Diapositiva 1 - Magnetismmagnetism.eu/esm/2018/slides/vavassori-slides3.pdf · P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018 Localized surface

P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

FT-3: Magneto-optics and Magneto-plasmonics Part 2

P. Vavassori

-IKERBASQUE, Basque Fundation for Science and CIC nanoGUNE Consolider, San Sebastian, Spain.

550 600 650 700 750 800

-4

0

4

8

(mra

d)

Wavelength (nm)

-1x105

0

1x105

2x105

1/

(rad

-1)

684 687 690 693

Reflected electric field Et

Et

Ei

-

Et

H -HEi

Incident electric field Ei

MO-LPR phase

y

x

EiMO

H

LPR phase

Substrate

l’

FWHM


Outline

NANOANTENNAs COMBINING MAGNETIC AND PLASMONIC FUNCTIONALITITES

➢ Localized surface plasmons & Magneto-optical Kerr effects (MOKE): Introduction

➢ Physical picture and modeling

➢ LSPR-based sensing: Towards molecular sensing

➢ Photonics technology: control of the non-reciprocal light propagation

MAGNETOPLASMONIC METAMATERIALS

➢ Surface lattice resonances in arrays of nanoantennae

➢ Arrays of elliptical nanoantennae

➢ Magnetoplasmonic gratings: arrays of antidots

CONCLUSIONS


Localized surface plasmon resonances (LSPRs)

Small d for excitation of a

LSPR in the optical visible

range (air, glass….)

Subwavelength localization

of electromagnetic energy

G

0 0.5 1 1.5 2

0

0.2

0.4

0.6

0.8

1

Localized surface plasmon resonances (LSPRs or LSPs) collective oscillations of

conduction electrons in metallic nano structures.

G

axx

wavelength

frequency

p

ph

ase

F(t)

( )

( )tF

txxx

~=a( )tx~

p

d < l/2

+50

-50

0

0

12

10

8

6

4

2

d=150nm

h=32nm Au

Air

Glass

-100 0 +100 -100 0 +100[nm]

[nm]

λ=717nm λ=663nm|E|2 [V2·m2]

(a) (b)

Fig. 1 Example of strong lightconfinement related to excitation of plasma

resonance in a nano-disk of Au

Ellipsoid

=

zzzyzx

yzyyyx

xzxyxx

aaa

aaa

aaa

a~


p

Electric field lines due to an electric dipole oscillating vertically at the origin. Near the dipole,

the field lines are essentially those of a static dipole.

At a distance of the order of half wavelength or greater, the field lines are completely

detached from the dipole

q

a Imext

2a sca

Scattering and absorption remove energy from the incoming EM

Absorption

Scattering

Extinction

Wavelength

absscaext +=

sample

spectrometer

EM field irradiated by an oscillating dipole


Extinction

Wavelength

LSPR

Localized surface plasmon resonances (LSPRs)

Size Embedding medium

Red-shift

Red-shift

Size Embedding medium

Red-shift

Red-shift

a Imext

2a sca

Scattering and absorption remove energy from the incoming EM

Absorption

Scattering

absscaext +=

a Imabs

+50

-50

0

0

12

10

8

6

4

2

d=150nm

h=32nm Au

Air

Glass

-100 0 +100 -100 0 +100[nm]

[nm]

λ=717nm λ=663nm|E|2 [V2·m2]

(a) (b)

Fig. 1 Example of strong lightconfinement related to excitation of plasma

resonance in a nano-disk of Au

sample

spectrometer


G

displacement

km

Displacement

in phase with E

Displacement

in anti-phase with EDisplacement 90°

out of phase with E

F

Phase

( )tx~

( )tx~

Phase (

px) Im

(a) (a

.u.)

