1. A revolution in micro-manipulation
Optical Tweezers
A revolution in
micro-manipulation
Jonathan Leach
University of
Glasgow

2. Today’s talk What are optical tweezers?
Dynamic movement and multiple particles
Current research around the World

3. 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)

4. 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

5. Optical tweezers in action

6. 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

7. 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. 

8. 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

9. 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

10. 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.

11. 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 ≈ )

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

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

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

15. Trapped particle in fluid
Solution is of damped
simple harmonic motion

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

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

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

19. Real data

20. Coming next

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

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

23. 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.

24. 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

25. 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.

26. 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

27. 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.

28. 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

29. Moving particles and multiple particles

30. 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.

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

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

33. 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.

34. 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

35. Holograms at work split the beam focus the beam transform the beam
combinations of the above

36. 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

37. 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)

38. 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)

39. Rotating cube

40. Coming next ?

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

42. Applications of optical tweezers

43. 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)

44. 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)

45. 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

46. 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)

47. 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

48. Physical applications

49. 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

50. 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)

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

52. Microfluidic applications

53. 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)

54. Vortex Arrays
Ladvac and Grier, Optics Express, 2004

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

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

57. Work at Glasgow
Flow meter

58. Work at Glasgow
Flow meter results

59. 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

60. Conclusions Trap dynamics and mechanisms Bio, micro, physical
applications
Positioning,
manipulation and
control

61. 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

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