2016 swieca school campinas · eff np np np10 10 χχ χ χ= fl l fl l ... de araújo et al. j....
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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
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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
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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
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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
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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
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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
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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= +
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“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
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( ) )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
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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
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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
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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
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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
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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
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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⎛ ⎞∂ ∂ ∂
− + = + + + +⎜ ⎟∂ ∂ ∂⎝ ⎠
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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
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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
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56
Cross-phase modulationCo-propagating beams
Reyna, de Araújo - Optics Express 22 (2014) 22456
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57
Experiment
Theory
Experiment
Inputprobebeam profile
Pump beam profile
Induced focusing due to the seventh-order susceptibility
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Bright Spatial Soliton
58
Self-focusing Diffraction
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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
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CS2: stable (2+1)D soliton
Is it possible to observe a stable (2+1)D soliton in a system with:
?
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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
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62experiment theory
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41 (2016) 191
GW/cm2
0.1
3.0
Z= 0 3 5 10 mm10 mm - 25 ZR
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IOVS = 3.0 GW/cm2
IHeNe= 0.1 GW/cm2
HeNe Guided HeNe
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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
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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
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67Reyna, de Araújo, Opt. Express 23 (2015) 7659
Optimization procedure for the design of all-optical switchesbased on metal-dielectric nanocomposites
1/TW
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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
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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
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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.
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Thank you for your attention
Our work has been supported by the Brazilian agencies