LSPR

Frequencywavelength

frequency

[ ] a

Polarizability phasePhase

(px) 1.0

0.5

0.0

amplitude

G

[ ] a

LSPR as a damped harmonic oscillator


Magnetoplasmonics

(SPPs MKSPP → K’SPP = KSPPKSPP)

Control of MO activity

Control of plasmon properties

G.Armelles , A. Cebollada , A. García-Martín , and M. Ujué González, Adv. Optical Mater. 2013, 1, 10–35


Adv. Mater. 19, 4297 (2007)➢ Large areas

➢ Disordered distribution

➢ Insulating substrates

➢ Low concentration to avoid interactionsChalmers

Hole-Mask Colloidal Lithography


E-beam lithography on glass

Au

nanoGUNE – Aalto – Stockholm – Singapore


Negative e-beam lithography on glass

nanoGUNE – Aalto – Stockholm – Singapore


650 nm490 nm350 nm

Ni nanoantennas

LSPR LSPR

LSPR

Disks 60x30 nm Disks 100x30 nm Disks 160x30 nm

Extin

ctio

n

Extin

ctio

n

Extin

ctio

n

Hole-Mask Colloidal Lithography (Ni disks on glass)Adv. Mater. 19, 4297 (2007)


Is the effect due to a LSPR?

In press on SmallSmall 7, 2341 (2011)

Scanning Near-Field Optical (SNOM) microscopy: amplitude and phase!

Exticn

tio

n

In the NF, electric field is like the one

produced by a static electric dipole

Intense E fields of opposite sign

(p out of phase)

-p/2

+p/2

+p/2-p/2


A real LSPR?

In press on SmallSmall 7, 2341 (2011)

Scanning Near-Field Optical (SNOM) microscopy: amplitude and phase!

sample

spectrometer

60 nm

160 nm

100 nm


qK,F

K,F

P. Vavassori, APL 77, 1605 (2000)

Magnetic characterization

Magneto-Optical Kerr effect configurations


Spectroscopic Polar MOKE

H

sample

x,y,z

Supercontinuum

Source

(400-2000 nm)

AO

Monochrom

(400-800 nm)

5mW

1nm

Lock-in ref (w, 2w)

I PEM (w)

pol

photodiode

pol

lens

lens

DC w 2w

q(H)(H)I0

P. Vavassori, APL 77 1605 (2000)

Modulation polarizationtechnique for recordingthe longitudinal and polarKerr effects, both q and .

H

sample

x,y,z

Supercontinuum

Source(420-2000 nm)

AO filter

(420-2000 nm)

5mW

1nm

ref (w,2w)PEM (w)

pol

photodiode

pol

lens

lens

Lock-in

(H) q(H)

t

H -H

l < l

l > l

lq

q,

H

y

x

EiEi

SO

M

ErqK K

EtqF F


Polar MOKE spectra: polarization of reflectedlight linked to the LSPR position

➢ Maximum of qK and crossing

of K follow the LSPR position

Film – no crossings in the visible range

Ni film

450 600 750 900-2.0

0.0

2.0

4.0

Ni film

qk

k

Angle

(m

rad)

Wavelenght (nm)

650 nm

LSPR

Extin

ctio

n

450 500 550 600 650 700 750 800

-4,0x10-3

-2,0x10-3

0,0

2,0x10-3

4,0x10-3

Experimental

Disks 100 nm

Pol P

q

Pol S

q

An

gle

(ra

d)

Wavelength (nm)

450 500 550 600 650 700 750 800-3,0x10

-3

-2,0x10-3

-1,0x10-3

0,0

1,0x10-3

2,0x10-3

3,0x10-3

Experimental

Disks 60 nm

Pol S

q

Pol P

q

An

gle

(ra

d)

Wavelength (nm)

450 500 550 600 650 700 750 800-5,0x10

-3

-2,5x10-3

0,0

2,5x10-3

5,0x10-3

Experimental

Disks 160 nm

Pol P

q

Pol S

q

An

gle

(ra

d)

Wavelength (nm)

350 nm

LSPR

Extin

ctio

n

490 nm

LSPR

Extin

ctio

n

qK

K

P-MOKE Extinction

Refence Ni film

P. Vavassori, Appl. Phys. Lett. 77, 1605 (2000)

Phys. Rev. Lett. 111, 167401 (2013)

650 nm

2.0

1.0

0.0

-1.0


0 0.5 1 1.5 2

0

0.2

0.4

0.6

0.8

1

Damped harmonic oscillator

Phase contribution

Simple physical picture: two coupled damped harmonic oscillators!!!

