Introduction to non linear optical microscopy

Transcription

1 MicroCARS: Chemical Imaging by means of CARS microscopy Introduction to non linear optical microscopy Herve Rigneault Institut Fresnel, Mosaic group, Marseille, France

2 Outline Principles of non-linear optics The concept of non-linear susceptibility Overview of different nonlinear optical processes CARS: Resonant / Non Resonant susceptibility Phase matching Collimated beams Tight focusing: the Gouy shift The line dipole NLO signal generation (SHG, THG, THG) in microscopy Optical sectioning in nonlinear optical microscopy

3 Elastic scattering I -Principles of nonlinear optics: Linear Optics Lorentz force: F=qE Dipole moment: p(t)=qr(t) atom Incident optical wave: E i Scattered wave: E S n: refractive index 2π Etot = Ei (,) zt + Es(,) zt = E(,)exp t i nz λ I - Principles of non linear optics

4 Principles of nonlinear optics: Linear Optics E P p: dipole moment α: polarizability χ: suceptibility p( ) = εα ( ) E loc P( ) = N p( ) = Nε α( ) E E= E loc loc t t ( ) ε α( ) ε χ (1) P = N E= Ε I - Principles of non linear optics

5 Linear Optics: gently bouncing the spring Evolution Equation 2 d x dx Γ + 2 = ( ) m m m x ee t dt dt Fourier Transform x e f Induced polarisation χ (1) ( ) = 2 Ne ε md( ) D( ) = ( 2 iγ) 2 2 I - Principles of non linear optics

6 χ (n) non linear suceptibility tensors : tensor product I - Principles of non linear optics Principles of nonlinear optics: origin Linear regime Non Linear regime P( ) = ε χ (1) E P E E E E E E (1) (2) (3) ( ) = ε( χ + χ : + χ : : +...)

7 Non Linear Optics: strongly bouncing the spring e Evolution Equation 2 d x dx Γ β = ( ) m m m x m x ee t dt dt 2 (1) (1) (1) (2) (2) (1) d x dx 2 (1) xt () = x () t + x () t with x x and m + 2 mγ + m 2 x = eet () dt dt x f 2 d x dt dx + Γ + = β + β dt 2 (2) (2) (2) (1) (2) 2 (1) 2 x x x x Frequency 2 β Ne 3 (2) (2) (2) 2 (2) = = εχ with χ = 2 [ ] 2 εmd(2 ) D( ) P Nex E χ (2) non linear suceptibility - frequency dependant - complex=dispersion D( ) = ( 2 iγ) 2 2

8 II- Overview of non linear optical processes P E E E E E E (1) (2) (3) ( ) = ε( χ + χ : + χ : : +...) (1) (2) (3) i = ε( χij j + χijk j k + χijkl j k l +...) P E EE EE E Einstein notation Linear optics Non linear tensor Symmetry dependant Introduction / mixing of frequencies Need to be strong Non linear optics requires strong optical field -Hydogen atom, E at e = 2 4πε a ; Bohr radius a=5.1 m - Sun on earth: 1 3 V.m -1, linear optics regime - 1kW laser focused on a 1µm spot: 1 8 V.m -1, non linear optics regime - Non linear microscopy needs to focus the incident fields!! V m II Overview of NLO processes

9 Overview of non linear optical processes P (1) (2) (3) ( ) = ε( χ E+ χ E : E + χ E: E: E+...) First Order χ (1) : χ (1) is a second rank tensor. Is associated to the linear properties: refractive index, absorption, anisotropy. χ (1) does not permit wave coupling. Second Order χ (2) : χ (2) is a third rank tensor responsible from second order processes. A second order process mixes three fields (, 1, 2 ) with = χ (2) (, 1, 2 ).

10 Overview of non linear optical processes Second harmonic generation (SHG) χ (2) (2,,). 2 Optically Pumped Semiconductor Laser DEL 88nm 488nm-46nm SHG 976nm-92nm e 2 f NB: χ (2) is present only in non-centrosymmetric media χ (3) is always present (centro and non-centrosymmetric media) In centro symmetric media: r -r E(-r)=-E(r), P(-r)=-P(r) P(-r)~ χ (2) E(-r)E(-r)= χ (2) E(r) 2 =P(r)=-P(r) Therefore P(r)=

11 SHG 347.2nm Ruby nm quartz II Overview of NLO processes

12 Overview of non linear optical processes Optical rectification χ (2) (,,-). +V THz generation via optical rectification (E(-)=E * ()) e f P E E (2) ( Ω THz ) = χ ( ΩTHz,, ) ( ) ( ) Sum frequency generation (SFG) χ (2) ( 1 + 2, 1, 2 ) Sum-frequency generation (SFG) is e 2 f a high sensitive optical probe of surfaces and interfaces. SFG is strongly enhanced when the incident IR beam resonantly excite a vibrational transition. II Overview of NLO processes

