light transfers momentum to matter
TRANSCRIPT
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Light transfers momentum to matter
p = h/λ 6.55 × 10−34 J·s/λ
Slides mostly from Yann Chemla—
blame him if anything is wrong!
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Optical Traps
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Key points
Trap strength depends on light intensity, gradient
Trap is harmonic: k ~ 0.1pN/nm
Light generates 2 types of optical forces:
scattering, gradient.
Gradient leas to radiation pressure.
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Optical scattering forces – reflection
Pi = h/λ
Pf
ΔP
Newton’s third law – for every action there is an equal and opposite reaction
F = ΔP/Δt = (Pf-Pi)/Δt
Pi
θ
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Optical forces – Refraction
Pi
Pf
Pi
ΔP
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Lateral gradient force
Bright ray
Dim ray
Object feels a force toward brighter light
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Axial gradient force
Pi
Pf
Pi ΔP
Force ~ gradient intensity
Object feels a force toward focus
Focused
light
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IR traps and biomolecules are compatible
Neuman et al. Biophys J. 1999
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Biological scales
www.alice.berkeley.edu www.cnr.berkeley.edu/~hongwang/Project
www.scripps.edu/cb/milligan/projects.html
Force: 1-100 picoNewton (pN)
Distance: <1–10 nanometer (nm)
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Requirements for a quantitative optical trap:
1) Manipulation – intense light (laser), large gradient
(high NA objective), moveable stage (piezo stage) or
trap (piezo mirror, AOD, …) [AcoustOptic Device- moveable laser pointer]
2) Measurement – collection and detection optics
(BFP interferometry)
3) Calibration – convert raw data into forces (pN),
displacements (nm)
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Laser Beam expander
Objective Condenser
Photodetector
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1) Manipulation
DNA
Want to apply forces – need ability to move stage or
trap (piezo stage, steerable mirror, AOD…) (Acouto Optic Device:
variable placement of laser)
By using two beads, and taking
difference, capable of removing floor
movement! Get to Angstrom level!
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2) Measurement
Want to measure forces, displacements – need to
detect deflection of bead from trap center
1) Video microscopy
2) Laser-based method – Back-focal plane interferometry
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BFP imaged onto detector
Trap laser
BFP
specimen
PSD
Relay lens
Conjugate image
planes
∑
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N
P
N
P
In1 In2
Out1
Out2
Position sensitive detector (PSD)
Plate resistors separated by reverse-
biased PIN photodiode
Opposite electrodes at same potential
– no conduction with no light
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N
P
N
P
In1 In2
Out1
Out2
ΔX ~ (In1-In2) / (In1 + In2)
ΔY ~ (Out1-Out2) /(Out1+Out2)
POSITION
SIGNAL
Multiple rays add their currents linearly to the electrodes, where each ray’s power
adds Wi current to the total sum.
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Calibration
Want to measure forces, displaces – measure voltages
from PSD – need calibration
Δx = α ΔV
F = kΔx = α kΔV
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Glass
Glass
water
Glass
Calibrate with a
known displacement
Calibrate with a
known force
Move bead relative to trap Stokes law: F = γv
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)(tFkxx
Brownian motion as test force
Langevin equation:
Drag force γ = 3πηd
Fluctuating
Brownian
force
Trap force
<F(t)> = 0
<F(t)F(t’)> = 2kBTγδ (t-t’)
kBT
kBT= 4.14pN-nm
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Δt Δt Δt
)()( txtx
Autocorrelation function )()( txtx
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)()( txtx
Δt Δt Δt
Autocorrelation function )()( txtx
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)(tFkxx
Brownian motion as test force (will continue next time)
Langevin equation:
22
1
14
c
Bx
ffk
TkfS
FT → Lorentzian power spectrum
Corner
frequency
fc = k/2π
k
Tkx B 2ttkB e
k
Tktxtx
)()(
Exponential autocorrelation function
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Class evaluation
1. What was the most interesting thing you learned in class today?
2. What are you confused about?
3. Related to today’s subject, what would you like to know more about?
4. Any helpful comments.
Answer, and turn in at the end of class.