➢ Damped H.O.: confinement

➢ S.O. coupling: material property

Phase (p)

Amplitude

Fundamental hypothesis here: linear and perturbative regime


Induced electric dipoles

➢ MO enhancement depends only on ayy (shape can improve enhancement)

➢ Relative phase on both ayy and yx

1. Oscillator along x

3. Oscillator along y

2. S.O. Coupling

EPMO

M

pyS.O. = cyx Ex

i = yx Exi

px = cxx Exi = ( – m) Ex

i

Exi = E0 – Ex

d

EyS.O. = py

S.O./cyy = pyS.O./( –m)

py = ayy EyS.O. = Ex

i (ayy yx) / ( – m)

( )2

m

yyyx

x

y

p

p

a

−=

px = axx E0

Gives the polarization of the far-field radiated

in the z-direction by these two mutually

orthogonal oscillating electric dipoles


Simple physical picture: two S.O. coupled damped harmonic oscillators: relative phase

➢ Damped H.O.: confinement

➢ S.O. coupling: material property

Kerr

Faraday

0< < p/2

p/2 < < p

qK = 0

K

K

= p/2

= p

= 0

( ) yy

m

yx

xy

x

ypp

p

p

a

+

−=

=−=

=

2

~~~

~Polarization of the radiated field

Wavelength

( )2m

yx

x

y

p

p

−=

ayy

Phys. Rev. Lett. 111, 167401 (2013)

z

E(z, t)

S.O.


N. Maccaferri et al., Opt. Express 21, 9875-89 (20113)

p = ( – m) Ei ; Ei = E0 + Ed

External field

Depolarizing field

Internal field

Oblate ellipsoidCilindrical disk

E0

Ed

p

++

+

---

Embedding medium

˜

Depolarizing field is the key


Static depolarization: the sphere case

pE Lm

d

1−=

pNE~1

m

d

−=

3

1=L

More in general, for an ellipsoid:

Ei = E0 + Ed

0~Ep a=

( ) im Eεp −= ~

( )

( ) 02~

~3E

ε

εp

m

mm

+

−=

( )

( )

( )

( ) 00

3

02~

~4

2~

~3EE

ε

εE

ε

εP a

p

=

+

−=

+

−=

m

mm

m

mm aV

( )( )INI

IIεα ~~~~

~~~~

mm

mm

−+

−=

( ) ( ) ( )13 1

2 2 222 2

02

i j k

i i j k

a a aL q a q a q a dq

−− −

= + + +

Nii = Li

ak

ai

aj

a

Clausius-Mossotti

Internal and depolarizing fields: quasi static approx


Wavelength dependent corrections to polarizability: modified long-wavelength approximation (MLWA)


Oblate ellipsoidCilindrical disk

pp 64

32 VkiD

VkLN iiiiii −−=pNE

~1

m

d

−= zyxxdVr

rxD i

V

ii ,,;

2

22

=+

=

( )3 2

3

ˆ ˆ3 ˆ ˆ2 ( )

3 2d d

Pd i k k dV

r r

− = = + +

u P u P u P u

E E

k is the light wave vector modulus,

r the distance from the center of

the ellipsoid, and a unit vector in

the direction of r.

u

Static depolarization due

to a uniform E0 (shape of

the nanoparticle) → Li

Radiative reaction due to

the recoil force (Abraham–

Lorentz force) acting on an

oscillating dipole emitting

electromagnetic radiation

Dynamic depolarization

arising from de-phasing

of the radiation emitted

by different points in the

ellipsoid

DiLi


400 600 800 1000

-0.5

0.0

0.5

1.0

Wavelength (nm)

0.0

D = 160 nm

xy pp ~/~

..OS

yya yyaIm

[

py/

px]

(p

)

Im[a

yy ]

It is a phase business

350 400 450 500 550 600 650 700 750 800 850 900-8,0x10

-3

-6,0x10-3

-4,0x10-3

-2,0x10-3

0,0

2,0x10-3

4,0x10-3

6,0x10-3

8,0x10-3

Pol P

q

Pol S

q

NF Calculated

Disks 160 nm

An

gle

(ra

d)

Wavelength (nm)

( )

yyOSyy

m

yx

x

y

p

paa

+=+

−=

= ..2

( )2~

~

m

yyyx

x

y

p

p

a

−=

The polarization of the far-field

radiated in the z-direction by these

two mutually orthogonal oscillating

electric dipoles is given by the ratio

z

Kerr rotation and ellipticity spectra

for an isolated nanostructure

qK= Re[py/px] and K= Im[py/px].

qK

Eox

E(z,t)

