Plamonics and Metamaterials

Tao Li

Tao Li

Š

[email protected]

@ j

Š

Nat. Lab. of Solid State Microstructures

Department of Materials Science and Engineering

Nanjing University

y

Basic principles

y

Surface Plasmon

y

Metamaterial

-

+

--

-+

atom or

molecule

decoupled positive and

negative charges

-

+

Positive charge background

free electron gas

metal

Positive charge background

Jellium model

metal

Jellium model

Collective oscillation of free elctronsÆ quanta h

ω

_q

Plasmon

METAMATERIAL

SOLID, CYSTAL

atom

METAMATERIAL

artificial atom

Notice:

¾This artificial material (atom) is not exist naturally!

“meta” is “beyond”

¾Th

t i

ith

t t th EM

y

Basic principles

y

Surface Plasmon

y

Metamaterial

Objective:

Electromagneitcs of Metals

⎪

⎧

_{∇ D}

_⋅

r

₌

_ρ

_f

D

E

⎧ r

r

_{( )}

Objective: Electromagneitcs of Metals

⎪⎪

⎪

⎪

⎨

∂

∂

−

=

×

∇

∇

t

B

E

D

_f

r

r

ρ

0

0

D

E

B

H

εε

μμ

⎧ =

⎪⎪

₌

⎨

r

r

( )

( )

ε ε ω

μ μ ω

=

=

⎪

⎪

⎪

⎪

⎨

∂

=

⋅

∇

∂

D

B

t

r

r

0

0

j

E

μμ

σ

⎨

⎪ =

⎪⎩

r

r

( )

( )

k

μ μ

ω ω

=

⎪

⎪

⎩

∂

∂

+

=

×

∇

t

D

j

H

r

r

_f

‹ Field distribution: E and H

‹ Field distribution: E and H

μ

Electric part can be described by

( , )

'

(

,

') ( , ')

(

)

'

(

') (

')

t

dt d

t

t

t

d

d

ε

ε

=

∫

−

−

∫

D r

r'

r

r'

E r'

J

( , )

t

=

∫

dt d

'

'

σ

(

−

'

,

t

−

t

') ( , ')

E

'

t

J r

r'

r

r'

E r'

Taking Fourier Transformation

g

0

( , )

( , ) ( , )

(

)

(

) (

)

ω

ε ε

ω

ω

ω

σ

ω

ω

=

=

D K

K

E K

J K

( , )

ω

=

σ

( , ) ( , )

K

ω

E K

ω

J K

K

E K

According to Equations

_D

=

ε

_E

+

_P

_J

=

∂

P

According to Equations

We get the

dielectric function

of metal

0

,

t

ε

=

+

=

∂

D

E

P

J

0

( , )

( , )

1

i

σ

ω

ε

ω

ε ω

= +

K

K

0

For a spatially local response,

ε

₍

_K

=

_{0, )}

ω

=

ε ω

_{( )}

2

∂ D

From wave equation

0

₂

t

μ

∂

∇ × ∇ × = −

∂

D

E

2

2

ω

2

= K

ε

ω

ω

m

&&

x

+

m

γ

x

&

= −

e

E

an external E field

Plasma frequency

( )

( )

(

)

e

t

t

m

ω

i

γω

=

+

x

E

( ) 1

i

ω

ε ω

ω

γω

= −

+

N e

m

ω

ε

=

(

)

ne

m

ω

i

γω

= −

+

P

E

( ) 1

i

ω

γω

ω

ε ω

ω

+

= −

(1

)

i

ω

ε

ω

γω

=

−

+

D

E

Drude Model

ω

If neglecting the loss

2

2

2 2

P

K c

with resonance frequency

ω

₀

e.g. geometric boundary, interband transition, or other forces…

g g

y,

,

It is more popular case in real metallic system

0

m

&&

x

+

m

γ

x

&

+

m

ω

x

= −

e

E

2

2

2

2

0

( ) 1

P

i

ω

ε ω

ω ω

γω

= +

−

−

Lorentz Model

Optical property of medium

p

p

p

y

refractive index n, extinction coefficient

κ

2 2

2

,

2

n

n

and

ε

=

−

κ

ε

=

κ

1

(

(

) )

2

n

=

ε

+

ε

+

ε

1

(

(

) ) .

2

κ

=

− +

ε

ε

+

ε

ε

_%

%

2

( ) 1

ω

P

ε ω

ω

= −

,

n

ε

ω ω

=

>

%

n is real

,

,

ω ω

ω ω

=

<

Plasma frequency

n=0

n is imaginary

Optical reflectivity

)

1

(

1

~

+

κ

.

)

1

(

)

1

(

1

~

1

+

κ

+

κ

+

−

=

+

−

=

n

n

n

n

R

y

Concepts

Concepts

y

Basic principles

y

Surface Plasmon

y

Surface Plasmon

SPP at flat metal surfaces

Optical excitation of SPP

Optical excitation of SPP

Localized Surface plasmon (LSP)

Application of SPP

pp

y

Metamaterial

y

Summary

Considering the waveguide modes in x direction, then

For TE case

ε

₂

Z>0

ε

₁

Z<0

Z<0

Z>0

ε

₂

Z<0

ε

₁

According to the continuity of H and

εE at the interface

According to the continuity of H

and εE

at the interface

Bulk Plasmon

Light

The God close a door

with a window open!

