Optical Tweezers A revolution in micro-manipulation Jonathan Leach [email protected] University of Glasgow

Optical Tweezers

A revolution in

micro-manipulation

Jonathan [email protected]

k

University of Glasgow

Today’s talk

• What are optical tweezers?

• Dynamic movement and multiple particles

• Current research around the World

What are optical tweezers?

Optical tweezers use light to trap, manipulateand position micron sized objects.

Invented approximately 20 years ago by A. Ashkin et al.

K.C. Neuman and S. M. Block, Optical Trapping, Rev. Sci. Inst., (2004)

J. E. Molloy and M. J. Padgett, Lights, Action: Optical Tweezers, Cont. Phys., (2002)

What are optical tweezers?

A tightly focused laserproduces a force great enough to trap micron sized dielectric particles.

Require……1. Laser2. Lens3. Object4. Damping medium

Fscatt

Fgrad

Optical tweezers in action

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The equipment

Optical tweezers are based on high magnification microscope lenses

–produces tightly focussed beam–provides visualisation of image

Samples suspended in fluid

–provides cooling–provides buoyancy

The equipment

Require tight focusing so needhigh numerical aperture, N.A.

Magnification typically X100

N.A. = n sin()

n is the refractive index of the medium between the objective lens and the sample. Using oilimmersion lenses, n ~ 1.3 so N.A >1is possible.

Optical Trapping - a>> Conditions for Mie scattering when the particleradius a is larger than the wavelength of the light .

We can use a ray optics argument andlook at the transfer of momentum

a

Optical Trapping - a<< Condition for Rayleigh scattering when the particleradius a is smaller than the wavelength of the light .

Scattering force and gradient force are separable

Fgrad > Fscatt requires tight focusing

a

The scalesCan trap 0.1 to 10’s m

1m is…..…the same as 1/100th diameter of a hair.

In water, you can move a particle at about 20-30m per sec.

Require 10mW per trap.

Can rotate at 100’s of Hz.

If absorbed by particle of refractive index n, a beam of power P produces a reaction force

F = nP/c

(e.g. P = 1mW: F = 5pN)

The Q factor of optical tweezers

The efficiency Q, of optical tweezers is defined as

Q = Factual/ (nP/c)(typically Q ≈ 0.05-0.3)

Optical Trap Dynamics

Equation of motion of particle in a potential well

restoring force

Brownian motion

Newtonian force

drag force

Particle in fluid

Solution is of exponential decay

Damping provided by water

Particle in ideal trap

Solution is of simple harmonic motion

Spring constant

Trapped particle in fluid

Solution is of damped simple harmonic motion

The whole picture

Time averaged effect is 0

Stochastic events introduce fluctuations in the particle’s position

Add in the effect of Brownian motion

Trap dynamics

Look at the movement of the particle in x and y

Power spectrum

Trap strength

Fourier transform to get the power spectrum

Lorenzian

Real data

Coming next

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Exam question?

In groups of 3 or 4, create two exam questions, one long, (6 marks), one short (3 marks).

5mins

Collecting data

How can we collect this data?

Moving 100s nm at a few kHz!!!

3 options

Option 1 - Camera

Camera placed in the image plane ofthe objective lens.

Uses the light fromthe illumination source.

Fast shutter speed to take clean image of particle.

Option 1 - Camera

Advantages

• Easy to use• Visual image of particle• Multiple particles

Disadvantages

• 2D measurement • Bandwidth limitations <100Hz• Very slow compared to f0

• Require very fast shutter so need a sensitive camera

Option 2 - Quadrant Photodiode A

Quadrant photodiode placed in the image plane of the objective lens (exactly the same as the camera).

Uses the light fromthe illumination source.

Option 2 - Quadrant Photodiode A

Advantages

• Large bandwidth 100s kHz• Very fast compared to f0

Disadvantages

• Single particle• Low light level, so small signal• 2D measurement

Option 3 - Quadrant Photodiode B

Quadrant photodiode collects the laser light transmitted through the condenser lens.

Small changes in the transmitted and scattered light are measured.

Option 3 - Quadrant Photodiode B

Advantages

• Large bandwidth 100s kHz• Very fast compared to f0

• 3D measurement•High light level as collecting

laser light

Disadvantages

• Complex arrangement• Single particle

Moving particles and multiple particles

Some background optics

An angular shift in the object plane results in a lateral shift in the imageplane.

Collimated light is brought to a focus a distance f, from a lens of focal length f.

Object plane

Image plane

Some background optics

If the beam is not collimated there isa shift in the axial position of the focus.

Moving objects around

f f f f f’ f’

Relay lenses

Beam steeringmirror

Angular deflection at mirror gives lateral shift of trap

Diffractive optics

Placing a diffractive optical element in theobject plane can generate a number of focused spots.