K = 0

qK = 0

0=

x

y

p

p

2

p =

x

y

p

p

Phase difference between the two radiating dipoles px and py

Phys. Rev. Lett. 111, 167401 (2013)


-5.0

-2.5

0.0

2.5

K

70 nm

100 nm

160 nm

Angle

(m

rad)

450 600 750 900

-2.0

0.0

2.0

4.0

Wavelength (nm)

qK

70 nm

100 nm

160 nm

Angle

(m

rad)

It is a phase business

400 600 800 1000

-0.5

0.0

0.5

1.0

Wavelength (nm)

0.0

70 nm

100 nm

160 nm

100 nm 160 nm70 nm

Im[a

yy ]

[

py/

px]

(p)

( )

yyOSyy

m

yx

x

y

p

paa

+=+

−=

= ..2~

~

( )2~

~

m

yyyx

x

y

p

p

a

−=

qK = 0

2~

~p

=

x

y

p

p

qK

Eox

E(z,t)

K = 0

0~

~

=

x

y

p

p

Phys. Rev. Lett. 111, 167401 (2013)


Model system

400 500 600 700 800 900 1000

Absorp

tion (

arb

. units)

Wavelength (nm)

m

Glass substrate, g

Ambient, o

d

Glass substrate, g

d EMA

Modeling the spectra

Our system


D. Stroud, Phys. Rev. B 12 (8), 3368 (1975)M. Abe, Phys. Rev. B 53 (11), 7065 (1996)M. Abe and T. Suwa, Phys. Rev. B 70, 235103 (2004)

M. Schubert, T. E. Tiwald and J. A. Woollam, Applied Optics 38 (1), 177 (1999)J. Zak, E. R. Mook, C. Liu and S. D. Bader, JMMM 89, 107 (1990)S. Visnovsky et al., Optics Express 9 (3), 121 (2001)

Step 2 (far-field)

qK

K

pp

sp

r

rRe

ss

ps

r

rRe

pp

sp

r

rIm

ss

ps

r

rIm

Fictitious MO film

Step 3 (far-field including substrate)

qK

K

pp

sp

r

rRe

ss

ps

r

rRe

pp

sp

r

rIm

ss

ps

r

rIm

Complete system

Transfer matrix method(multilayers)

Effective medium approximation (EMA)

Modeling the spectra: steps 2&3


N. Maccaferri et al., Phys. Stat. Solidi (a) (2014)


450 500 550 600 650 700 750 800

-4,0x10-3

-2,0x10-3

0,0

2,0x10-3

4,0x10-3

Experimental

Disks 100 nm

Pol P

q

Pol S

q

An

gle

(ra

d)

Wavelength (nm)

450 500 550 600 650 700 750 800 850-3,0x10

-3

-2,0x10-3

-1,0x10-3

0,0

1,0x10-3

2,0x10-3

3,0x10-3

Calculated

Disks 100 nm

Pol S

q

Pol P

q

An

gle

(ra

d)

Wavelength (nm)

450 500 550 600 650 700 750 800-5,0x10

-3

-2,5x10-3

0,0

2,5x10-3

5,0x10-3

Experimental

Disks 160 nm

Pol P

q

Pol S

q

An

gle

(ra

d)

Wavelength (nm)

450 500 550 600 650 700 750 800-3,0x10

-3

-2,0x10-3

-1,0x10-3

0,0

1,0x10-3

2,0x10-3

3,0x10-3

Experimental

Disks 60 nm

Pol S

q

Pol P

q

An

gle

(ra

d)

Wavelength (nm)

450 500 550 600 650 700 750 800 850 900

-5,0x10-3

-2,5x10-3

0,0

2,5x10-3

5,0x10-3

Pol P

q

Pol S

q

Calculated

Disks 160 nm

An

gle

(ra

d)

Wavelength (nm)

450 500 550 600 650 700 750 800-4,0x10

-3

-3,0x10-3

-2,0x10-3

-1,0x10-3

0,0

1,0x10-3

2,0x10-3

3,0x10-3

4,0x10-3

Calculated

Pol S

q

Pol P

q

Disks 60 nm

An

gle

(ra

d)

Wavelength (nm)

Response of an ensemble of such oscillators randomly distributed on a glass substrate (EMA)

No adjustable parameters:

tabuled optical and MO constants;

sizes and nanoantennaedensity from SEM images

Substrate plays a role

N. Maccaferri et al., Phys. Status Solidi A 211, 1067-75 (2014)


Agreement between

calculated and

experimental spectra is

almost perfect!


