Nonlinear optical effects in ordered and disordered photonic crystals

Transcription

Nonlinear optical effects in ordered and
disordered photonic crystals, and applications
Ramon Vilaseca,
Vilaseca, José
José F. Trull,
Trull, Crina M. Cojocaru,
Cojocaru,
V. Roppo,
Roppo,
K. Staliunas
Universitat Politècnica de Catalunya, Dept. de Física i Enginyeria Nuclear
Terrassa (Barcelona), Spain
Collaboration (in part of the work) with:
S. M. Saltiel,
Saltiel,
Faculty of Physics, University of Sofia, Bulgaria
W. Krolikowski,
Krolikowski, D. Neshev,
Neshev, Y.Kivshar
Centre for Ultrahigh Bandwidth Devices for Optical Systems (CUDOS),
Nonlinear Physics Centre , Australian National University, Canberra, Australia
Menu for today:
1.- Loooong Introduction:
● Research Group DONLL in Terrassa
● Nonlinear Optics
● Photonic crystals
2.- Nonlinear optics in photonic crystals
3.- Nonlinear Optics in random nonlinear crystals
- Application to short-pulse measurement
4.- Influence of the random nonlinear domain distrib.
5.- Conclusions
Menu for today:
1.- Looooong Introduction:
4.- Influence of the nonlinear domain distribution.
5.- Conclusions
Research activities of the Group on
Nonlinear Dynamics & Optics and Lasers (DONLL)
Universitat Politècnica de Catalunya
(Campus de Terrassa)
Terrassa)
Photonics
Biology
Research lines:
Photonics:
Biology:
Nonlinear Optics,
Nonlinear Dynamics
Nonlinear dynamics
Kestutis Staliunas
José F. Trull
Cristina Masoller
Crina Cojocaru
Ramon Herrero
Josep Lluís Font
Juanjo Fernández
(Muriel Botey)
Ramon Vilaseca
Jordi García-Ojalvo
M. Carme Torrent
Antoni Pons
Núria Domedel
Lorena Espinar
Belén Sancristóbal
Pau Rué
Marta Dies
Jordi Tiana
Jordi Zamora
Cristian Nistor
Vito Roppo
Research lines:
Photonics
Linear & nonlinear
light propagation
in
spatially modulated
materials
Nonlinear light
dynamics,
in
semiconductor
lasers
Kestutis Staliunas
José F. Trull
Crina Cojocaru
Ramon Herrero
Ramon Vilaseca
Jordi García Ojalvo
Cristina Masoller
M. Carme Torrent
(Cristina Martínez)
Cristian Nistor
Vito Roppo
Jordi Tiana
Jordi Zamora
Nonlinear light
dynamics,
in
other structures
and systems
Kestutis Staliunas
Ramon Herrero
Ramon Vilaseca
Josep Lluís Font
Juanjo Fernández
Research lines:
Linear & nonlinear
light propagation
in
spatially modulated
materials
Kestutis Staliunas
José F. Trull
Crina Cojocaru
Ramon Herrero
Ramon Vilaseca
Cristian Nistor
Vito Roppo
Subdiffraction & spatial filtering in linear materials:
- Spatial dispersion in PC materials (index-modulated),
and PC resonators. cw case
Short-pulse case
Extention to BEC systems.
- In linear gain-modulated materials
Subdiffraction in NL PC materials and resonators:
- Modified phase-matching (broad & narrow angular spectrum).
- Nonlinear wave mixing: SHG and parametric amplific.
with narrow beams.
- Spatial solitons (Bloch cavity solitons in Kerr PC resonators)
Ultrafast all-optical tuning of NL PC response:
- PC waveguide. Control of a ω pulse by a 2ω pulse
Materials with random spatial distribution of χ(2):
- Study of SHG
- Application: femtosecond pulse measurement.
Phase-locked SHG and THG in resonators and PC’s
