nonlinear optical methods for biophotonics applications · second-order nonlinearity in materials...
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![Page 1: Nonlinear Optical Methods for Biophotonics Applications · Second-order nonlinearity In materials with inversion symmetry 2nd order nonlinear processes are absent: (1; 2, 3) 0 (2)](https://reader034.vdocuments.mx/reader034/viewer/2022051909/5ffe79c6839efd10432d05f4/html5/thumbnails/1.jpg)
Nonlinear Optical Methods for Biophotonics Applications
Valdas Pasiskevicius [email protected]
Applied Physics
School of Engineering Sciences Royal Institute of Technology (KTH)
Stockholm, Sweden
ADOPT Winter school 2016 1
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Outline
Introduction Nonlinear material response Applications: SFG, SHG, MPEF SRS, CARS, SERS Tissue ablation
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Outline
Introduction: the classics Nonlinear material response Applications: SFG, SHG, MPEF SRS, CARS, SERS Tissue ablation
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Applications: Clinical diagnostics, Cell functional imaging
Picture by Dr. Sonja Pyott University of North Carolina, Wilmington Wilmington, NC, USA
Fluorescent dye Stained biopsy
“Gold standard” for diagnostics
Imaging Spectroscopy
Cochlea and Hair Cells
• Depth resolution • Functional imaging
Exogenous Fluoresece Imaging - Confocal scanning laser microscopy (CSLM)
• Tissue specific • ”Molecular” resolution
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CSLM principle
Lichtman, J. W. and J.-A. Conchello (2005). "Fluorescence microscopy." 2(12): 910-919 5
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CSLM resolution: point spread function (PSF)
T. Wilson, Journal of Microscopy, Vol. 244, 2011, pp. 113–121
PSFConfocal ~(PSFwide field)2
𝐿𝐹𝑊𝐻𝑀𝑐𝑜𝑛𝑓 = 0.37𝜆/𝑁𝐴
𝐿𝐹𝑊𝐻𝑀𝑤𝑖𝑑𝑒 = 0.51𝜆/𝑁𝐴
𝐴𝐹𝑊𝐻𝑀𝑐𝑜𝑛𝑓 = 0.64𝜆
𝑛 − 𝑛2 − 𝑁𝐴2
𝐴𝐹𝑊𝐻𝑀𝑤𝑖𝑑𝑒 = 0.89𝜆
𝑛 − 𝑛2 − 𝑁𝐴2
Lateral resolution Axial resolution
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Field shaping with opposing lenses and Superresolution
S. W. Hell, R. Schmidt, A. Egner, Nat. Phot. , 3, 381 (2009)
STED is also a nonlinear optical method regardless of claims to opposite!
STED – simulated emission depletion PALM – photo-activation localization iPALM – interferometric PALM STORM – stochastic optical reconstruction
sm IInz
/
2ln,
STED:
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Sensitivity to surroundings Bleaching (excitation triplet states)
Some aspects to take into account in fluorescence methods
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Excitation Fluorescence
Endogenous fluorophores in tissue
A. Wagnieres, et al, Photochem. Photobiol. 68, 603 (1998)
Some aspects to take into account in fluorescence methods
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Outline
Introduction Nonlinear material response Applications: SFG, SHG, MPEF SRS, CARS, SERS Tissue ablation
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Material response to EMG fields
• Strongest response form bond-forming (valence) electrons • Delocalised
Electron density: peptide bond in anifreeze protein
Generated by MoPro package
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Some definitions
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• Constitutive relations:
;
;0
t
DEJ
MHB
;0 PED
Usual simplifications: nonconductive (=0), nonmagnetic (M =0), no space charge (=0).
EP :0 EPolarization vector:
• Polarization P and magnetization vectors fully describe material response to external
electromagnetic wave.
Magnetization vector: HM :0 M
• Material parameters: dielectric susceptibility E and magnetic susceptibility M
;D
Polarization = dipole moment per unit volume
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)1(
0
)1(
00 PPEPP
Linear response
Harmonic oscillator model:
22222
22
0
2)1(
4)()Re(
m
Ne22222
0
2)1(
4)(
2)Im(
m
Ne
- damping of material resonance at .
n
w1 w2 w3
RF-FIR Visible UV
w Acoustic )1Re(,1 )1()1( n
Dielectric tensor, refractive index:
)1Im(2 )1(
c
Power absorption coefficient:
13
Electronic Vibrational Rotational
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Nonlinear response to EMG fields
P
E
Polarization due to anharmonic oscillator driven by external field E:
...... )3()2()1(
0
)3()2()1(
00 PPPPEEEEEEPP
inter-atomic electric field ~ ]/[1010 1110
2
0
mVr
e
n
nnnEEχP n
nn
...
