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Nonlinear Optical Microscopy

Nonlinear Optical Microscopy. Non-linear?. Y. X. Nonlinear response. 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

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Nonlinear Optical Microscopy

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  1. Nonlinear Optical Microscopy

  2. Non-linear? Y X

  3. Nonlinear response Actual response can be written as y = c1 x+ c3 x3 (this is called a cubic distortion) Assuming the input is a periodic signal x = cos (t) y=c1 cos(t)+c3[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)c1] cos(t)-(1/4)c3cos(3t) Thus a small cubic nonlinearity gives rise to a modified response at w but also generates a new signal at 3w

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

  5. Linear polarization P = c1 E ; P is the polarization c1 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 C1 = n - 1 where n is the refractive index of the medium

  6. Nonlinear polarization A more realistic equation for polarisation is P = (1)E + (2)E2 + (3)E3 +  where (2), (3) etc are the second and third order nonlinear susceptibilities Normally, (3)E3 << (2)E2 << (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) = nth order non-linear susceptibility E = electric field (3) << (2)<< (1)(5-7 orders of magnitude per term) Linear Processes ·    Simple Absorption/Reflection ·   Rayleigh Scattering Third Order Processes ·      Multi-Photon Absorption* ·      Stimulated Raman Scattering ·      Optical Kerr Effect ·      White Light Generation Second Order Processes ·      Second Harmonic Generation* ·      Sum-Frequency Generation

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

  10. One and 2-photon absorption characteristics One Photon2 photon d (10-50 cm4s) e (50,000) Absorption Coefficient units 10-50 cm4s= 1 GM (Goppert-Mayer) s (10-16 cm2) p P2 (gives rise to sectioning) Power (photon) dependence Laser Temporal dependence 1/t none Absorption probability p2 s p d /t Cannot use cw lasers (Ar+)

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

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

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

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

  16. Emission Spectrum 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

  17. Some Generalities about Multi-photon absorption • Emission spectrum is the same as 1-p • Emission quantum yield is the same • Fluorescence lifetime is the same • 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)

  18. Non-decanned Detection

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

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

  21. 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) 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

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

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

  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. Human Skin Two-photon imaging Strata corneum Keratinocytes Dermal layer (elastin, collagen) fibers 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 Measure Fluor. Measure wavelength Measure pulse width Measure power Control power Xu and Webb, 1996 Measure by fluorescence intensity, need quantum yield (same as 1 photon)

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