artificial magnetic resonators and potential applications in nonlinear field yongmin liu applied...

Artificial Magnetic Resonators and

Potential Applications in Nonlinear Field

Yongmin Liu

Applied Science & Technology

Physics 208A Presentation

Oct. 18th, 2004

Outline

I. Background of Metamaterials

II. Artificial Magnetic Resonators at THz

III. Potential Application in Nonlinearity

IV. Summary

What are Metamaterials?What are Metamaterials?

Artificially fabricated structures or media that exhibit electrodynamic properties not found in naturally occurring materials.

* Dimension of the unit cell is less than the wavelength of excitation EM wave, thus the effective-media theorem can be applied.

Why Metamaterials are Interesting?Why Metamaterials are Interesting?

* We can design and control the properties of materials. Some novel properties, such as negative electric permittivity, negative magnetic permeability, negative refractive index etc. have been explored.

Negative PermittivityNegative Permittivity

The permittivity of metal is given by

)(1)(

2

i

ep

eep m

ne

0

22

Plasma frequency:

where n is the electron density, and me is the electron mass

Damping factor: 0

where is the electric conductivity

In the visible region, is negative for most metals. At lower frequencies, permittivity is imaginary.

(typically in the UV region)

Negative with small loss in low frequencies can be achieved by metallic wire lattice

Pendry J.B. et al., Phys. Rev. Lett. 76, 4773 (1996)

Negative PermittivityNegative Permittivity (cont’d) (cont’d)

,2

2

a

rnneff

)/ln(

2

20 rane

meff

eff

effep m

en

0

22

,100.1 6 mr

,100.5 3 ma

31710675.5 mn

!!2.8 GHzep

)1.0(1

2

ep

epeff i

lattice constant:

radius of wire:

Negative can be achieved by split-ring resonator (SRR)

Negative PermeabilityNegative Permeability

Magnetism originates from

1) orbital motion of electrons

2) unpaired electron spins

The magnetic response of most nature materials fades away in GHz region.

Artificial magnetism can be realized by conducting, nonmagnetic split-ring resonators. The magnetic response is able to extend to THz, even higher frequency with lar

ge positive or negative permeability.

Will discuss in detail later !

Left-handed Materials (LHM) with Left-handed Materials (LHM) with Negative Refractive Index (NIR)Negative Refractive Index (NIR)

2n

n

When andsimultaneously, we have to choose

Refractive index:

E

H

k

S

Right handed materials (RHM)

E

H

k S

Left handed materials (LHM)

n > 0

n < 0

,HEk

EHk

Maxwell’s equation:

LHM with NRI (cont’d)LHM with NRI (cont’d)

1. Snell’s law: n sin

sin

2

1

Exotic properties of LHM:

Negative refraction !

2. Flat superlens

Diffraction-limit (min) free !

Veselago V.G. Sov. Phys.10, 509 (1968); Pendry J. B. PRL 85, 3966 (2000)

S kLHM

RHM

Fourier Expansion of 2D object:

, ,

, , exp

x y

x y z x yk k

t k k ik z ik x ik y i t

E r E

2 2 2 2 2 2 2 2, ,z x y x yk c k k c k k

2 2 2 2 2 2 2 2, .z x y x yk i k k c c k k

Propagating waves:

Evanescent waves:

Z


Artificially engineered metamaterials implements the concept of LHM!

Photograph of LHM

Shelby R. A. et al., Science 292, 77 (2001); Smith D. R. et al., Science 305, 788 (2004)

Negative refraction by LHM prism

LHM with NRI (cont’d)LHM with NRI (cont’d)Imaging properties of LHM

Houck A. A. et al. PRL 90, 137401 (2003); Kolinko P. et al. Opt Exp 11, 640 (2003)

Simulation of subwavelength imging by FDTD

Imaging experiment in microwave region

Electric field of a point source focused by a LHM slab

http://physics.ucsd.edu/~drs/ Prof. Smith D.R. in UCSD


Metamaterials open a new field in physics, engineering material science and optics!

Negative refraction is among the Top 10 highlights of 2003 by Physicsweb

Outline




IV. Summary

Concept:

1. The magnetic-flux induced current loop to form magnetic dipole.

2. The intrinsic conductance and inductance will cause strong paramagnetic or diamagnetic activity around the resonance frequency.