- Study of the resonant growth of SHG
Menu for today:
5.- Conclusions
Nonlinear Optics:
ω
E(t)ω
r r
E (r , t )
ATOM
x
ω
r r
P(r , t )
y
ω
z
r
P(t )ω
Material response:
(
r
r
rr
rrr
P = ε 0 χ (1) ⋅ E + χ ( 2 ) ·EE + χ ( 3) ⋅ EEE + L
r
P (1)
r
P ( 2)
)
P
r
P ( 3)
Linear
E
r
P NL
Nonlinear
Nonlinear Optics
Example: SECOND HARMONIC GENERATION (SHG)
(
r
r
rr
rrr
P = ε 0 χ (1) ⋅ E + χ ( 2 ) ·EE + χ ( 3) ⋅ EEE + L
E·eiωt
)
E2·ei·2ωt
Ε2
2ω
ω
ω
2ω
ω
ω
Ε1
E(t)
ω
ATOM
ω
x
2ω
ω
y
r
P (t )ω
z
ω
2ω
NONLINEAR OPTICS: Generalizing
Generalizing: examples of nonlinear processes:
electron
E4
E3
E2
ω
ω’
ω’
ω
hω
ω
ω+ω’
2ω
ω
ω’
ω
ω−ω’
E’1
E1
Variety of features: non-resonant↔resonant; without↔with energy exchange with the atom;
spontaneous↔stimulated; effects over diffraction, effects over light pulses, …
NONLINEAR OPTICS: Generalizing
Generalizing: examples of nonlinear processes:
electron
ω’
hω’
E2
ω’
ω
ω
ω
ω
E4
E3
3ω
ω1
ω3
ω1
ω2
ω2
ω4
ω3
ω
ω4
hω
E1
Variety of features: non-resonant↔resonant; without↔with energy exchange with the atom;
spontaneous↔stimulated; effects over diffraction, effects over light pulses, …
Nonlinear Optics: SHG
Problem with SHG: “Phase matching” condition !
· Classical description: In general, dispersion ⇒
λω
n(ω) ≠ n(2ω)
⇒
λω ≠ 2λ2ω
ω
Back
conversion!:
Destructive
interference!
2ω
z
λ2ω
To have 2λ2ω = λω ⇒
n(2ω) = n(ω)
· Quantum description:
Photon momentum conservation:
2ω → ω
“Phase-matching condition”
r
r
r
hk 2 = hk1 + hk1
k2 = 2k1
k1
k1
k2
Nonlinear Optics: SHG
I2 ω
Phase matching (∆k = 0)
Non phase matching (∆k ≡ k2ω-kω ≠ 0)
0
Lc =
π
∆k
“Coherence length”
Ways to achieve phase matching?:
■
■
■
■
Crystal birefringence
Temperature
“Quasi-phase matching”
Photonic crystals
z
(penetration distance
within the crystal)
Menu for today:
5.- Conclusions
Photonic crystals
Photonic crystals: structures with a built-in periodic distribution of dielectric material, with lattice
dimensions comparable to the wavelength of the light.
(E. Yablonovitch, Phys. Rev. Lett. 58 (1987) and S. John, Phys. Rev. Lett. 58 (1987))
1D
multilayer film
AlGaAs/air
waveguide
AlOx/GaAs
2D
square lattice of dielectric
columns surrounded by air
AlGaAs/air
3D
spheres in a FCC configuration
inverted opals
Photonic crystals: regular structures
Joannopoulos et al. (MIT)
(proposed theoretically, on Si)
A. Blanco et al., Nature (2000) -
Opal
Colloidal crystal
AlGaAs /air
E. Yablonovitch et al., PRL (1991)
“Yablonovite”
Soukoulis et al. (Ames Lab., Iowa State Univ.)
(proposed theoretically)
Photonic-crystal fiber
Photonic crystals: with “defects”
x
L
z
⇒ Light confinement (to make micro-lasers, etc.)
18
Photonic circuits: the dream……..
• These optical circuits should provide active functions for all-optical information processing.
use of nonlinear optics
sub-λ structures: photonic crystals
laser µ-sources
Tunable filters, amplification,
frequency conversion…..
change the propagation
direction
resonators
1µm
waveguides
http://ab-initio.mit.edu/photons/micropolis.html
Photonic crystals
Reduced zone
scheme
Extended zone
scheme
ω
ω
n=3
n=3
Forbidden band
n=2
n=2
Forbidden band
n=1
n=1
