Light transfers momentum to matter

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p = h/λ 6.55 × 10 −34 J·s/λ Slides mostly from Yann Chemlablame him if anything is wrong!

Transcript of Light transfers momentum to matter

Page 1: Light transfers momentum to matter

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.