Optical Tweezers

1. Optical Tweezers A revolution in micro-manipulation Jonathan Leach j.leach@physics.gla.ac.uk 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. Fscatt Fgrad 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

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

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

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 ≈ 0.05-0.3)

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

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

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

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

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

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

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

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 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. Object plane Image plane Collimated light is brought to a focus a distance f, from a lens of focal length f. An angular shift in the object plane results in a lateral shift in the image plane. Some background optics

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

34. Spatial Light Modulators SLM Calculated pattern Incoming beam 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 focus the beam split the beam combinations of the above transform the beam

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. trapped bead biological object imaging lens quadrant detector 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! 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. 5 microns Work at Glasgow • 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. Half- waveplate Circularly polarised light Direction of propagation If the particle Is birefringent it will absorb angular momentum and rotate. Transfer of angular momentum Angular momentum per photon = -hbar Angular momentum per photon = hbar

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