0
π/a
g
2π/a
kx
0
π/a
1st
Brillouin
zone
kx
DISPERSION CURVES, CALCULATED,
FOR PHOTONIC CRYSTALS
Reduced-zone scheme
(J.F. Trull, Tesis doctoral, UPC, 1999).
Menu for today:
5.- Conclusions
21
Nonlinear optics & Photonic crystals
Advantages of photonic crystals for nonlinear effects?
1) To achieve the phase matching condition n(ω) = n(2ω)
2) Slower light propagation (and/or lower diffraction) ⇒ larger intensity
(it occurs near the photonic band gaps)
3) Take advantage of narrow resonances
(it occurs near the photonic band gaps or in defect states)
4) Interesting multifunctions for all-optical processing:
tunable PC, switch, amplification, laser effect,…
ANALYSIS IF THE DISPERSION CURVES,
CURVES,
FOR PHOTONIC CRYSTALS
(real part)
24
,
inside a 11-D PHOTONIC CRYSTAL (the light is incident from the
left)
left)
4.00
3.00
|E|^2
5.00
4.00
2.00
4.00
1.00
2.00
0.00
|E|^2
3.00
0.00
2.00
4.00
6.00
8.00
distance into the crystal (period units)
“air“
band
10.00
|E|^2
1.00
0.00
2.00
4.00
6.00
8.00
2.00
ωn
0.00
5.00
3.00
10.00
n=3
1.00
4.00
0.00
n=2
3.00
0.00
2.00
4.00
6.00
8.00
10.00
|E|^2
2.00
4.00
1.00
n=1
0.00
0.00
2.00
4.00
6.00
8.00
10.00
3.00
4.00
|E|^2
1ª zona π/a
Brillouin
2.00
kx
|E|^2
0
3.00
2.00
“Dielectric”
band
1.00
1.00
0.00
0.00
0.00
2.00
4.00
6.00
8.00
J. Trull, C. Cojocaru, J. Martorell, R. Vilaseca
10.00
2.00
4.00
6.00
8.00
10.00
0.00
26
PHOTONIC CRYSTAL WITH A “DEFECT”
DEFECT”
x
y
Field amplitude within the structure, for
two different input fields (cases A and B)
L
500
z
B
Field amplitude (arb. units)
400
300
200
A
100
0
-2.0
-1.5
-1.0 -0.5
0.0
0.5
z (µm)
1.0
1.5
2.0
2.5
Research line: Linear & Nonlinear light propagation in
spatially modulated materials
SubSub-diffraction (or selfself-collimation)
collimation)
()
r
k⊥
ωk
k⊥
k||
k⊥
k II
k ||
1,0
ky
output
Input
M
0,5
Diffractive
Non‐diffractive
0,0
Γ
kx
X
0,0
1,0
K. Staliunas, R. Herrero (UPC)
28
“DONOR”
DONOR” and “ACCEPTOR”
ACCEPTOR” DEFECTS
x
Regular-period value: L=137.7 nm
period ic structure
L=100 nm
L=50 nm
L=10 nm
(c)
“Donor” defect
1
1
0.8
0.8
Transmissivity
Transmissivity
periodic structure
L=275 nm
L=325 nm
L=350 nm
y
0.6
0.4
z
L
(b)
“Acceptor” defect
0.6
0.4
0.2
0.2
0
0
0.8
0.85
0.9
0.95
1
1.05
ω/ω
ο
1.1
1.15
0.8
0.85
0.9
0.95
1
ω /ω
ο
1.05
1.1
1.15
Nonlinear Optics
Menu for
in random
today: nonlinear crystals
Menu for today:
Our past contributions…
Photonic crystals
First experiment on SHG
in a photonic crystal
(Martorell, Vilaseca, Corbalán,
APL + PRA, 2007)
Nonlinear slab
First experiment on
modification of SHG from
a localized source inside
a photonic crystal
(Trull, Martorell, Vilaseca,
Corbalán, OL 1995)
M. botey
ω
Truncated 1-dimensional
photonic crystal
2ω
(a)
Time division demultiplexing
Reflected signal at ω
1 2
1
3 1 2
transmitted signal at ω
1 2
2
3
2
2
Multiplexed signal at ω
[110]
control signal at 2ω
C. Cojocaru, J. Trull, J. Martorell, R. Vilaseca
CONFIGURATIONS for the MATERIAL
STRUCTURE
Microcavity
ω
NL material
ω
ω
2ω
2ω
AlGaAs/air
AlGaAs/air 1D structure in guided configuration
C. Cojocaru, J. Trull, J. Martorell, R. Vilaseca
Measurements of the induced transmission and reflection in