1
)(
...0
)(
1
111)())(,...,;()(
Anharmonicity results in nonlinear polarisation at combination frequencies
Summations: n ...1
over Cartesian coordinates (x,y,z)
over different sets of frequencies
n
n
...
,...,,
21
21
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Microscopic viewpoint Alternative description, nonlinear response of a single dipole (molecular bond):
)()(:),...,;( 11
)()(
, nmmn
nn
m EEe γr
),,;(),,;(
),;(),;(
);();(
321
)3(
321
21
)2(
21
1
)1(
1
γγ
γ
γ
Common notation in literature:
polarizability
hyperpolarizability
)()1()0( ... n
mmmm eeee rrrr
Nonlinear response of a dipole characterized by polarizability tensor:
Local fields
;3/))(2()()( jExternaljLocaljm EE
For isotropic spherical molecules:
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2. Resonant
1. Perturbative
...... )3()2()1(
0
)3()2()1(
00 PPPPEEEEEEPP
• Photon far from electron transition resonances • Optical electric field complies :
km
mkaE
)(
km - dipole moment for k <->m
b
aea
E 0
No bound-bound multiphoton transitions
No bound-free multiphoton transitions
ba - Bohr radius, e – electron charge
Typically intensity < 1013 W/cm2
• P Series diverges if
• Nonlinearities for specific processes can be resonantly enhanced
0)( nmk
Regimes of nonlinear optics
Bound-bound multiphoton transitions
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3. Strong-field
4. Relativistic
b
aea
E 0
• Bound-continuum transitions: atom and molecule ionization with optical field
• High-harmonic generation in plasma
• as-pulse generation and detection
• Electron acceleration in optical field close to
• High-coherence -ray generation by laser Compton scattering
• Electron-positron pair generation
• Laser proton sources
• Thermonuclear fusion
2mc
1.03pm2MeV2.1 20 cme
218W/cm10I
Regimes of nonlinear optics
Bound-free multiphoton transitions
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Outline
Introduction Nonlinear material response Applications: SFG, SHG, MPEF: imaging SRS, CARS, SERS Tissue ablation
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)()(:),;()( 32321)2(
1 EEχP NL
Sum-frequency mixing (SFM) Second harmonic generation (SHG)
32321 ,
32321 ,
Second-order nonlinearity
Processes useful for imaging:
32 1
Forward and backward processes
LkkkkL )( 321Momentum conservation requires:
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Second-order nonlinearity
In materials with inversion symmetry 2nd order nonlinear processes are
absent: 0),;( 321
)2( ijkχ
Inversion symmetry exists in:
• Crystal symmetry classes (432),(622) ,(422).
• Isotropic solids.
• Atomic gasses.
• Molecular gasses.
• Liquids.
Inversion symmetry absent in:
• Remaining 29 symmetry classes.
• Surfaces of isotropic media.