13 Overview of non linear optical processes Parametric amplification χ (2) ( 3 1, 3, 1 ). Optical Parametric Amplification e f Electro-optics (Pockels) effect χ (2) (,,). Coupling between a optical field and a static field. A phase shift is induced in the optical field. Voltage variable waveplate Electro-Optic Modulation P ( 2 ) ( ) = χ : E E Ammonium Dihydorgen Phosphate, known as ADP (NH4H2PO4). II Overview of NLO processes

14 Electro Optic Microscopy T. Toury, S. Brasselet, J. Zyss Opt. Lett (26) Electro-optic microscopy (EOM): P ( 2 ) ( ) = χ : E E E φ Phase shift contribution: χ ( 2 ) ( ;, ) : E E Measured: φ χ π n λ ( ) V - Sign of φ : molecular alignement direction -Value of φ : estimation of χ (2) - Sensitive detection (Homodyne detection)

15 Second Harmonic Microscopy D.A. Dombeck, et al. PNAS, 1 (23) IR 76nm-88nm Micro-tubules in mitotic cells Red: NADPH Auto-TPF; green: Microtubules SHG Moreaux et al, Biophys. J. 8, 1568 (21)

16 Overview of non linear optical processes P( ) = ε ( E+ E: + χ E E: E+...) (1) (2) (3) χ χ E : Third harmonic generation χ (3) (3;,,, ). 3 e 3 Intensity (counts) THG SHG TPF f wavelength (nm) Pump 164nm II Overview of NLO processes

17 Third Harmonic Microscopy Squier, Opt Expr (1998) W. Supatto et al., PNAS (25) II Overview of NLO processes

18 Overview of non linear optical processes Optical Kerr effect Re[χ (3) (;,,, )]. Modification of the medium properties under illumination: refractive index change, induced anisotropy Autofocalisation n= n + n2i Self phase modulation ϕ 2π ϕ() t = t+ ( n + n2i() t ) L λ II Overview of NLO processes

19 Overview of non linear optical processes Two photons absorption Im[χ (3) (;,,, )]. e I 2hν ~(I ext ) 2 1-photon 2-photon f Émission (nm) C. Xue, et al, Proc. Natl. Acad. Sci. Vol. 93,1996 II Overview of NLO processes

20 Overview of non linear optical processes Four waves mixing (non degenerated) χ (3) ( ± 3 ; 1, 2,± 3, ). 1 Four waves mixing (Non Resonant / Resonant) χ (3) ( ± 3 ; 1, 2, 3, ). e ± f v v f Ω v f Ω Non Resonant Non Resonant Resonant Ω acoustic frequency: stimulated Brillouin scattering Ω optical frequency: stimulated Raman scattering Valencia II Overview of NLO processes

21 P S Stokes III- CARS: Resonant / Non Resonant Suceptibility Ω AS = + = 2 Degenerated FWM as p p s p s AntiStokes e e s p p p s p as p as p s as p t v f Ω f v v f Ω f v χ A = + χ + (3) R (3) t NR ΩR ( p s) + iγr t 2p iγt A (3) χ R Far from two photons absorption III Resonant / Non Resonant χ (3)

22 CARS: Resonant / Non Resonant Suceptibility P NL I ( ( AS AS ) ) = P ( (3) (3) χ ) R + χ NR NL ( AS ) 2 = E P ( ) P E (3) 2 (3) 2 χ R + χ NR + 2 S ( ) S * 2 Re ( (3) (3) ) 2 χ Rχ NR I P I S From Cheng J. Opt. Soc. Am. B, 19, 1363 (22) v f p p s as Ω Resonant e s p Strong NR Weak NR f p as v Non Resonant p s as v f Ω From Potma and Xie J. Raman. Spect. 34, 42 (23) III Resonant / Non Resonant χ (3)

23 IV- Phase matching P (1) (2) ( ) = ε( χ E+ χ E: E+...) Exemple on second harmonic generation (SHG) NL I(2 ) P (2 ) 2 P NL (2 ) = χ E( ) (2) 2 2 = + k = k k k k 2 2 k 2 IV Phase matching

24 NL P (2 ) = χ E( ) P NL (2) (2) 2 Phase matching 2 π λ /2 = 2k n (2k ) E(2) (k 2 ) l c 2π 2π λ = = k k (2 k ) 2( n n ) 2 2 π λ = = k 4( n n ) 2 I 2 2 π λ /2 = k n 2 2 x l c IV Phase matching

