# A revolution in micro-manipulation

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A revolution in micro-manipulation
Optical Tweezers A revolution in micro-manipulation Jonathan Leach 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, manipulate and 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 laser produces a force great enough to trap micron sized dielectric particles. Require…… 1. Laser 2. Lens 3. Object 4. Damping medium Fscatt Fgrad

Optical tweezers in action

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 need
high 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 oil immersion lenses, n ~ 1.3 so N.A >1 is possible.

Optical Trapping - a>>
Conditions for Mie scattering when the particle radius a is larger than the wavelength of the light . We can use a ray optics argument and look at the transfer of momentum a

Optical Trapping - a<<
Condition for Rayleigh scattering when the particle radius a is smaller than the wavelength of the light . Scattering force and gradient force are separable a Fgrad > Fscatt requires tight focusing

The scales Can trap 0.1 to 10’s m 1m is…..
…the same as 1/100th diameter of a hair. In water, you can move a particle at about 20-30m per sec. Require 10mW per trap. Can rotate at 100’s of Hz.

The Q factor of optical tweezers
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 efficiency Q, of optical tweezers is defined as Q = Factual/ (nP/c) (typically Q ≈ )

Optical Trap Dynamics Equation of motion of
particle in a potential well Newtonian force restoring force drag force Brownian motion

Particle in fluid Damping provided by water 
Solution is of exponential decay

Particle in ideal trap Spring constant  Solution is of simple
harmonic motion

Trapped particle in fluid
Solution is of damped simple harmonic motion

The whole picture Add in the effect of Brownian motion
Time averaged effect is 0 Stochastic events introduce fluctuations in the particle’s position

Trap dynamics Look at the movement of the particle in x and y

Power spectrum Fourier transform to get the power spectrum Lorenzian
Trap strength

Real data

Coming next

Exam question? In groups of 3 or 4, create two exam questions,
one long, (6 marks), one short (3 marks). 5mins

Collecting data 3 options Moving 100s nm at a few kHz!!!
How can we collect this data? 3 options

Option 1 - Camera Camera placed in the image plane of
the objective lens. Uses the light from the 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 from the 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
Collimated light is brought to a focus a distance f, from a lens of focal length f. Object plane Image An angular shift in the object plane results in a lateral shift in the image plane.

Some background optics
If the beam is not collimated there is a shift in the axial position of the focus.

Moving objects around Beam steering mirror Relay lenses f f f f f’ f’ Angular deflection at mirror gives lateral shift of trap

Diffractive optics Placing a diffractive optical element in the
Diffraction grating Placing a diffractive optical element in the object plane can generate a number of focused spots.

Spatial Light Modulators
Incoming beam SLM Calculated pattern reflected/diffracted beam optical addressing Video signal 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 also: plane waves conserved SLM
SLM imaged on beam-steering mirror microscope objective beam-steering mirror mirror imaged on microscope entrance pupil

Holographic optical tweezers can do (just about) anything!
Holographic beam generation can create multiple beams modified beams focussed beams or all these at the same time REAL TIME control of the beams Hologram Incident beam Diffracted beams Curtis et al. Opt. Commun. 207, 169 (2002)

Dynamic multiple traps
Use spatial light modulator to create multiple traps Lateral displacement Axial displacement Update trap positions Video frame rate Eriksen et al. Opt. Exp. 10, 597 (2002)

Rotating cube

Coming next ?

Exam question? In groups of 3 or 4, create two exam questions,
one long, (6 marks), one short (3 marks). 5mins

Applications of optical tweezers

Bio-applications The size of particles that can be
trapped is ~0.1m to 10’s m Approximately the same size as many 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
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! biological object trapped bead quadrant detector imaging lens Molloy et al. Biophys J. 68, S298 (1995)

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
Attach handles to ends of DNA molecule Pull, let go and observe what happens! understanding of protein folding Perkins et al. Science. 264, 822 (1994) Wang et al. Science. 282, 902 (1998)

Work at Glasgow 5 microns 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 Jordan et al., J. Mod. Opt.,2004

Physical applications

Transfer of angular momentum
Angular momentum per photon = -hbar Half- waveplate Circularly polarised light Direction of propagation If the particle Is birefringent it will absorb angular momentum and rotate. Angular momentum per photon = hbar

Physical applications
Polarisation vectors rotate (circular polarisation) Phase structure rotates (helical phase fronts) Spin angular momentum Orbital angular momentum Padgett and Allen, Contemp. Phys. 41, 275 (2000)

Absorption of orbital and spin angular momentum
Orbital AM O’Neil et al. Phys. Rev. Lett (2002)

Microfluidic applications

Micro-machines driven by optical tweezers
Translational (or rotational) control Fluid pumps Optically driven stirring optical micro-pump Terray et al. Science. 296, 1841 (2002)

Vortex Arrays Ladvac and Grier, Optics Express, 2004

Work at Glasgow Optically driven pump using two counter
rotating birefringent particles

Work at Glasgow Flow meter d Flow v = d/t
Turn laser on and off and measure particle displacement.

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 Bio, micro, physical
applications Positioning, manipulation and control

Constants N.A. = numerical aperture n = refractive index = angle
a = radius of particle  = wavelength of light I0 = intensity nm = refractive index trapping medium np= refractive index particle m = np/nm (in the Fscatt, Fgrad equation) c = speed of light m = mass (in the equation of motion) P = power Q = trapping efficiency a = acceleration v = velocity x = position t = time T = temperature kB = Boltzmann’s constant S = power spectrum = 6a = viscosity  = trap strength

Exam question? In groups of 3 or 4, create two exam questions,
one long, (6 marks), one short (3 marks). 5mins