 5 mm 20 mm

1005 mm 1000 mm

( )= / 1

e i

M m

M

D D L

R R

n r R r


Microwave circuit made up of the two ports and the spherical waveguide

11 12

21 22

s s

d d

V VS S

S SV V

21

11

d s

s s

V S V

V S V

22

21

2

21

| |1| |

2

(1 | | )

sI T I

o

R I

VP P P S

Z

P P S

SGW

S

Is+

Is−

Id+

Id−

Vs+

Vs−

Z0 Z0

Vd+

Vd−

Source port Drain port

When 0, 0d dV I


Outline

1. Introduction



4. Conclusions


Meshing in Comsol


Transmitted power for different frequencies

Z0

Source Drain (passive)


Transmitted power for different frequencies

Z0

=2º, l=l/33 l=1.15m

l Source

Drain (passive)


Simulation of l/500 super-resolution

Source Drain (passive)


Outline

1. Introduction



4. Conclusions


Conclusions

• Super-resolution properties of the Maxwell Fish-eye are analyzed using

Spherical Geodesic Waveguide (SGW).

• Simulations of the SGW show super-resolution up to l /500 at

microwave frequencies.

• The super-resolution is achieved using an approximate model of the

SGW (the model having n=1 inside the waveguide) conveniente for

manufactoring.

super-resolution properties of the maxwell fish-eye · 2011-12-01 · • super-resolution...

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