microcavities
Experimental set-up in Terrassa, with Nd:YAG and Ti:Sapphire pulsed lasers
Nd:YAG LASER
1064 nm 35 ps
SHG KDP crystal
MSH
MFF
λ/4
waveplate
MFF
FD1
(trigger)
Translation stage
λ/2
waveplate
MFF
F(RG610)
MFF
F(KG5)
F(KG5)
MSH
Translation stage
P1
P2
Crystal
plate
L
400
x
0
z/zR
18
Sub-diffraction
GLM
400
Homogeneus
m=0.1 and Q||=0.85
a)
x
49% of
energy
0
0
d
Microcavity
D
MFF
Corner
cube
Corner
cube
Spatial filtering
0 .84 Z R
F(RG610)
F(RG610)
MFF
F(RG610)
0
FD2
(transmission)
z/zR
10
K. Staliunas, R. Herrero, R. Vilaseca, PRA, 2009
In a “photonic
crystal” with
modulation of the
gain and losses
(instead of
modulationn fo the
refractive index)
Menu for today:
5.- Conclusions
Nonlinear
Menu
ininrandom
today:
NonlinearOptics
opticsfor
randomnonlinear
nonlinearcrystals
crystals
The spatial modulation, can affect:
☼
The
linear properties: χ(1) ,
Phase-matching
condition:
n(ω)
(Most photonic crystals)
k2 = 2k1
k1
n(2ω) = n(ω)
k1
k2
☼
The
nonlinear properties: χ(2)
(“Nonlinear” photonic crystals)
k2 = 2k1 + G
k1
k1
k2
G
k1
k1
k2
G
Nonlinear optics in random nonlinear crystals
χ(2) periodic
1-D : “Quasi-phase matching” (PPLN)
G
k2
k2 = 2k1 + G
k1
Lc =
2ω
π
∆k
ω
χ(2) spatial Fourier
components
Phase-matched
Problem of all these phase-matching
techniques:
Power
(Refractive index ∼uniform)
QPM
not phase-matched
Narrow frequency bandwidth
Distance (z/Lc)
Do not work for different frequencies
⇒ Do not work for several NL processes simultaneously
Λ=2Lc
Multiple‐channel wavelength conversion by use of engineered quasi‐phase‐matching structures in
LiNbO3 waveguides. Opt.Lett, 24, 1157 (1999)
Generalizing
Quasi - Phase
matching:
matching:
1-D
▪ Fibonacci distribution
Zhu et al., Science 278, 843 (1997)
▪ Generalized Q-P structure
Fradkin-Kashi et al., PRL 88 (2002)
▪ Tranversed-pattern PPLN
Kurtz et al., IEEE JSPQE 8 (2002)
<<<<
χ(2) periodic
k2 = 2k1 + G
2-D
G
Berger, PRL 81, 4136 (1998)
Momentum space, and
Reciprocal lattice
Phys.Rev.Lett, 84, 4346 (2000)
χ(2) periodic, with some degree of aperiodicity or randomness
k2 = 2k1 + G
2-D
▪ 2-D Quasi-crystal
(Penrose pattern)
Bratfalean et al., OL 30, 424 (2005)
χ(2) random distribution ??
k2 = 2k1 + G
G
z y
2-D
Continuous set of
reciprocal-lattice vectors,
in x-y plane
x
c-axis
χ (2) > 0
χ (2) < 0
“Random quasi Phase matching”
matching”
Does it exist ?
χ(2) random distribution
k2 = 2k1 + G
It appears naturally in unpoled (as-grown)
ferroelectric (relaxor-type) crystals:
▪ Strontium Barium Niobate (SBN):
Tetragonal 4mm point symmetry
SrxBa1-xNb2O6, with 0.25<x<0.75 (standard x=0.61)
[P. Molina et al. Adv. Funct. Mat. 18, 709 (2008)]
V.V. Shvartsman et. Al.,
Ferroelectrics 376,1 (2008)
“Quenched Electric random fields”
c-axis
χ (2 ) > 0
χ (2 ) < 0
z y
x
SBN
• Coercive field (Ec)
• Maximum χ(2) coefficient
70 ºC
d33= 200pm/V
20 kV/mm
260 ºC
1210 ºC
d33= 55 pm/V
d15=70 pm/V
Results so far?
G
x
c-axis
χ (2 ) > 0
LiNbO3
< 500 V/mm
• Curie Temperature (Tc)
z y
CBN
χ (2 ) < 0
References
G. Dolino. Phys.Rev.B, 6, 4025 (1972)
M. Horowitz et al. Appl.Phys.Lett. 62, 2619 (1992)
A.R. Tunyagi et al. Phys.Rev.Lett. 90, 243901 (2003)