500 1000 1500 2000 2500-4,0x10

-3

-3,0x10-3

-2,0x10-3

-1,0x10-3

0,0

1,0x10-3

2,0x10-3

3,0x10-3

4,0x10-3

Ni film

Pol S

q

Pol P

q

An

gle

(ra

d)

Wavelength (nm)500 1000 1500 2000 2500

-1,0x10-2

-8,0x10-3

-6,0x10-3

-4,0x10-3

-2,0x10-3

0,0

2,0x10-3

4,0x10-3

6,0x10-3

8,0x10-3

1,0x10-2

NF Calculated (n=1.125)

Pol S

q

Pol P

q

Disks 100 nm

An

gle

(ra

d)

Wavelength (nm)

Confinement

❑ Confinement (LSPR) – redistribution (blue shift) of the main spectral features due to intrabandtransitions (material properties, q and linked via Kramers-Kronig relations)

Phase adjustment: spectral features redistribution

LPS

IntrabandInterband


450 500 550 600 650 700 750 800 850-3,0x10

-3

-2,0x10-3

-1,0x10-3

0,0

1,0x10-3

2,0x10-3

3,0x10-3

Calculated

Disks 100 nm

Pol S

q

Pol P

q

An

gle

(ra

d)

Wavelength (nm)

400 500 600 700 800 900 1000 1100 1200-8,0x10

-3

-6,0x10-3

-4,0x10-3

-2,0x10-3

0,0

2,0x10-3

4,0x10-3

6,0x10-3

8,0x10-3

Disks 100 nmPol S

q

Pol P

q

EMA Calculated (f = 0.1)

An

gle

(ra

d)

Wavelength (nm)

500 1000 1500 2000 2500-4,0x10

-3

-3,0x10-3

-2,0x10-3

-1,0x10-3

0,0

1,0x10-3

2,0x10-3

3,0x10-3

4,0x10-3

Ni film

Pol S

q

Pol P

q

An

gle

(ra

d)

Wavelength (nm) 500 1000 1500 2000 2500-1,0x10

-2

-8,0x10-3

-6,0x10-3

-4,0x10-3

-2,0x10-3

0,0

2,0x10-3

4,0x10-3

6,0x10-3

8,0x10-3

1,0x10-2

NF Calculated (n=1.125)

Pol S

q

Pol P

q

Disks 100 nm

An

gle

(ra

d)

Wavelength (nm)

Confinement

Substrate

❑ Confinement (LSPR) – redistribution (blue shift) of the main spectral features (material properties, qand linked via Kramers-Kronig relations)

❑ Substrate – reduction of MOKE contrast and slight additional blue shift of the spectral features

Step 1

Step 2 Step 3

Let’s have a look at the individual steps

LPS

IntrabandInterband

Phys. Rev. Lett. 111, 167401 (2013); Phys. Status Solidi A 211, 1067-75 (2014)


MM

450 600 750 900

Wavelength (nm)

100 nm

ErEr

MM

450 600 750 900

Wavelength (nm)

100 nm

ErEr

qkk

qk

k

PhaseAmplitude

Wavelength

Summary for an individual magnetic nano-antenna

The concerted action of LSPRs and MO activity allows for the controlled

manipulation of Kerr rotation/ellipticity of ferromagnetic nanostructures

(beyond intrinsic material properties).

MO-LSPR

pEr

Er

EiEi

t

PMO

PO

t

PMO

PO

lG lR

Phase delay tuning

lR

lG

Phys. Rev. Lett. 111, 167401 (2013)


Control of magneto-optics via magnetoplasmonic anisotropy

Nano Letters 14, 7207 (2014)

L-MOKE

170/240 nm; t = 30 nm

“Magnetoplasmonic design rules for active magneto-optics”

Shape engineeringActive tuning

MO enhancement (3D structures)

Enhancement by a factor of 20

450 600 750 900 1050-0.14

-0.07

0.00

0.07

0.14

qK (

mra

d)

Wavelength (nm)

