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

nicolas.sandeau@ida.ens-cachan.fr

Aims & applications

Measurement of the 3D orientation of single nonlinear nano-emitters:

• To understand physical and chemical properties of nano-structures;

• To probe local environment of this nonlinear tag;

• To probe local electromagnetic field;

⇒ We use 2-photon excitation microscopy

Polarized nonlinear microscopy

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

SHG mapping and localorientation information2-photon confocal ellipsometer

C. Anceau et al., Chem Phys Lett (2005)

XY

SHG

φ0 ~ 18°

φ0 ~ 6°-8° a

b

5 μm

abAnalysis direction

IX IY

Polarized 2PE-microscopy in nano-crystals

Diagnostics of the crystallinenature of nano-crystals (2PF)

S. Brasselet et al., Phys Rev Lett (2004)

150

Y

X IXIY

Eω

2-photon Fluorescence

Same polar plot for each analysis direction ⇒ mono-crystallinity

Second Harmonic Generation

Optical axis

Projection of the nonlinear induced

dipole in the focal plane

2D or 3D orientation of thecrystalline structure (SHG)

Non-centrosymetricstructure

Bad precision on one of the 3 Euler angles

Defocused imaging helps to read this information!

emission

excitation

camerafocal plane

« Defocused image » of the dipole

10 mmx

z

emission

excitation

camera-40

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m)

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.)

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Defocused orientation imaging

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m)

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.)

dipole

Image of the dipole

focal plane

Information about the source orientation

is conserved across the microscope!

M. Böhmer & J. Enderlein, JOSA B 20 (2003)

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z

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Defocused orientation imaging

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defocusedimaging 10 mm

defocusedimaging 5 mm

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m)

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dipole100

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m)

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.)

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m)

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3020100

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.)

Image in the focal plane

No visible structure

Visible structures

Visible sub-structures

Enhancement of the defocus

Improvement of the precision of the orientation measurement

ApplicationDefocused orientation & position imaging (DOPI)

A

A D. Patra, I. Gregor, J. Enderlein, J. Phys. Chem. A 108 (33) p. 6836-6841 (2004)

B E. Toprak et al., PNAS 103 (17) p. 6495-6499 (2006)

DOPI of myosin V along an actin fiber

SHG microscopy in nano-crystals

SHG 2ω

Excitation ω

camerafocal plane

15 mmx

zy

Nano-crystal

Objective NA=1.4 in oil

m=100

ParametersMicroscope: Numerical aperture (NA=1.4), index of immersion liquid

(n=1.518), magnification (m=100), Camera position (15 mm)

Excitation: Wavelength (λ=945 nm), polarization (linear), shape (Gaussian)

Sample: Orientation (Euler angles), χ(2), size (~77 nm)

Tube lens

Induced non-linear dipoles

Epi Forward

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

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6005004003002001000

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2.01.51.00.50.0

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2.01.51.00.50.0

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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

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300x

μ m

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120010008006004002000

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-200 0 200y μm

6000

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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

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300x

μ m

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120010008006004002000

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0

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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

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μ m

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12080400

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0° 10° 20°

30° 40° 50°

60° 70° 80°

90°

x

zAxis ‘3’θ

Coherent defocused orientation imaging

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μ m

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120010008006004002000

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0

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200

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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

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0

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x μ m

-200 0 200y μm

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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°

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300025002000150010005000

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6000500040003000200010000

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α=60° / X axis

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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

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100806040200

5000

4000

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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

And all members of LPQM…

Thanks for your attention.