Download - Nonlinear Optical Microscopy
Nonlinear Optical Microscopy
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Non-linear?
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(3t)
The output is thus given by
y=[a1+(3/4)c1] cos(t)-(1/4)c3cos(3t)
Thus a small cubic nonlinearity gives rise to a modified response at w but also generates a new signal at 3w
Nonlinear response
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
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
Linear polarization
Nonlinear polarizationA 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
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
Interaction of Light with Matter...3)3(2)2(1)1( EEEP
P = induced polarization,(n) = nth order non-linear susceptibilityE = 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
One and two photon absorption physics
Requires high power:Absorption onlyIn focal plane
Greatly Reduces out of plane bleaching
Simultaneous absorptionVirtual State:Very short lifetime ~10-17 s
Goeppart-Mayer, ~1936
e.g. fluorescein
One Photon 2 photon
Absorptionprobability
AbsorptionCoefficient units
(50,000)
(10-16 cm2)
(10-50 cm4s)
10-50 cm4s=1 GM (Goppert-Mayer)
Power (photon)dependence
p P2 (gives rise to sectioning)
Laser Temporaldependence
none 1/
p p2 /
One and 2-photon absorption characteristics
Cannot use cw lasers (Ar+)
Xu and Webb, 1996
Slope of 2 atAll wavelengths:2-photon process
Fluorescein and rhodamine
Power Dependence
2-photon excitation of fluorescein: 3D confinement
Absorption, Fluorescence only in middle at focal point
Compare 1 and 2-pAbsorption1-p excites throughout
Radial PSF Axial PSF
Comparable Lateral and Axial Resolution to confocal
Cro
ss s
ectio
n G
M
Max 820 nmnot 1050 nm
Two-photon Absorption Spectrum
10 SS Nominally forbidden in 2-p
20 SS Nominally forbidden in 1-p:Allowed and stronger in 2-p
Rhodamine Photophysics
10-12 s
1000 nm TPE
500 nm OPE
800 nm TPE
400 nm OPE
10-9 s
S0
S1
S2
800 nm stronger than 1000 nm band
Reverse of 1-photonFor all xanthenes:Fluorescein,rhodamines
All max ~830 nmNot ~1000 nm
1 and 2-photon bands
Same emission spectrumfor 1-p, 2-p excitation
Relaxation is independent ofMode of excitation
Same emission spectrumFor different 2-p wavelengths:750 and 800 nmJust like 1-photon emission
Xu and Webb, 1996
Emission Spectrum
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
Non-decanned Detection
White, Biophys J, 1998
Confocal (1-p)<2-p descanned< 2-p direct
2-p direct collects ballistic and scattered photons
X-Zprojection
Non-descanned Detection Increases Sensitivity
White, Biophys J, 1998
1-p
2-p
Improved Imaging Depth Due to Reduced Scattering
All images are descanned
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)
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)
Piston,2000
NADH=3.65Coumarin=5.1
Indo-1=3.5
Highly nonlinear:Higher order processesExcitation to higher states
Non-linear bleaching (ctd)
For same transition 2-pDoes not bleach moreThan 1-p!
Applications
Autofluorescence of endogenous species in tissues
Need multi-photon excitation, non-descanned detectionFor enough sensitivity: small cross sections and quantum yields
Autofluorescence in Tumors
Mitochondria:NADH, Flavins
NAD not fluorescentNADH emission toMonitor respiration
NADH good diagnosticOf cell metabolism
Small cross sectionQuantum yield ~10%Small delta ~0.1 GMHigh concentration
Need non-descannedDetection to be viable
Imaging Muscle (NADH)With TPE Fluorescence
Low cross section butHigh concentration
Balaban et al
Strata corneum
Keratinocytes
Dermal layer(elastin, collagen)fibers
Human Skin Two-photon imaging
So et alAnn. Rev. BME2000 More versatile than dyes (but weaker)
MPM enabling, very weak in confocal
Multiphoton bleaching
Need 3D treatment, both radial, axial PSF
Two-photon cross section measurement
Xu and Webb, 1996
Measure by fluorescence intensity, need quantum yield(same as 1 photon)
Measure wavelength
Measure pulse widthMeasure power
MeasureFluor.
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hcNAPna
Control power