1. Nonlinear Optical Microscopy

2. X Y Non-linear?

3. Actual response can be written as y = c 1 x+ c 3 x 3 (this is called a cubic distortion) Assuming the input is a periodic signal x = cos ( t) y=c 1 cos( t)+c 3 [cos ( t)] 3 Trigonometric identity tells us [cos ( t)] 3 = (3/4) cos( t) + (1/4) cos(3 t) The output is thus given by y=[a1+(3/4)c 1 ] cos( t)-(1/4)c 3 cos(3 t) Thus a small cubic nonlinearity gives rise to a modified response at w but also generates a new signal at 3w Nonlinear response

4. 1.Applied field distorts the cloud and displaces the electron 2.Separation of charges gives rise to a dipole moment 3.Dipole moment per unit volume is called the polarisation

5. P = c 1 E ; P is the polarization c 1 is called the linear susceptibility This describes linear propagation giving rise to speed of propagation through the medium (real part) absorption in the medium (imaginary part) It can be shown that C 1 = n - 1 where n is the refractive index of the medium Linear polarization

6. Nonlinear polarization A more realistic equation for polarisation is P = (1) E + (2) E 2 + (3) E 3 + where (2), (3) etc are the second and third order nonlinear susceptibilities Normally, (3) E 3 << (2) E 2 << (1) E Unless, E is very very big. Symmetry arguments can be used to show that for isotropic materials even order susceptibilities are zero

7. Typical Nonlinear Optical Phenomena Second Order Processes –Second Harmonic Generation –Sum-Frequency Generation Third Order Processes –Multi-Photon Absorption* –Stimulated Raman Scattering –Optical Kerr Effect –White Light Generation

8. Interaction of Light with Matter P = induced polarization, (n) = n th order non-linear susceptibility E = electric field Linear Processes · Simple Absorption/Reflection · Rayleigh Scattering (3) << (2) << (1) (5-7 orders of magnitude per term) Second Order Processes · Second Harmonic Generation* · Sum-Frequency Generation Third Order Processes · Multi-Photon Absorption* · Stimulated Raman Scattering · Optical Kerr Effect · White Light Generation

9. One and two photon absorption physics Requires high power: Absorption only In focal plane Greatly Reduces out of plane bleaching Simultaneous absorption Virtual State: Very short lifetime ~10 -17 s Goeppart-Mayer, ~1936 e.g. fluorescein

10. One Photon2 photon Absorption probability Absorption Coefficient units (50,000) (10 -16 cm 2 ) (10 -50 cm 4 s) 10 -50 cm 4 s= 1 GM (Goppert-Mayer) Power (photon) dependence pP 2 (gives rise to sectioning) Laser Temporal dependence none 1/ p p2p2 / One and 2-photon absorption characteristics Cannot use cw lasers (Ar+)

11. Xu and Webb, 1996 Slope of 2 at All wavelengths: 2-photon process Fluorescein and rhodamine Power Dependence

12. 2-photon excitation of fluorescein: 3D confinement Absorption, Fluorescence only in middle at focal point Compare 1 and 2-p Absorption 1-p excites throughout

13. Radial PSFAxial PSF Comparable Lateral and Axial Resolution to confocal

14. Cross section GM Max 820 nm not 1050 nm Two-photon Absorption Spectrum Nominally forbidden in 2-p Nominally forbidden in 1-p: Allowed and stronger in 2-p

15. Reverse of 1-photon For all xanthenes: Fluorescein, rhodamines All max ~830 nm Not ~1000 nm 1 and 2-photon bands

16. Same emission spectrum for 1-p, 2-p excitation Relaxation is independent of Mode of excitation Same emission spectrum For different 2-p wavelengths: 750 and 800 nm Just like 1-photon emission Xu and Webb, 1996 Emission Spectrum

17. 1)Emission spectrum is the same as 1-p 2)Emission quantum yield is the same 3)Fluorescence lifetime is the same 4)Spectral positions nominally scale for the same transition: 2-p is twice 1-p wavelength for 5) Selection rules are often different, especially for xanthenes (fluorescein, rhodamine and derivatives) Some Generalities about Multi- photon absorption

18. Non-decanned Detection

19. White, Biophys J, 1998 Confocal (1-p)<2-p descanned< 2-p direct 2-p direct collects ballistic and scattered photons X-Z projection Non-descanned Detection Increases Sensitivity

20. White, Biophys J, 1998 1-p 2-p Improved Imaging Depth Due to Reduced Scattering All images are descanned

21. Registration Issues · Focus of White light vs Laser often different by 10-20 microns · Overlapping visible and near-infrared lasers difficult for uncaging · Second Harmonic Generation Alignment is different than Laser Problems can arise from high peak power giving rise to unwanted non-linear effects Plasma formation leading to cell destruction (makes holes) Accidental 3 photon absorption of proteins and nucleic acids (700-800 nm) (abnormal cell division) ~ 10 mW at 1.4 NA is good limit at sample (Scales for lower NA)

22. Piston, Biophys J. 2000 488 nm 1-photon Slope=1.2 Bleaching of fluorescein dextran in droplets 710 nm 2-photon Slope=1.9 (low power)

23. Piston,2000 NADH=3.65 Coumarin=5.1 Indo-1=3.5 Highly nonlinear: Higher order processes Excitation to higher states Non-linear bleaching (ctd) For same transition 2-p Does not bleach more Than 1-p!

24. Applications

25. Autofluorescence of endogenous species in tissues Need multi-photon excitation, non-descanned detection For enough sensitivity: small cross sections and quantum yields

26. Autofluorescence in Tumors Mitochondria: NADH, Flavins NAD not fluorescent NADH emission to Monitor respiration NADH good diagnostic Of cell metabolism Small cross section Quantum yield ~10% Small delta ~0.1 GM High concentration Need non-descanned Detection to be viable

27. Imaging Muscle (NADH) With TPE Fluorescence Low cross section but High concentration Balaban et al

28. Strata corneum Keratinocytes Dermal layer (elastin, collagen) fibers Human Skin Two-photon imaging So et al Ann. Rev. BME 2000 More versatile than dyes (but weaker) MPM enabling, very weak in confocal

29. Multiphoton bleaching Need 3D treatment, both radial, axial PSF

30. Two-photon cross section measurement Xu and Webb, 1996 Measure by fluorescence intensity, need quantum yield (same as 1 photon) Measure wavelength Measure pulse width Measure power Measure Fluor. Control power