Artificial Magnetic Resonators at THzArtificial Magnetic Resonators at THz

+ + +

+ + +

_ _ _

_ _ _

Ha

2r

Pendry J.B. et al, IEEE MTT 47, 2075 (1999)

Artificial Magnetic Resonators at THz (cont’d)Artificial Magnetic Resonators at THz (cont’d)

Current distribution of SRR simulated by Microwave Studio


H-field of SRR simulated by Microwave Studio

320

20

2

2

321

1

Crri

ar

eff

30

20

3

Cr

)/1(

3223

02 arCrmp

Resonance frequency:

Magnetic plasma frequency:

mr 3100.2

GHzfGHzf mp 17.4,94.20

Typical value:

mdma 43 100.1,100.5

Artificial Magnetic Resonators at THzArtificial Magnetic Resonators at THz

Pendry J.B. et al, IEEE MTT 47, 2075 (1999)

Dispersion of eff with frequency

50um

Sample

L :

len

gth

G: gap

S: space

W:

wid

th

quartz

Cu

Au/Ti

L:26m, S:10m, W:4m

d=L+S, G: 2m, :1.5x103


Ye T.J. et al., Science 303, 1494 (2004)

DieSimulation

(THz)Experiment

(THz)

D1 1.22 1.27±0.07

D2 0.88 0.96±0.05

D3 0.91 0.85±0.15

=30o

IRI0


Experimentally and theoretically ellipsometric results


k (cm-1) f (THz) λ/a

LSR400 1100 33.00 2.52525

LSR350 1282 38.46 2.47629

LSR300 1490 44.70 2.48571

0 10000 20000 30000 40000 50000 60000-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Re(

Mue

)

Frequency (GHz)

LSR300 LSR350 LSR400

Near-infrared (45THz) magnetic resonance is achieved by novel design. Final goal is visible

region.

Outline




IV. Summary

Potential Application in NonlinearityPotential Application in Nonlinearity

Extremely high intensity is the key to nonlinear phenomena!Brabec T et al., Rev. Mod. Phys. 72, 545 (2000)

Potential Application in Nonlinearity (cont’d)Potential Application in Nonlinearity (cont’d)

When resonance takes place, the energy is strongly localized inside the small resonators. Local fields can be many orders higher than that in free space.

For a capacitor of , one single photon can create an electric field about 108V/cm.

nmnmnm 111

Localized E-filed with 103 times larger than the external field.


Embed the magnetic resonator into dielectric matrix whose permittivity is intensity-dependent.

Two aspects of the nonlinear response:

1) The strong localized field changes the dielectric permittivity, since D D (|E|2)

2) Nonlinear eigenfrequency adjusts correspondingly due to the change of capacitance.

External H fieldIntensity of the local E fieldValue of permittivity Capacitance Eigenfrequency


Effect nonlinear permittivity:

)1()|(|)|(|

222

i

EE pDeff

Effective permeability:

i

daH

NLeff 2

02

222 )/(1)(

)|)((|)()(

222

0 HEh

d

a

cH

gD

gNL

where

Consider Kerr nonlinearity:

220

2 /||)|(| cDD EEE

Ec is a characteristic electric field, and corresponds to focusing or defocusing nonlinearity respectively.

1

Zharov A.A. et al., PRL 91, 037401 (2003)


6

222222222 ]))[(1(

||X

XXEAH c

,/,/ 000 NLX is the eigenfrequency in linear limit

Jump of eff due to

external H field Transition of eff from – to +

Outline




IV. Summary

SummarySummary

The unprecedented properties associated with metamaterials, such as negative refraction, superlensing etc. are reviewed.

The principle of achieving negative permeability, which is critical in realizing LHM is interpreted. Magnetic resonators with resonance frequency above THz is successfully demonstrated.

The strong localized field inside the resonator can cause nonlinear effect. As one example, the hysteresis-type dependence of the magnetic permeability on the field intensity is theoretically studied.

It is the right time to start the new topic--nonlinear effects in metamaterials. The engineering of nonlinear composite materials will open a number of applications such as swithers, frequnecy multipliers etc.

artificial magnetic resonators and potential applications in nonlinear field yongmin liu applied...

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