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