• Chiral media
• Aligned polymers
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SHG imaging microscopy (SHIM), beginnings: I. M. Freund, et al, ”Connective tissue polarity,” Biophys. J. 50, 693 (1986)
Second Harmonic generation imaging
SHIM Features: • No fluorescent labels • No toxicity • No photobleaching • High contrast 3D imaging • Spatial resolution • Polarized SH signals: information about structural anisotropy
Sources of SHG in tissue: • Membranes • Colagen (connective tissue fibrils) • Chiral protein structures (e.g. Tubulin structures , myelin sheaths)
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SHG signal (for interaction length < Lc): • Inversely propotional to beam area and pulse length • Depends quadraticaly on molecule concentration
Second Harmonic generation imaging
Beam area
power Pulse length
SHG microscopy image 250 µm deep in muscle tissue. Scale bar – 50 µm
P. J. Campagnola, et al, Biophys. J., 81, 493 (2002) 22
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Sum-frequency generation imaging
• Conceptually similar to SHG • Except for the cases where one wave is on
molecular resonance • Typically NIR (~1 µm) and resonant MIR (~3
µm) • Linear SFM power dependence on the
powers of exciting waves
32321 ,
Picture source: V. Raghunathan et al Optics Lett. , 36, 3891 (2011)
Picosecond OPO
Resonant Off-Resonant
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Nonresonant SFM can make interpretation complicated
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Sum-frequency generation imaging
V. Raghunathan et al Optics Lett. , 36, 3891 (2011)
Colagen SFM imaging on methylene mode 2959 cm-1
MIR wave off resonance MIR wave on resonance
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Two-photon excitation of fluorescence TPEF relies on two-photon absorption (TPA) process
• Third-order resonant nonlinearity • Absorption coefficient depends on intensity
R. W. Boyd, Nonlinear optics, 3rd ed. 2007
In dielectrics
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Predicted by Maria Goeppert-Mayer in 1931 in her doctoral dissertation (Göttingen)
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Picture source: UCF, College of Sciences
Two-photon excitation of fluorescence W. Denk, J. H. Strickler, W. W. Webb, Science, 248, 73 (1990)
M. Drobyzhev, et al, Nature Methods, 8, 393 (2011)
...32 IIInPA
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Two-photon excitation of fluorescence
TPA cross-section
M. Drobyzhev, et al, Nature Methods, 8, 393 (2011)
Goeppert-Mayer units, 1 GM = 10−50 cm4 s photon-1
Sensitivity to local electric field )()( 1
2
10 gA
)()( 2
2
10
2
102 gB E)(5.0 21
0
1010
Linear extinction
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• Spatial resolution
• Sensitivity to surounding fields
• NIR excitation: less scattering
• Lower infuence of auofluorescence
Two-photon excitation of fluorescence
V. E. Centonze et al, Biophys. J. 75, 2015 (1998)
Confocal vs TPEF
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Multiphoton excitation ”guide star”
R. Aviles-Espinosa et al, Biomed.Opt.Exp. 2, 3125 (2011) X. Tao, et al ,SPIE Proc. 8978, 89780D (2014)
TPFE imaging with NADH autofluorescence guide star: • In vivo • 30 ms/WF measurement • Depth 51 µm
C Elegans in vivo
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Combined SHG, TPEF (autofluorescence)
Zipfel W R et al. PNAS 2003;100:7075-7080
©2003 by National Academy of Sciences 30
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Upconversion fluorescence in nanoparticles
H. Liu, C. T. Xu, S. Andersson-Engels, Opt. Express, 22, 17782 (2014)
2PE
3PE
Core-shell NaYF4 : Yb3+, Tm3+ @NaYF4
Increasing imaging resolution through scattering medium 31
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Outline
Introduction Nonlinear material response Applications: SFG, SHG, MPEF: imaging SRS, CARS, SERS: imaging, sensing Tissue ablation
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.:))((
:))(( )0(
)0(EE
αEα
rr
X
XX
X
XeXeH m
mm
mI
Orientation energy Rayleigh scattering Raman scattering IR absorption
Electric dipole energy:
0))(( )0(
X
Xe mr
0))((
X
Xmα
If molecular vibration mode is called IR-active.
If differential polarizability tensor molecular vibration is Raman-active.
Symmetric stretching mode Asymmetric stretching mode Bending mode
)(Xmα X X X
X )()0( Xe mr X X
Raman activity
IR activity
yes
yes yes no
no no
Raman Scattering, basics
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Vibrational RS
E
X
Stokes
Anti-Stokes
|n2m2l2>
|n1m1l1>
E
X
|n1m1l1>
<n2m2l2|
Electronic resonant RS
,...2,1,
,
mm
m
pa
ps
Raman Scattering, basics
Stokes
Antistokes
• Spontaneous Stokes efficiency is higher • Ratio is temperature dependent
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spsppsRs EEP2
)3(
0 ),,;(
SRS: Stimulated Raman Scattering
Stimulated Raman Scattering
Combined EDFA+Raman Amplifier
),,;()3(
sppsR
affects amplitude (gain) and phase (refractive index) at
• Vibrational and rotational (molecular gasses) Raman scatering • SRS automatically phase-matched • Efficiency (contrast in microscopy) depends on intensity of the pump
s
Raman susceptibility: a complex quantity
))0(exp()0()( LIgILI pRss
Nnnc
TNg
sp
RsR
220
2
2
4
Stimulated Raman gain:
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sprpasprpsprpaRa EEEP ;),,;( *)3(0
CARS Coherent Antistokes Raman Scattering:
• Four wave mixing process: phase sensitive • Epr should be applied before vibrational (rotational) coherence relaxation • Phase-matching is required
kp
ks
ka
kpr ks
kpr
ka
kp
0 asprp kkkkk
Two-beam scheme BOXCARS scheme
• In CARS nonresonant background from FWM process: • Bacground suppression: polarization and time gating, heterdyne CARS
),,;()3(
sprpa
p s pr a
v=0 v=1
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CARS imaging
Antistokes scattering reported: P. D. Maker and R. W. Terhune, Phys. Rev. 137, A801(1965). CARS name invented: R. F. Begley,et al, Appl. Phys. Lett. 25, 387 (1974). First CARS microscope: M. Duncan, et al, Opt. Lett. 7, 350 (1982).
