Cid B. de Araújo

High-order nonlinearities in disordered media

Universidade Federal de Pernambuco, Recife, Brasil

XV J. A. Swieca School and SPSAS Nanophotonics– Campinas July, 2016

Second lecture Transverse high-order nonlinear phenomena in

composites

Metal-dielectric nanocomposites

• Glasses (bulk and thin films) with metallic NPs• Polymers with metallic nanostructures• Liquid colloids with metallic NPs

Optical response is controlled through the volume fraction of the NPs

Nanoparticles

Dielectric

Metallic NPs asoptical nanoantennas

Optical response may be enhanced due to the NPs

Why metal-dielectric nanocomposites?

Fractalsand

hot-spotss

[ ])(2)()(3ωεωε

ωεη

hNP

NP+

=

[ ] 0)(2)(Re =+ spmsp ωεωεLocalizedSurfacePlasmons

Colloids with Ag spherical NPs

PVP PVASodium citrate

several shapes and sizes

spheres

Stabilizing agents toprevent agregation

diameter: 4 nm≈ 1500 atoms

≈ 30% in the surface42

431

Silver Nanoprisms

Mater. Chem. Phys. 2014 – to appear

29

Metallic nanoshellsPlasmon frequency depends on the ratio between

the shell thickness and the core radiussílica

gold

Hallas et al. Langmuir 201329, 4366-4372

Synthesis of silver nanoprisms:A photochemical approachusing light emission diodes

Saade, de AraújoMater. Chem. Phys. 148 (2014) 1184

High-order nonlinearity of silica-gold nanoshells in chloroform at 1560 nm

Falcão-Filho et al. Opt. Express 18 (2010) 21616

Improved synthesis of gold and silver nanoshellsBrito-Silva et al.Langmuir 29 (2013) 4366

44

Fast response is due to the

induced dipole relaxation

Surface plasmon optical dephasing, T2

Almeida et al., Appl. Phys. B 108(2012) 9

Measured using the “Persistent Hole-Burning Technique”

Large optical nonlinearity and fast response

T2 is influenced by the environment

Nonlinear optics of a nanocomposite

Nonlinear response depends strongly on the laser frequency

Nonlinear refraction Nonlinear absorption

Effective 3rd. order susceptibility

2(3) 2 (3) (3) ,eff np hf L Lχ χ χ= +

Local field factor

( ) (L) ( )3 ( 2 )L Lh np hL ε ε ε= +

“Closed-aperture” Z scan

“Open-aperture” Z scan

When high-order nonlinearities are present:

46

NL refraction

NL absorption

)3(χ I (r)

Self – focusing medium

( ) )3()3()3( 0.13.2 hostNPeff if χχχ ++≈

22220)3( )/(105.3109.2 Vmihost−− ×+×=χ 216)3( )/(10)9.13.6( VmiNP

−×−−=χ

( ){ })3()3()3(2 ReIm0.1Re3.2 hostNPNPfn χχχ +−∝

( ){ })3()3()3(2 ImRe0.1Im3.2 hostNPNPf χχχα ++∝

This experiment

Silver NPs in CS2 532 nm80 ps

Single pulses7 Hz

47

Observation of fifth-order refraction in a metal-colloid

Silver NPs in acetone

0.0 0.5 1.0 1.5 2.0 2.5-20

246

8

0.00 0.25 0.50 0.75-1.0-0.50.0

0.51.01.5

2.0

α4x I

α2(10

-9 c

m/W

)

f (10-4)

(b)(a)

n2

n4x I

(10-1

4 c

m2 /W

)

f (10-4)

-15 -10 -5 0 5 10 15

1.0

1.2

1.4

1.6

1.8

Tran

smitt

ance

Z (mm)

2

4

6

8

9

Z-scan

532 nmSingle pulses5 GW/cm2

2(3) 2 (3) (3) ,eff np hf L Lχ χ χ= + ( ) (L) ( )3 ( 2 )L Lh np hL ε ε ε= +

( )2 24 4 6(5) 2 (5) 3 (3) (3)6 3 ,10 10eff np np npf L L f L L f L Lχ χ χ χ= − −

Generalized Maxwell-Garnet modelAg NPs in acetone

Maxwell-Garnet modela < b < λ

Reyna, de Araújo, Optics Express 22 (2014) 22456

50

Nonlinearity Management

It is possible to supress one specific order of nonlinearityand enhance another one

Example: n2=0 and n4≠0

A procedure to obtain exotic metal-dielectric composites

0 1 2 3 4 5-3

-2

-1

0

1

2

I = 4 x 1012 W/m2

n6 x I2

n4 x I

n2

(10-1

7 m2 /W

)

f (10-5)0 1 2 3 4 5

-8

-4

0

4

8

12

35/64Re(χ(7)eff)|E0|

6

3/4Re(χ(3)eff)|E0|

2+5/8Re(χ(5)eff)|E0|

4

(10-6

)

f (10-5)