25 Phase matching: collimated beams (text books) l c π λ = = k 4( n n ) 2 I 2 k= k x l c Type I Phase matching Birefringent Type I Phase matching Birefringent IV Phase matching

26 Phase matching: Tight Focusing Pump Gouy phase shift SHG 2 k = k k 2 2 Many k s!!!!!! L. G. Gouy, "Sur une propriété nouvelle des ondes lumineuses", Compt. Rendue Acad. Sci. Paris 11, 1251 (189) L. G. Gouy, "Sur la propagation anomale des ondes", Compt. Rendue Acad. Sci. Paris 111, 33 (189) phase λ λ φ g =π λ z Volkmer, J. Phys. D. Appl. Phys. 38 (25) IV Phase matching

27 Phase matching: the line dipole k k 2 IV Phase matching

28 Phase matching: the line dipole Correct NLO field emission under tight focusing condition requires electromagnetic numerical simulation. BUT SHG if l c < NLO volume extension there is a signal along the optical axis Let s calculate l c (including the Gouy shift) I 2 x k = k2 (2 k + kφ ) g 4π k2 2 k = ( n2 n) λ π π π k φ = + = π Gouy phase shift over 2λ g 2λ 2λ λ l c π π π = = = = λ k π / λ k φ g l c SHG signal In the Forward direction For thick objects IV Phase matching

29 Phase matching: the line dipole THG k = k3 (3 k + k ) k = k φ g CARS 3π 2λ φ φ l c g π = = k φ g λ 3 k = k (2 k k + k ) as p s k k k (2 ) φ AS kp ks g 2π π ( λs λp ) k φ = = π g 2λp 2λs λpλs π λpλs lc = = λ λ k φ s p φ g g I 2 l c Weak / No THG In the Forward direction For thick objects CARS signal In the Forward direction For thick objects x IV Phase matching

30 Phase matching: the line dipole SHG k y d k x d=2µm ky k y d= (one dipole) d=1nm d=2nm k x kx x kx kx kx Moreaux, Mertz, Biophys J 21

31 V- NLO signal generation in microscopy Excitation beam: wave packet Hertzien dipole radiation Coherent superposition = Far field radiation pattern In (x,y,z) plane In (k x,k y ) plane V NLO signal generation

32 SHG: Second Harmonic Generation E-SHG 2 2 z F-SHG XZ plane x nm nm 7nm 1nm x nm x x1 3 x nm x z nm z nm 2 Forward Epi x 1 Epi/Forward -2 2 z nm KTP along X axis Euler angles: θ=9, ϕ=, ψ= Intensity (A.U.) sides length (nm) 3 4 V NLO signal generation

33 CARS (xyz space) F-CARS XZ plane S AS AS z P x z (nm) z (nm) Ø=1nm -2 2 x (nm) z (nm) x (nm) Ø=1µm z (nm) Ø=2nm -2 2 x (nm) z (nm) z (nm) x (nm) Ø=5nm -4 4 x (nm) -2 2 x (nm) Ø=1.5µm Ø=2µm F-CARS E-CARS F-CARS E-CARS E-CARS D.Gachet, N. Sandeau, H. Rigneault, Proc. SPIE (26) V NLO signal generation

34 CARS (k space) F-CARS emission more directive than the excitation beam along one direction D.Gachet, N. Sandeau, H. Rigneault, Proc. SPIE (26) V NLO signal generation

35 CARS (Epi Forward ratio) E-CARS x 2 F-CARS E/F A. Volkmer et al, PRL (21) N. Djaker, D. Gachet, N. Sandeau, P.F. Lenne, H.Rigneault Appl. Opt. (26) V NLO signal generation

36 z nm XZ plane d=1nm d=2nm -1 d=5nm x nm 15 THG (xyz space) x nm x nm z nm d=1nm z nm z nm y nm d=1nm -1 d=2nm V NLO signal generation

37 Thin in z but various lateral diameter: THG (k space) d=5nm d=2nm d=7nm V NLO signal generation

38 THG (Epi Forward ratio) V NLO signal generation

39 VI- Optical sectioning in NLO microscopy FCARS 1-photon 2-photon E-CARS VI Optical sectioning

40 CARS 3D sectioning C-H bond Three dimensional distribution of lipids in epithelial cells. CH2 stretching vibration (2845 cm -1 ). Lipid granules and plasma membranes. VI Optical sectioning

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42 CARS FCS Dynamic organization of living cells and tissues Dynamic Multiple Optical Tweezers Single Particle Detection Pulse shaping Laser nanoscissors imaging Micro-stereolithography Nanostructures