• Stimulated Raman scattering is automatically phase matched
• CARS is not • In CARS microscopy: large NA
collinear excitation works fine
NR )3(
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CARS imaging
Typical numbers: • Picosecond pulses t>1/Raman spectral width • Pulse energy <1 nJ: avoid damage • Average powers ~10 mW: avoid heating • Easy region 2500-3500 cm-1, • More difficult but more important 800-1800 cm-1
Example: 0.1 nJ, 5ps, 1.2NA, gives 0.2 TW/cm2 in focus, and 500 antistokes photons per pulse at OH 3300cm-1 mode
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CARS imaging with chirped pulses
Th. Hellerer, et al, Appl. Phys. Lett. 85, 25 (2004)
C-N
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Vibrational spectra in tissue (H-C-H, O-H stretching)
Cholesterol Lipid tristearin
HOH
• Multiple overlapping vibrational bands • Work in sweet-spot or ”quiet region” in vibrational spectrum (good for some molecules) • In CARS – phase sensitivity adds more complexity • Advanced algorithms required for extraction of vibrational spectrum
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Heterodyne CARS
E. Potma, et al, Opt. Lett. 31, 241 (2006)
sinImcosRe2 )3()3()3(22
RRNRpLOaLO EEEES
1. Add ELO field at a and use interferometer to control phases 2. Modulate phase of ELO and use heterdyne detection
d-DMSO
• =90 gives background-free Raman response • Amplification by increasing and not pump ELO
• Imaging 103x faster than with spontaneous Raman
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Th. Hellerer et al PNAS, 104, 14658 (2007)
CARS @2845 cm-1 (CH2) TPEF: Nile red
CARS imaging: comparison with TPEF
• Sensitivity ~105 lipid molecules in focus volume (sub mM concentrations) • Somewhat better with heterodyne CARS
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M. Lee, et al, IntraVital, 4, e1055430 (2015)
CARS multispecies imaging
CH2 2845 cm-1 CH3 2930 cm-1 OH 3030 cm-1
Lipid (b)-(f) Amino (d)-(b)-(f) HOH (f)-(d)
Overlay
Chemically selective imaging of tumor histopathology in MMTV-PyMT mammary tumors
• Stokes: 7 ps, 1064 nm, 80 MHz. Pump(probe): 5ps, 750-920 nm SPOPO. • Combined power on sample: 30-60mW • Dwell time: 10 µs • Acquisition: 2.6 s/frame
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M. Lee, et al, IntraVital, 4, e1055430 (2015)
CARS combined multimodal imaging Red: SHG (colagen) Green: TPFE GFP expressing cancer cells Cyan: CARS CH3 2930 cm-1 host cells
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CARS (red)+SHG (green)
Hyperspectral CARS multimodal imaging
Lipids in mamary tumor tissue
CARS
Source of picture: Eric Potma, UC Irvine 45
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SRS microscopy
• No nonresonant background • No labels • Linear dependence on concentration • Sensitivity similar and better than CARS (50 µM retinol, 5 mM methanol) • Spatial resolution similar to multiphoton imaging
Ch. W. Freudiger, et al, Science, 322, 1857 (2008)
7 ps Nd:YVO4 + OPO. <40 mW, 30 MWcm-2
Efficiency ~ 4 , but avoid short due to autofluorescence background
• Stimulated Raman Gain (SRG) • Raman-stimulated pump loss (SRL)
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SRS imaging Comparison with CARS
Ch. W. Freudiger, et al, Science, 322, 1857 (2008)
SRS Brain
SRS Skin
Through 1 mm
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Stimulated Raman spectroscopy
RIKE – Raman-induced Kerr effect dual comb spectroscopy
T. Ideguchi, et al, Optics Lett., 37, 4498 (2012)
• Measures amplitude and phase of vibrational modes • Single spectral measurement in ~3 µs
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Resonantly enhanced near-field
Surface enhanced Raman scattering (SERS) Albrecht MG, Creighton JA. 1977..J. Am. Chem. Soc. 99:5215–17
Nie S, Emory SR. 1997. Science 275:1102–6