4 x 108 W/cm2 1 x 108 W/cm2

51

Nonlinearity management: Silver NPs + CS2

52

f = 3.3 x 10-5

Input plane out of thelens focus

I = 70 GW/cm2

-4 -3 -2 -1 0 1 2 3 40.0

0.2

0.4

0.6

0.8

1.0

Nor

mal

ized

Inte

nsity

ρ

Experimental result Numerical simulation

Ppico = 0.5 kW Ppico = 40 kW

-4 -2 0 2 40.0

0.2

0.4

0.6

0.8

1.0

Nor

mal

ized

Inte

nsity

x/w0

Ppico

= 0.5 kW

Ppico

= 40 kW

Reyna, de Araújo Phys. Rev. A 89 (2014) 063803

53

Cross-phase modulation with two counter – propagating beams

Third-order Fifth-order

( ) ( )2 2

2 2 4 2 2 41 1 1 2 41 2 1 1 1 2 2 12 2

0 0

2 6 3 ,2

A A A ikn ikniA A A A A A A A

z k x y n n⎛ ⎞∂ ∂ ∂

− − + = + + + +⎜ ⎟∂ ∂ ∂⎝ ⎠

( ) ( )2 2

2 2 4 2 2 42 2 2 2 42 1 2 2 1 2 1 22 2

0 0

2 6 3 ,2

A A A ikn ikniA A A A A A A A

z k x y n n⎛ ⎞∂ ∂ ∂

− + = + + + +⎜ ⎟∂ ∂ ∂⎝ ⎠

Pulse-picker

P

S.F.

Nd:

YAG

1064

, 5

32nm

Spatial Cross-Phase Modulation

NPs: 9 nm, L=5 cm, Ipump=2 GW/cm2 , Iprobe = 0.1 Ipump

Lens Lens B.S.

B.S.

B.S.

λ/2

Mirror

CCD

Sample

beam waist : 90 µm

54

55

Probe beamprofile

Theory

Profiles fromthe images

2 0n = 25 4 24 3.2 10 /n cm W−= + ×

Reyna, de Araújo, Phys. Rev. A 89 (2014) 063803

Counter-propagating beams First observation of Spatial Modulational Instability due to

Ag NPs + acetone

56

Cross-phase modulationCo-propagating beams

Reyna, de Araújo - Optics Express 22 (2014) 22456

57

Experiment

Theory

Experiment

Inputprobebeam profile

Pump beam profile

Induced focusing due to the seventh-order susceptibility

Bright Spatial Soliton

58

Self-focusing Diffraction

First demonstration of (2+1)D soliton propagating in a homogeneous medium with

local nonlinearity

59

Very important: contributions of third and fifth orderof opposite signs

Falcão-Filho, de Araújo, Boudebs, Leblond, SkarkaRobust two-dimensional spatial solitons in liquid carbon disulfidePhys. Rev. Lett. 110 (2013) 013901.

Low intensity soliton

60

CS2: stable (2+1)D soliton

Is it possible to observe a stable (2+1)D soliton in a system with:

?

61

First observation of 2D Spatial-Solitons in a quintic-septimal medium

experiment theory

Silver NPs in acetone

Reyna, Jorge, de Araújo, Phys. Rev. A 90 (2014) 063835 de Araújo et al. , J. Lumin. 169 (2016) 492-496

62experiment theory

63

41 (2016) 191

GW/cm2

0.1

3.0

Z= 0 3 5 10 mm10 mm - 25 ZR

64

IOVS = 3.0 GW/cm2

IHeNe= 0.1 GW/cm2

HeNe Guided HeNe

How to address the long standing problem of discovering a very good material for all-optical switching?

We need a material with largeNL refraction and low NL absorption

In general large NL refraction presents large NL absorption

66

Germanatefilm

As grown 8.3 x 10-4

With Au NPs >2.1 x 10-1

PbO-GeO2 films with gold NPs for all-optical switching

RF sputtering

800 nm 150 fs

de Araújo et al. J. Luminescence 133 (2013) 180

Figure-of-merit enhanced by twoorders of magnitude

67Reyna, de Araújo, Opt. Express 23 (2015) 7659

Optimization procedure for the design of all-optical switchesbased on metal-dielectric nanocomposites

1/TW

Challange for materials scientists

These results show that it is possible to have an efficient all-optical switch if a nanocomposite is madeaccording to the nonlinearity managementprocedure presented

Summary

Metallic NPs can be nucleated inside different media allowing enhancement of: • luminescence properties (Stokes and anti-Stokes)• optical gain/amplification in waveguides• random lasers, DFB lasers• all-optical switching, etc.

Metal composites present large NL susceptibility which depends on the shape and volume fraction of NPs

Nonlinearity Management

The control of NPs volume fraction allows supression and/or enhancement of nonlinear optical contributions

70

An optimization procedure for the design of all-optical switches basedon metal-dielectric nanocomposites. Opt. Express 23 (2015) 7659 .

Spatial phase modulation due to quintic and septimal nonlinearities in metal colloids. Opt. Express 22 (2014) 22456.

Robust self-trapping of optical vortex beams in a saturableoptical medium. Phys. Rev. A 93 (2016) 013840.

Nonlinearity management of photonic composites and observation of spatial-modulation instability due to quintic nonlinearity.Phys. Rev. A 89 (2014) 063803.

Two-dimensional solitons in a quintic-septimal medium.Phys. Rev. A 90 (2014) 063835.

Robust two-dimensional spatial solitons in liquid carbon disulfidePhys. Rev. Lett. 110 (2013) 013901.

Taming the emerging beams after the split of optical vortex solitons in a saturable. Phys. Rev. A 93 (2016) 013843.

Guiding and confinement of light induced by optical vortex solitons in a cubic-quintic medium. Opt. Lett. 41 (2016) 191.

Thank you for your attention

Our work has been supported by the Brazilian agencies