M. Baudrier-Raybaut et al; Nature, 432, 374 (2004)
S.E. Skipetrov; Nature,432, 285 (2004)
R. Fischer et al. Appl. Phys.Lett., 89, 191105, (2006)
X. Vidal, J., Phys.Rev.Lett. 97, 013902 (2006)
P. Molina et al. Adv.Funct. Mater.18, 709 (2008)
J. Trull et al. Optics Express, 15, 15868 (2007)
SHG for propagation perpendicular to c-axis
Avalilable grating vectors in the plane allow the phase matching in different directions
Planar SHG
k1
c-axis
[M. Horowitz, et al. APL 62, 2619 (1993)]
r
r
r
k 2 = 2 k1 + G
ee‐e
[P. Molina et al. Adv. Funct. Mat. 18, 709 (2008)]
Random quasi Phase matching
Advantages:
Advantages
Phase matching for any second order parametric process
Extremely large spectrum range (limited only by the transparency
window of the crystal: from λ =0.4 to λ =6 µm !) and broad angular
bandwith.
⇒ Full bandwith conversion, without need of alignment or temperature
control (SHG of short pulses, …)
Multiple directions converter.
(Simultaneous phase-matching of different processes)
Limitations/
Limitations/Drawbacks:
• Lower efficiency (good for pulse characterization: no pulse depletion)
• Intensity grows linearly with distance
• Radiation emitted in broad directions
• (Simultaneous phase-matching of different processes)
SHG of short pulses
Top view low power
Front view
Also: Self- and cross- correlations functions (seen in space)
R. Fischer et al, ”Broadband fs frequency doubling in random media,” Appl. Phys. Lett. 89, 191105 (2006).
R. Fischer et al. ”Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in
random media,” Appl. Phys. Lett. 91, 031104 (2007).
SHG for propagation along c-axis
Z
G
k2
c-axis
G
α
2k1
cos( α ) =
k2
Applications:
● Super prism effect:
X
ω1,ω2
ω1< ω2
A.R. Tunyagi et al. Phys.Rev.Lett. 90, 243901 (2003)
2 k1
k2
2ω1
2ω2
ω1,ω2
Z
● Radial polarization ⇒ Better focusing
SHG with two fundamental beams
Configuration
with countercounterpropagating
pulses:
Application:
Application: Autocorrelation measurements of fs pulses
Image of the background and of
the autocorrelation trace (visible in the center).
R. Fischer, D.N. Neshev, S.M. Saltiel,
A.A. Sukhorukov, W. Krolikowski and Yu S. Kivshar,
Appl. Phys. Lett. 91, 031104 (3) (2007)
3.- SHG with two non-colinear fundamental
beams
Configuration
with nonnoncollinear
pulses:
y
z
x
800 nm
Application:
Application: Autocorrelation measurements of fs pulses
V. Roppo, J. Trull, S. Saltiel, C. Cojocaru, D. Dumay, W. Krolikowski, D. Neshev, R. Vilaseca, K. Staliunas and Y.S.
Kivshar, Optics Express 18, 14192 (2008)
J. Trull, S. Saltiel, V. Roppo, C. Cojocaru, D. Dumay, W. Krolikowski, D. Neshev, R. Vilaseca, K. Staliunas and Y.S.
Kivshar, Appl.Phys.B 95 , 609 (2009)
Menu for today:
5.- Conclusions
3.- SHG with two non-colinear fundamental
beams
Application:
Application:
Autocorrelation measurements of fs pulses
z
k1+k’1
3.- SHG with two non-colinear fundamental beams:
Application to pulse measurements
Noncollinear planar SHG in SBN
“Long” pulse
“Short” pulse
τ >> 2ρ tanα u
τ << 2ρ tanα u
z
10 ns pulse
190 fs pulse
AUTOCORRELATION
Noncollinear autocorrelation in SBN
E1 = e
2

