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Nonlinear Optical Microscopy

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X Y Non-linear?

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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

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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

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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

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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

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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

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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

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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 ~ s Goeppart-Mayer, ~1936 e.g. fluorescein

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One Photon2 photon Absorption probability Absorption Coefficient units (50,000) ( cm 2 ) ( cm 4 s) 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+)

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

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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

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Radial PSFAxial PSF Comparable Lateral and Axial Resolution to confocal

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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

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

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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

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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

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Non-decanned Detection

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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

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

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Registration Issues · Focus of White light vs Laser often different by 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 ( nm) (abnormal cell division) ~ 10 mW at 1.4 NA is good limit at sample (Scales for lower NA)

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

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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!

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Applications

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

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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

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

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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

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

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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

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