E

45°

@ 800nm

0

1

-1

0° 90°


LPRS phase-sensitivity in the reflected/transmitted light polarization

N. Maccaferri et al., Nature Commun. 6, 6150 (2015)

Extin

ctio

nE

xtin

ctio

nE

xtin

ctio

n

Wavelength

Wavelength

Wavelength

Extinction

Min l detectable ~ 0.5 nm

of PA-6.6MLtMin10

1=

ALD deposition Talk by N. Maccaferri


LPRS phase-sensitivity in the reflected/transmitted light polarization

Extin

ctio

nE

xtin

ctio

nE

xtin

ctio

n

Wavelength

Wavelength

Wavelength

Extinction

Min l detectable ~ 0.5 nm

of PA-6.6MLtMin10

1=

ALD deposition

R. Verre et al. Nanoscale 8, 10576 (2016)

Au dimers


Near field interactions: Magnetoplasmonic ruler

Plasmon ruler is an emerging concept where strong near-field coupling of plasmon nanoantenna

elements is employed to obtain the structural information at the nanoscale (nanoscale distances).

Magnetoplasmonic ruler concept

MP ruler: two orders of

magnitude higher precision

compared to the state-of-the-art

plasmon rulers.

Nano Letters 15, 3204 (2015)

Kerr

q (

rad)

4.0

3.0

2.0

1.0

0.0

x 10-4


NANOANTENNAs COMBINING MAGNETIC AND PLASMONIC FUNCTIONALITITES

➢ Localized surface plasmons & Magneto-optical Kerr effects (MOKE): Introduction

➢ Physical picture and modeling

➢ LSPR-based sensing: Towards molecular sensing

➢ Photonics technology: control of the non-reciprocal light propagation

MAGNETOPLASMONIC METAMATERIALS

➢ Surface lattice resonances in arrays of nanoantennae

➢ Arrays of elliptical nanoantennae

➢ Magnetoplasmonic gratings: arrays of antidots

CONCLUSIONS

Outline


Ordered arrays of metallic nano-antennas (MNAs) placed in symmetric or quasi-

symmetric refractive index environment exhibit surface lattice resonances

(SLRs) which arise from diffraction-induced coupling between LSPRs of the

MNAs.

This coupling may result in significant reduction of plasmon radiative damping,

and therefore, narrowing of plasmon resonance, which is of interest for plasmon

based sensors.

Reduced plasmon radiative damping – Fano-like resonance

Ex

MNAs

l = dy * n

dy

l = dy * n





MNAs.


and therefore, narrowing of plasmon resonance which is of interest for plasmon

based sensors.

MNAs

Ey

l = dx * n dx

l = dx * n

Reduced plasmon radiative damping – Fano-like resonance





MNAs.


and therefore, narrowing of plasmon resonance which is of interest for plasmon

based sensors.

Arrays of magnetoplasmonic nanoantennas

Magnetic

MNAs

Ei

M

x

lMO = dx * n

dy

dx

lO = dy * n

l = dy * n


From random to ordered arrays: Polarizability

l = d * n

600 800 1000 1200

0.1

0.2

0.3

0.4

0.5

Im[a

lph

a]

(no

rm)

Wavelength (nm)

Periodic

Random

Ni

100 nm

30 nm

400 nm

n = 1.5

400 nm

500 600 700 800 900 1000-5000

0

5000

10000

15000

S (

m

-3)

Wavelength(nm)

Re[S]

Im[S]

l =d * n


550 600 650

-1

0

1

2

3

Wavelength (nm)

S-p

ha

se

(ra

d)

0

5000

10000

15000

20000

S-a

mp

litud

e (

m-3)

600 800 1000 1200

0.1

0.2

0.3

0.4

0.5

Im[a

lph

a]

(no

rm)

Wavelength (nm)

Periodic

Random

500 600 700 800 900 1000-5000

0

5000

10000

15000

S

(m

-3)

Wavelength(nm)

Re[S]

Im[S]

The S coupling factor shows

a suddend and large phase

change around l*.

Constructive/destructive

interference.l* =d * n

On the origin of SLMs


l ≈d * n

]1Im[]Im[

]Re[]1Re[

]Im[

Im

Re

2Im

2Re

Im*

a

a

a

−=

−=

+

=

S

S

]Im[]Im[ * aa

]Im[]Im[ * aa <<

500 600 700 800-10000

-5000

0

5000

10000

15000

S,

/a

m

-3]

Wavelength (nm)

Re[S]

Re[1/a] Im

*1

]Im[

=a

500 600 700 800-10000

-5000

0

5000

10000

15000

S,

/a

m

-3]

Wavelength (nm)

Im[S]

Im[1/a]

]Im[]Im[ * aa

600 800 1000 1200

0.1

0.2

0.3

0.4

0.5

Im[a

lpha] (n

orm

)

Wavelength (nm)

Periodic

Random

On the origin of SLMs

Resonance position mainly determined

by crossing points of real parts.