 X1  

 
 t−
2
u  
 − Z1 − 
 2ρ 2
2T 2 
0




E2 = e
2

 X2  

 
t−
2
u  
− Z2 − 
 2ρ 2
2T 2 
0




 Z cos (α ) + X sin (α )   (Tu − X cos(α )) 2 + Z 2 sin 2 (α ) 
−
 −

ρ 02
u 2T 2

 

2
I SH = e
Model
τ << 2ρ tanα u
2
2
2
e
 2 Z 2 sin 2 (α ) 

I 2ω (Z ) = I o , 2ω exp −
u 2T 2


τ=
2 ∆Z fwhm sin (α ext )
c
z
190 fs pulse
τ= 2
AUTOCORRELATION
∆z FWHM sin α
c
Femtosecond pulses from a Ti:saphire laser at 810 nm
τ= 2
∆z sin α
= 193 fs
c
2αext=22º
V. Roppo et al. Optics Express 18, 14192 (2008)
z
Calibration of the measurement technique ?
δz
By changing the delay between the pulses an amount δt, the autocorrelation line is displaced a
distance δz=c δt/2sin(αext) in z direction:
δt
α α
z
Properties of noncollinear autocorrelation measurements in SBN:
• Real time monitoring of pulse duration for large frequency bandwith without any tuning
parameter (we are planning to try with pulses below 30 fs, in collab. with Salamanca).
parameter (we are planning to try with pulses below 30 fs, in collab. with Salamanca).
• Background-free autocorrelation measurement
(a)
(b)
(c)
(b)
(a)
(c)
X
2
1
Z
parameter
• Background free autocorrelation measurement
• Pulse changes its duration during propagation: pulse initial chirp measurement
C: chirp parameter
parameter
• Recording of a train of pulses as parallel traces in the crystal
parameter.
• Pulse tilting can be observed
V. Roppo et al. Optics Express,18, 14192 (2008)
parameter
• The autocorrelation trace can be observed for any polarization of the incident fields
Menu for today:
5.- Conclusions
5.- Modelling of SHG in these materials,
sample characterization
y z
Influence of
domain size,
shape and
distribution ?
x
Φ
Homogeneous emission
Angular emission with maxima
Is SH light
actually emitted
uniformly in all
directions ?
(as it is usually
assumed …)
10x5x5 mm
20x5x5 mm
3.- Influence of light polarization
Influence of
light
polarization ?
← bea
← bea
mA
mB
eo → o
This is in contrast to previous claims
[Horowitz et al. APL 62, 2619 (1993)] that in
SBN crystals only e-pol SH could be
generated
J.Trull et al, Opt. Express 15, 15868 (2007)
3.- Influence of light polarization
e-pol
o-pol
e-pol SH signal detected
o-pol SH signal detected
▪ The NL coefficient ratio:
d32/d33=0.44
This allowed us to determine:
▪ The domain average size and variance:
a=3.25µm, σ=1.15µm
Angular distribution of transverse SHG
Influence of domain size,
shape and distribution ?
A. R. Tunyagi PhD thesis : Noncollinear SHG in SBN
Universität Osnabrück (2004)
x=0.75
[M. Ramirez et al., JAP
SBN as a multifunctional 95,6185 (2004)]
2D nonlineal “photonic glass”
P. Molina, M. Ramirez, L. Bausá
Domain observation by
chemical etching + optical microscopy
Domain observation by PFM (Piezoelectric Force Microscopy)
▪ Strontium Barium Niobate (SBN):
SrxBa1-xNb2O6, with 0.25<x<0.75 (standard x=0.61)
x = 0.40
x = 0.75
Domain observation by PFM (Piezoelectric Force Microscopy)
MODELLING of
The role of ferroelectric domain structure in second harmonic generation in random quadratic media
V.Roppo, W.Wang, K.Kalinowski, Y.Kong, C.Cojocaru, J.Trull, R.Vilaseca, M.Scalora, W.Krolikowski, Yu.Kivshar
