Nonlinear Optical Microscopy
Non-linear?
Y
X
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
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
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
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
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
P   E 
(1)
1
(2)
E   E  ...
2
(3)
3
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
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
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
One and 2-photon absorption characteristics
One Photon
Absorption
Coefficient
units
Power (photon)
dependence
2 photon
e (50,000)
d (10-50 cm4s)
s
10-50 cm4s=
1 GM (Goppert-Mayer)
(10-16 cm2)
p
Laser Temporal
dependence
none
Absorption
probability
sp
P2 (gives rise to sectioning)
1/t
2
d p /t
Cannot use cw lasers (Ar+)
Power Dependence
Fluorescein and rhodamine
Slope of 2 at
All wavelengths:
2-photon process
Xu and Webb, 1996
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
Comparable Lateral and Axial
Resolution to confocal
Radial PSF
Axial PSF
Cross section GM
Two-photon Absorption Spectrum
Max 820 nm
not 1050 nm
S 0  S1
Nominally forbidden in 2-p
S0  S2
Nominally forbidden in 1-p:
Allowed and stronger in 2-p
Rhodamine Photophysics
1 and 2-photon bands
S2
10-12 s
S1
10-9 s
500 nm OPE
400 nm OPE
1000 nm TPE
800 nm TPE
Reverse of 1-photon
For all xanthenes:
Fluorescein,
rhodamines
S0
800 nm stronger than 1000 nm band
All max ~830 nm
Not ~1000 nm
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
Some Generalities about Multiphoton absorption
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)
Non-decanned Detection
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
Improved Imaging Depth Due to
Reduced Scattering
2-p
1-p
All images are descanned
White, Biophys J, 1998
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)
Bleaching of fluorescein dextran in droplets
488 nm 1-photon
Slope=1.2
710 nm 2-photon
Slope=1.9 (low power)
Piston, Biophys J. 2000
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
Applications
Autofluorescence of endogenous species in tissues
Need multi-photon excitation, non-descanned detection
For enough sensitivity: small cross sections and quantum yields
Autofluorescence in Tumors
Mitochondria:
NADH, Flavins
NAD not fluorescent
NADH emission to
Monitor respiration
Small cross section
Quantum yield ~10%
Small delta ~0.1 GM
High concentration
Need non-descanned
Detection to be viable
NADH good diagnostic
Of cell metabolism
Imaging Muscle (NADH)
With TPE Fluorescence
Low cross section but
High concentration
Balaban et al
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
Multiphoton bleaching
Need 3D treatment, both radial, axial PSF
Two-photon cross section measurement
Measure
Fluor.
Measure wavelength
Measure pulse width
Measure
power
Control power
n a  dP t
2
1
[
 NA
hc 
2
]
2
Xu and Webb, 1996
Measure by fluorescence intensity, need quantum yield
(same as 1 photon)