Coherent defocused orientation imaging of nano-crystals in second harmonic generation microscopy Laboratoire de Photonique Quantique et Moléculaire - UMR CNRS 8537 Institut d'Alembert - IFR 121 École Normale Supérieure de Cachan 61 avenue du président Wilson F-94235 Cachan France Nicolas Sandeau*, Loc Le Xuan, Dominique Chauvat, Jean- François Roch, Joseph Zyss, Sophie Brasselet [email protected]
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Coherent defocused orientation imaging of nano-crystals in second harmonic generation microscopy
Laboratoire de Photonique Quantique et Moléculaire - UMR CNRS 8537Institut d'Alembert - IFR 121
École Normale Supérieure de Cachan61 avenue du président Wilson F-94235 Cachan France
Nicolas Sandeau*, Loc Le Xuan, Dominique Chauvat, Jean-François Roch, Joseph Zyss, Sophie Brasselet
The nano-crystal is smaller than the Excitation Efficiency Volume and it is centered on the focus
Coherent induced dipoles
Local excitation field
Nano-crystal
( )zyxE ,,ω
( )zyxPNL ,,2ω
( ) ( ) ( )zyxEzyxEzyxPNL ,,:,,:,, )2(22 ωωωω χ=
For KTP
Vpm
Vpm
Vpm
Vpm
Vpm
/9.16
/4.4
/5.2
/6.3
/9.1
)2(33
)2(32
)2(31
)2(24
)2(15
≈
≈
≈
≈
≈
χ
χ
χ
χ
χ
We define the KTP orientation by the
Euler angles (θ, ϕ, ψ)
Potassium TitanylPhosphase - KTiOPO4
Induced non-linear dipoles
ψθ
ϕ
1
2
X
Y
Z
x y
z
3
χ(2) of massive KTP
Far field intensity radiation pattern
10 nm long side 70 nm long side 100 nm long side
-40
-20
0
20
40
x nm
-40 -20 0 20 40z nm
250200150100500
-40
-20
0
20
40
y nm
-40 -20 0 20 40z nm
250200150100500
200
100
0
-100
-200
x nm
2000-200z nm
600
400
200
0
x103
200
100
0
-100
-200
y nm
2000-200z nm
6005004003002001000
x103
-200
-100
0
100
200
x nm
-200 0 200z nm
2.01.51.00.50.0
x106
200
100
0
-100
-200
y nm
2000-200z nm
2.01.51.00.50.0
x106
1.0
0.8
0.6
0.4
0.2
0.0
Inte
nsity
(A.U
.)
400300200100sides length (nm)
ForwardEpi x 100Epi/ForwardKTP along X axis
Euler angles:
θ=90°, ϕ=0°, ψ=0°
Coherent defocused orientation imaging
-300
-200
-100
0
100
200
300x
μ m
-200 0 200y μm
120010008006004002000
-300
-200
-100
0
100
200
300
x μ m
-200 0 200y μm
6000
4000
2000
0
Polarization of the pump laser beam:
α=0° / X axis
α=90° / X axis
Experimental images
3 points to determine the KTP 3D-orientation:
Structure & Sub-structures;
Intensity;
rotation of the symmetry axis;
for the 2 polarizations of excitation.
NA=1.45, n=1.518, m=100, λp=945 nm d=15 mm
Aquisition time = 10s
Coherent defocused orientation imaging
-300
-200
-100
0
100
200
300x
μ m
-200 0 200y μm
120010008006004002000
-300
-200
-100
0
100
200
300
x μ m
-200 0 200y μm
6000
4000
2000
0
Polarization of the pump laser beam:
α=0° / X axis
α=90° / X axis
Experimental images
•Structures give information about the angle (θ ) between the optical axis and the axis ‘3’ of the crystal.
•The variation of the intensity and the direction of the symmetry axis allows to determine the 2 other Euler angles.