Strength of resonance determined by

difference between imaginary parts


Material: Py; Lattice parameters: px 400 nm py 400 -500 nm

From random to ordered arrays: MP crystals

Refractive index matching oil (n = 1.5)

M. Kataya et al., Nat. Commun. 6, 7072 (2015)

py

40

0 -

50

0 n

m

px 400 nm

Exct.

qK


Rectangular arrays


ll=d*n

Relative position of the LSPR and the diffractive interference

Resonance lineshape evolution varying the relative position

of the LSPR with respect to the Rayleigh’s anomaly


N. Maccaferri et al., Nano Lett. 16, 2533 (2016)

LA

LA SA

SA

Enhanced and tunable O and MO-Anisotropy

MOA = 22KK q + MOALA-MOASA


N. Maccaferri et al., Nano Lett. 16, 2533 (2016)

Experiment

Enhanced and tunable O and MO-Anisotropy


Py

Py

Py

Py

Au Au

AuAu

Ei

Checkerboard hybrid arrays of Py and Au nanoantennae

Efficient radiative far-field coupling between the

magnetic and noble-metal components

M. Kataia et al., Opt. Express 24, 3652 (2016)

Integrating MO active

and pure plasmonic

nanostructures:

combination of intense

optical resonances with

strong MO activity.

Ni

50%Ni 50%Au

50%Ni

50%Au

Ni


LSMs with hybrid nanostructures

Another common strategy toovercome the excess ofdamping is to develop hybridstructures consisting of noblemetals and ferromagnets.

Banthí et. al Adv. Opt. Mat. 24,

OP36 (2012).

Dimers

Ni

Au

SiO2

Mikko Kataja, Pourjamal Sara &Sebastiaan van Dijken

Aalto, Finland


➢ Concerted action of LSPRs (or SPPs) and MO-coupling can beexploited to achieve a controlled manipulation of the MO response(control Kerr rotation/ellipticity) beyond what is offered by intrinsicmaterial properties.

Patterning magnetic nanostructures for resonant interaction with light: Magnetoplasmonic Crystals

➢ Magnetically tunable plasmonic crystal based on the excitation ofFano-like lattice surface modes in periodic arrays.

✓ Highly tunable and amplified magneto-optical effects as comparedto disordered systems.

➢ Two-dimensional magnetoplasmonic crystals supporting surfaceplasmon polariton modes and displaying a two-dimensional photonicband structure.

✓ Design of metamaterials with tailored and enhanced magneto-optical response by engineering the plasmonic band structure vialattice engineering.

Concluding remarks


Other directions explored: magneto-plasmonics with SPP s

SPPs are localized electromagnetic

modes/charge density oscillations at

the interface of two media with

dielectric constants of opposite

signs, e.g. a metal and a dielectric,.

s ↔ p-polarization coversion!!

p-polarization only


SP resonance: coupling with a grating (conservation of momentum)

ki

θ

ki sin(θ)kg

kSP

kSP = ki sin(θ) - kg

ki θ

ki sin(θ) kg

kSP

kSP = ki sin(θ) + kg

+1 order coupling -1 order coupling

grating


Magntoplasmonic gratings: MOKE enhancement due to resonant coupling with SPPs

Magnetic diffraction grating

Antidot array (square lattice ):

material Py (Fe20Ni80), thickness = 80 nm,

lattice parameter = 405 nm,

hole diameter = 265 nm

by deep-UV photolithography

(Prof. A. Adeyeye, Singapore)

N. Maccaferri et al., ACS Photonics 2, 1769 (2015)


k||

kSSP1

(-1,+1)kSSP2

k||(-1,0)

kSSP(-1,-1)

Gx

Gy

k||

kSSP1

kSSP2

k||

kSSP

(-1,0)(-1,-1)

(0,-1)

Gx

Gy

SPP band structure: perturbative approach

= 45°

= 0°

Type II

k|| = k0Sinq

Type I

Type IIType I

(-1,-1) (-1,0)