Diffraction grating

Spatial Light ModulatorsCalculated pattern

Video signal

Incoming beam

reflected/diffractedbeam

SLM

optical addressing

• Spatial light modulator = computer-controlled hologram– Liquid crystal (introduce phase or amplitude modulation)– Optically addressed SLMs convert intensity pattern to phase– diffraction efficiency >50%– >VGA resolution

Holograms at work

split the beam focus the beam

transform the beam combinations of the above

Whole beam path

SLM

beam-steerin

g mirror mirror imaged on

microscope entrance pupil

microscope objective

SLM imaged on beam-steering mirror

also: plane waves conserved

Holographic optical tweezers can do (just

about) anything!Hologram

Incident beam

Diffracted beams

Curtis et al. Opt. Commun. 207, 169 (2002)

• Holographic beam generation can create– multiple beams– modified beams– focussed beams– or all these at the

same time• REAL TIME control

of the beams

Dynamic multiple traps

Eriksen et al. Opt. Exp. 10, 597 (2002)

• Use spatial light modulator to create multiple traps– Lateral

displacement– Axial

displacement• Update trap positions

– Video frame rate

Rotating cube



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Exam question?


5mins

Applications of optical tweezers

Bio-applications

The size of particles that can be trapped is ~0.1m to 10’s m

Approximately the same size asmany biological specimen.

e.g. Blood cells, stem cells, DNA molecules

Either trapped directly, or beads used as handles to reduce optical damage.

Ashkin et al. Nature. 330, 768 (1987)

Block et al. Nature. 338, 514 (1989)

Measuring force/motion

Molloy et al. Biophys J. 68, S298 (1995)

biologicalobject

trapped bead

quadrant detector

imaging lens

• Image trapped bead (handle) onto quadrant detector

• Measure movement of shadow– nm accuracy!– kHz response

• Adjust trap to maintain position gives measurement of force– sub-pN accuracy!

e.g. Observation of myosin binding

• Handles attached to actin filament

• Intermittent binding to myosin suppresses thermal motion of beads due to stiff physical bond

e.g. Stretching/twisting of DNA

Perkins et al. Science. 264, 822 (1994)

Wang et al. Science. 282, 902 (1998)

• Attach handles to ends of DNA molecule

• Pull, let go and observe what happens!– understanding of

protein folding



Work at Glasgow

5 microns5 microns

Jordan et al., J. Mod. Opt.,2004

• Permanent micro-structures

• Use SLM to create tweezers arrays

• Trap pseudo 2D crystals (≈100) (Curtis 2002)

• What happens when you turn the light off?– Fix structure in gel

• Permanent micro-structures

• Use SLM to create tweezers arrays

• Trap pseudo 2D crystals (≈100) (Curtis 2002)

• What happens when you turn the light off?– Fix structure in gel

Physical applications

Transfer of angular momentum

Angular momentum per photon = hbar

Angular momentum per photon = -hbar

If the particle Is birefringent it will absorb angular momentum and rotate.

Half-waveplate

Circularlypolarised light

Direction of propagation

Physical applications

Polarisation vectors rotatePolarisation vectors rotate(circular polarisation)(circular polarisation)

Spin angular momentumSpin angular momentum

Phase structure rotatesPhase structure rotates(helical phase fronts)(helical phase fronts)

Orbital angular Orbital angular momentummomentum

Padgett and Allen, Contemp. Phys. 41, 275 (2000)

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Absorption of orbital and spin angular momentum

Orbital AMOrbital AMSpinSpin

O’Neil et al. Phys. Rev. Lett. 053601 (2002)





Microfluidic applications

Micro-machines driven by optical tweezers

optical micro-pump

Terray et al. Science. 296, 1841 (2002)

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• Translational (or rotational) control

• Fluid pumps• Optically driven stirring

Vortex Arrays



Ladvac and Grier, Optics Express, 2004

Work at Glasgow

Optically driven pump using two counter rotating birefringent particles



Work at Glasgow

Flow

Flow meter

v = d/t

Turn laser on and off and measure particle displacement.

d

Work at Glasgow

Flow meter

Work at Glasgow

Flow meter results

A few of the (many) active groups

• World-wide– Grier et al. NY USA– Glückstad et al. Risø Denmark– Rubinstein-Dunlop et al. Queensland, Australia

• UK– Us! Glasgow– Dholakia et al. St Andrews– Molloy et al. National Institute for Medical Research, London

Conclusions

Trap dynamics and mechanisms

Positioning, manipulation and control

Bio, micro, physical applications

ConstantsN.A. = numerical aperturen = refractive index= anglea = radius of particle = wavelength of lightI0 = intensity nm = refractive index trapping mediumnp= refractive index particlem = np/nm (in the Fscatt, Fgrad equation)c = speed of lightm = mass (in the equation of motion)P = powerQ = trapping efficiencya = accelerationv = velocityx = positiont = timeT = temperaturekB = Boltzmann’s constantS = power spectrum = 6a= viscosity = trap strength

Exam question?


5mins

Documents

Optical Tweezers A revolution in micro-manipulation Jonathan Leach [email protected] University of Glasgow