Example of image structure Vs θ angle
-200
0
200x
μ m
300-300y μm
2520151050 -200
0
200
x μ m
300-300y μm
60
40
20
0 -200
0
200
x μ m
300-300y μm
12080400
-200
0
200
x μ m
300-300y μm
2000150010005000
-200
0
200
x μ m
300-300y μm
300
200
100
0 -200
0
200
x μ m
300-300y μm
5004003002001000 -200
0
200
x μ m
300-300y μm
10008006004002000
-200
0
200
x μ m
300-300y μm
12008004000 -200
0
200
x μ m
300-300y μm
150010005000 -200
0
200
x μ m
300-300y μm
2000150010005000
0° 10° 20°
30° 40° 50°
60° 70° 80°
90°
x
zAxis ‘3’θ
Coherent defocused orientation imaging
-300
-200
-100
0
100
200
300x
μ m
-200 0 200y μm
120010008006004002000
-300
-200
-100
0
100
200
300
x μ m
-200 0 200y μm
6000
4000
2000
0
Polarization of the pump laser beam:
α=0° / X axis
α=90° / X axis
Experimental images
300
200
100
0
-100
-200
-300
x μ m
-200 0 200y μm
800
600
400
200
0
300
200
100
0
-100
-200
-300
x μ m
-200 0 200y μm
4000
3000
2000
1000
0
Calculated images
⇒ KTP orientation: θ=30°±5° ϕ=115°±5° ψ=90°±15°
Verification
Polarization of the pump laser beam:
α=120° / X axis
α=150° / X axis
Experimental images
Calculated images
⇒ orientation:θ=30°±5°ϕ=115°±5°ψ=90°±15°
-300
-200
-100
0
100
200
300
x μ m
-200 0 200y μm
300025002000150010005000
-300
-200
-100
0
100
200
300
x μ m
-200 0 200y μm
6000500040003000200010000
-300
-200
-100
0
100
200
300
x μ m
-200 0 200y μm
25002000150010005000
α=60° / X axis
300
200
100
0
-100
-200
-300
x μ m
-200 0 200y μm
1200
800
400
0
300
200
100
0
-100
-200
-300
x μ m
-200 0 200y μm
500040003000200010000
300
200
100
0
-100
-200
-300
x μ m
-200 0 200y μm
300025002000150010005000
4.744 103.
133
B Iytot aπ
180. b
π
180., c
π
180., αi, δ, γ,.
dataY j
α i angle j,
834
106
A Ixtot aπ
180. b
π
180., c
π
180., αi, δ, γ,.
dataX j
α i angle j,
Agreement with ellipsometric measurement
IXIY
APD2
APD1
X
YZ
Analysis directionIY IX
Laser 100fs 80Mhz 690 – 1020 nm
Rotation of the linear polarization of the excitation beam
ω2ω
SHG or 2PF
High numerical aperture objective 0 10002000300040005000
1000
2000
3000
4000
5000
0
45
90
135
180
225
270
315
polarXpolarY
Experimental SHG polarimetric analysis
Comparison with the modeling for a KTP orientation (θ=30° ϕ=115° ψ=90°)
100
80
60
40
20
0
100806040200
14121086420
x103
Diagnostic of mono-crystallinity
Excitation beam polarisedalong X axis (α=0°)
100
80
60
40
20
0
100806040200
5000
4000
3000
2000
1000
0
Excitation beam polarisedalong Y axis (α=90°) No symmetry axis
⇒ There is more than 1 nano-KTP in the excitation area.
One has an orientation close to the direction of the polarization of the exciting beam.
These nano-KTPs radiate coherently ⇒ Images are results of an interference phenomenon.
Conclusion
Non-linear defocused imaging is a simply tool to determine crystalline nature and 3D-orientation of single nano-crystals with a good precision.
⇒ these nano-crystals can be used as nano-probes of local fields.
⇒ to study rotational diffusion
⇒ to know radiation pattern of unknown nano-emitters…
( ) ( ) ( )zyxEzyxEzyxPNL ,,:,,:,, )2(22 ωωωω χ=
known To probe
Acknowledgements
For samples:Cédric Tard, Sandrine Perruchas, Thierry GacoinLaboratoire de Physique de la Matière Condensé, UMR CNRS 7643,École Polytechnique, 91128 Palaiseau cedex
Financing:Ministère de la Recherche, FranceCNRSInstitut D’AlembertÉcole Normale Supérieure de Cachan