(0,-1)

Type II:

both p- and s-pol

Type I:

only p-pol

Key property


500 600 700 8000.2

0.3

0.4

0.5

0.6

R

Wavelength (nm)

“Generalized scattering-matrix approach for magneto-optics in periodically patterned multilayer systems”

B. Caballero, A. García-Martín, and J. C. Cuevas, Phys. Rev. B 85, 245103 (2012)

Reflectivity maps: full calculations (antidots size and cross section)

Rpp (f = 0o )

Rpp (f = 45o ) Rss (f = 45o )

Rss (f = 0o )

(-1,0)&(0,-1)(-1,0)&(0,-1)

(+1,0)&(0,+1)

(-1,-1)

(+1,0)&(0,+1)

(-1,-1)&(-1,+1)(0,+1)&(0,-1)(0,+1)&(0,-1) (-1,-1)&(-1,+1)

(-1,0)

(+1,0)

Type I Type II

No channels for sp

conversion in the VIS

1 channel for sp

conversion in the VIS

Rss

Rpp

400 500 600 700 800

0.5

0.6

0.7

0.8

Wavelength (nm)

Rss

Rpp

R

G(-1,0)

G(0,-1)


400 500 600 700 800

0.2

0.4

0.6

0.8

Wavelength (nm)

MO activity enhancement mechanism (L-MOKE)

(-1,0)&(0,-1)

(-1,-1)

(-1,0)&(0,-1)

= 45°

q = 30°

Plasmonic channel “open” for resonant MO

induced polarization conversion.

= 0°

q = 30°

500 600 700 8000.1

0.2

0.3

0.4

0.5

0.6

Wavelength (nm)

Rss Rpp

Rss

Rpp

rps-rsp x 1000

rps-rsp x 1000

(-1,0)

(L-MOKE and P-MOKE involve s p polarization conversion

T-MOKE p p: no polarization conversion,)



450 525 600 675 750

0.5

1.0

1.5

2.0

2.5

30

45 60

(-1,0)

(0,-1)

(-1,-1)400 500 600 700 800

0.3

0.4

0.5

0.6

0.7

|rp

p|2

Wavelength (nm)

p-polarization

500 575 650 725 800

0.4

0.8

1.2

1.6

30

45

60

(-1,0)

400 500 600 700 800

0.3

0.4

0.5

0.6

0.7

|rp

p|2

Wavelength (nm)

p-polarization

Experimental MO-activity

500 600 700 800

0.4

0.8

1.2

1.6 30°

45°

60°

MO

A p

_pol (m

rad)

Wavelength (nm)

MO

A (

mra

d)

MO

A (

mra

d)

= 0° = 45°

Film


MOA = 22KK q +


mra

d = 45°

q = 30°

Rotation and ellipticity



SPP band structure engineering

(-1,-1) & (-1,+1)

(0,-1) & (0,+1)

(-1,0)

MO

activ

ity

Rectangular array:

two SPPs channels

Square array:

one SPP chasnnel

MO

activ

ityOne SPP assisted

MO enhancement

Two SPPs assisted

MO enhancement

Black dashed lines:

MO-active SPPs

Modes of different nature

bandgap opening

Resonant-antiresonant

lineshape

film

film



SPPs

Au

Ni

Zhou Xue & Adekulne O. Adeyeye

National University of Singapore


➢ Concerted action of LSPRs (or SPPs) and MO-coupling can beexploited to achieve a controlled manipulation of the MO response(control Kerr rotation/ellipticity) beyond what is offered by intrinsicmaterial properties.

Patterning magnetic nanostructures for resonant interaction with light: Magnetoplasmonic Crystals

➢ Magnetically tunable plasmonic crystal based on the excitation ofFano-like lattice surface modes in periodic arrays.

✓ Highly tunable and amplified magneto-optical effects as comparedto disordered systems.

➢ Two-dimensional magnetoplasmonic crystals supporting surfaceplasmon polariton modes and displaying a two-dimensional photonicband structure.

✓ Design of metamaterials with tailored and enhanced magneto-optical response by engineering the plasmonic band structure vialattice engineering.

Concluding remarks

Diapositiva 1 - Magnetismmagnetism.eu/esm/2018/slides/vavassori-slides3.pdf · P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018 Localized surface

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