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SRS and CARS: Relative (dis)advantages CARS microscopy • No labels required • Bond-specific imaging • Potentially background-free • Relaxed requirements for laser stability • Quadratic dependence on concentration • Phase matching required (propagation direction-sensitive) • Parasitic nonresonant FWM • CARS spectra need interpretation SRS microscopy • No labels required • Bond-specific imaging • Linear dependence on concentration • Free from parasitic FWM • Phase matching not required (insensitive to propagation direction) • Straighforward spectral information • Detection of small modulation on top of large signal • High demenads on laser stability
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Outline
Introduction Nonlinear material response Applications: SFG, SHG, MPEF: imaging SRS, CARS, SERS: imaging, sensing Tissue ablation: minimally invasive surgery, nanosurgery
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Cell surgery
• TW/cm2 intensties: fs pulses • MPA: subdiffraction resulution • Independent on linear absorption properties of biological object • Low-energy breakdown threshold • Low heat deposition in surrounding tissue
Processes: • Optical breakdown : ionization, plasma formation, chemical dissociation • Material removal: pressure wave, cavitation
• Avoid nonlinear propagation, self focussing • Large NA optics (NA>0.9)
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Optical breakdown processes
• Multiphoton ionization, tunelling tunelling: ”instantaneus” • Impact ionization: requires scattering, ”slow”
A. Vogel, et al, Appl. Phys. B, 81, 1015 (2005) 53
Keldysh parameter: γ<1 tunelling (short pulses, low ω) γ>1 multiphoton ionization
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Optical breakdown of water
Electron density dynamics
Electron density vs intensity
A. Vogel, et al, Appl. Phys. B, 81, 1015 (2005) Multiphoton ionization part 54
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Optical breakdown thresholds
For fs pulses: • Higher intensity threshold • Lower energy fluence • Less colateral damage
Breakdown in water
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The breakdown process
Chemical changes: • Reactive oxygen species (ROS) • Dissociation by electron capture
Thermoelastic stress: • Pulse shorter than thermalisation time • Stress confinement • Shock wave formation • Nucleation of bubble in the focal region
Typical values for cavitation • λ = 800 nm, NA = 1.3, T=20 C, 100 fs • Required ΔT = 131.5 C for critical tensile stress p=−71.5MPa • Corresponding Energy density in the focus 551 J cm-3
• Electron density 0.23x1021 cm-3
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Time-dependence of the bubble radius
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Cavitation @ tensile stress ~-70 MPa
Example for HOH breadown threshold: 800 nm, 100 fs, NA 0.65 0.1 µJ, 5.64 J/cm2, 56.4 TW/cm2
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Cell surgery: intensity regimes
A. Vogel, et al, Appl. Phys. B, 81, 1015 (2005) 58
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Cell optical trapping and surgery
Z. L. Shi, et al, Current Microscopy Contributions to Advances in Science and Technology (2012) 59
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K. König, et al Optics Lett. 26, 819 (2001)
DNA ablation and drilling
• ~0.5 nJ, 80 MHz, 800 nm, 170 fs • 1.3 NA , 320 nm spot • Dwell time 3.2 ms (1.6 µJ cummulative) • 200 nm cuts
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NLO methods: some advantages and disadvantages
Optimist’s view: • Spatial resolution not limited by PSF • Staining is not required in most of the methods • Specificity to molecular bonds • Sensitivity to interfaces and types of tissue • Sensitivity to local electric fields (SFIM)
Pessimist’s view: • High intensities required • Might be difficult to apply in light-scattering surroundings • No clear standards yet (except for surgery) • Perceived as technically complicated
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