(Optics Express, 2010)
The role of ferroelectric domain structure in second harmonic generation in random quadratic media
V.Roppo, W.Wang, K.Kalinowski, Y.Kong, C.Cojocaru, J.Trull, R.Vilaseca, M.Scalora, W.Krolikowski, Yu.Kivshar
(Optics Express, 2010)
15
400 nm
0
0
distance (μm)
1.2
λ=790nm
15 ‐25 spatial spectrum (μm‐1) 25
350 nm
~17°
0
15 ‐30
~23°
30
λ=790nm
λ=1064 nm
350 nm
0
15‐30
30
λ=790nm
Incident
wavelength: 1064 nm
950 nm
Beam propagation method
The time dynamics of both the fundamental and second harmonic pulses is
simulated using a fast fourier transform beam propagation method
•Complete control of the nonlinear terms
•Complete management of the dispersion
•Not any kind of approximations on the field shape or behaviour
Other factors that could contribute to the wide
angular emission ? :
● Linear scattering ? (is n actually uniform?)
(does it affect the FF or SH field?)
● Refraction (and total reflection) of the SH
light at the sample surfaces?
Linear scattering:
▪ Small, but it exists (due to some inhomogeneities of n at the domain walls).
▪ It is larger for the sample with broader (and more uniform) angular emission
(i.e., for the sample with smaller of domains).
▪ It affects more the SH than the FF
(⇒ the model of Molina et al., Adv. Func. Mater. 18, 709 (2008) does not seem
to apply here).
λ=790nm
No scattering
linear scattering
Refraction and total reflection:
c-axis
c-axis
SH
FF
Radiation emitted between 23.5º and 66.5º is not leaving the
crystal due to the large index contrast!.
⇒ Eventually it will be scattered
Controlling the aperture of the angular emission
(through the domain size and distribution) can be
useful:
● Wide angular emission:
Makes it easier applications in short-pulse
measurements, etc.
● Smaller angular emission:
Larger peak intensity can be generated
⇒ significant THG observed! [ω→2ω→3ω]
(more than in Molina et al., Adv. Funct. Mat. 18, 709 (2008))
W.Wang, V. Roppo, …, C. Cojocaru, J. Trull, R. Vilaseca, K. Staliunas, W. Krolikowski,…,
Optics Express 17, 20117 (2009).
Third-harmonic generation (THG):
W.Wang, V. Roppo, …, C. Cojocaru, J. Trull, R.
Vilaseca, K. Staliunas, W. Krolikowski,…,
Optics Express 17, 20117 (2009).
VIDEO !
Conclusions (about the random NL materials):
● Random quasiquasi-phase matching in SBN and similar crystals,
with nonnon-collinear dual fundamental beam,
beam, can be used for
shortshort-pulse measurements.
measurements.
● Random quasiquasi-phase matching occurs for any light
polarization, and allows to get information about the nonlinear
coefficients and the domain distribution of the sample.
● The angular distribution of SHG is sensitive to the domain
distribution and can have maxima. Modelling allows to
interpret these results.
● Linear light scattering can play a certain role.
● Different experimentalists seem to grow samples with quite
different domain distributions. Control of domain distributions
would be important for progress in the field.
Gràcies per la vostra atenció!!
☺

Nonlinear optical effects in ordered and disordered photonic crystals

Transcription

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