ω

_P

Forbidden band

Forbidden band

ω

_P

w e n

h

k

ω

→ ∞

ω

_SP

Surface Plasmon

Forbidden band

)

(

1

ω

ε ω

ε

ω

ω

ω

=

−

=

−

=

ω

=

S

k

k

Bulk Plasmon

Light

SPP:

k

_spp

>k

_light

2

2

2

2

0

0

x

y

z

k

k

k

k

k

for TM mode

=

+

+

SPP

Forbidden band

0

0,

y

x

k

for TM mode

and k

k

=

>

SPP

0

2

,

0,

Im

x

z

z

So k

<

k is an

Electric field distribution of SPP

δ

~ 100 nm

δ

~ 10 nm

zz

Dispersions of true SPPs at

a real system

(silver/air and silver/silica interfaces)

IMI multilayer

IMI multilayer

ε3

ε2

ε3

ε1

(1)

at z=a

(1)

Dispersion of coupled SPP

(2)

at z=a

( )

(3)

If aÆ

∞ this dispersion degenerate to

If aÆ

∞, this dispersion degenerate to

Decoupled

Decoupled

If

ε2=ε3 this dispersion splits to two Eqs

If

ε2=ε3, this dispersion splits to two Eqs.

Coupled SPP modes

Coupled SPP modes

antisymmetric

symmetric

MIM multilayer case

y

Basic principles

y

Surface Plasmon

y

Surface Plasmon

SPP at flat metal surfaces

Optical excitation of SPP

Optical excitation of SPP

Localized Surface plasmon (LSP)

Application of SPP

pp

y

Metamaterial

y

Summary

Bare light cannot couple

g

p

to SPP, due to the

mismatch of wave vectors

_k

spp

ω

_k

light

spp

Δ

If the light is not along surface

and incident with an angle

θ

Δ

and incident with an angle θ,

Then

Δ

’=

Δ

+(1-

(

sinθ

) k

)

_light

_light

K t h

t

Kretschmann geometry

ε

_prism

>1

(b) Grating coupling

k

_sp

G=2π/D

k

_light

sp

G

ti

i

Grating image

Detecting: SNOM

SEM image

SEM image

SNOM image

(c) Near-field excitation

k

E

r

k

r

E

r

incident beam

X

Z

X

Near field Scanning Optical Microscope

beam 100 nm200 nm

(d) Others:

y

Basic principles

y

Surface Plasmon

y

Surface Plasmon

SPP at flat metal/insulator surfaces

Optical excitation of SPP

Optical excitation of SPP

Localized Surface plasmon (LSP)

Application of SPP

pp

y

Metamaterial

y

Summary

Modes of Sub

Modes of Sub--wavelength metal particle

wavelength metal particle

Transverse mode

Longitudinal mode

Selective Switch

Selective Switch

y

Basic principles

y

Surface Plasmon

y

Surface Plasmon

SPP at flat metal surfaces

Optical excitation of SPP

Optical excitation of SPP

Localized Surface plasmon (LSP)

Application of SPP

pp

y

Metamaterial

y

Summary

Modulating light:

Modulating light:

Modulating light:

Modulating light:

Extraordinary Optical Transmission (EOT)

Extraordinary Optical Transmission (EOT)

Ebb

t l

Ebbesen et al,

S b

l

th

id b

Subwavelength waveguide by grooves

Enhanced detector

Enhanced Raman

Enhanced Raman

Scattering

and enhanced DOS

of SPP

t i

th

to improve the

internal Quantum

effeciency

Reciprocal vectors

h li h

to extract the light

from LED

to improve the

external Quantum

y

Basic principles

y

Surface Plasmon

y

Surface Plasmon

y

Metamaterial

A tifi i l M

ti

Artificial Magnetism

Negative Index Material (NIM)

Transformation Optics

Transformation Optics

Illumination Optics

Reconsider the plasma of metal

p

n is the electron density

it is fixed for a certain metal

1996, Pendry propose a dilute metal –

nanowire mesh

0

B

r

=

μ

μ

H

r

Always be neglected for optical material

Natural magnetism

(μ)

main comes from the spin,

In dynamic system, spin response to the external

alternative field, but frequency of the spin process

is limited up to

GHz

!

So at optical frequency we regard

μ=1

for almost

So at optical frequency, we regard

μ=1

for almost

all natural material

It is also the right reason we usually do not

g

y

consider

μ

in Maxwell’s Equations

Circuit resoance at

Out

F

Out

In

1

1

2

/

F

i

r

μ

ρ ω μ

= −

+

Array of metallic cylinder

1

f

ω

μ

1

i

μ

ω

ω

ω

= −

−

+ Γ

“magnetic” Lonretz model

g

SRR

2

2

2

1

f

i

ω

μ

ω

ω

ω

= −

−

+ Γ

Split Resonant Ring

0

i

~THz, 2001

NIR, 2005

VIS 2007

y

Concepts

Concepts

y

Basic principles

y

Surface Plasmon

y

Surface Plasmon

y

Metamaterial

A tifi i l M

ti

Artificial Magnetism

Negative Index Material (NIM)

Transformation Optics

Transformation Optics

Illumination Optics

What we are interested

“metamaterial”

metamaterial

An obtuse angle cone for

Cerenkov radiation

Cerenkov radiation

Reversed Goos–Hanchen

shift

y

Concepts

Concepts

y

Basic principles

y

Surface Plasmon

y

Surface Plasmon

y

Metamaterial

A tifi i l M

ti

Artificial Magnetism

Negative Index Material (NIM)

Transformation Optics

Transformation Optics

Illumination Optics

y

Concepts

Concepts

y

Basic principles

y

Surface Plasmon

y

Surface Plasmon

y

Metamaterial

A tifi i l M

ti

Artificial Magnetism

Negative Index Material (NIM)

Transformation Optics

Transformation Optics

Illumination Optics

Illusion Optics:

The Optical

T

f

ti

f

Transformation of

an Object into

Another Object

Another Object

A further

development of

Transformation

Optics

Optics

(a) Coupled metamaterial

(a) Coupled metamaterial