1. Single Tapered Fibre “Optical Tweezers”
Steven Ross
GERI-CEORG
Supervisors: Professor D. Burton, Dr. F. Lilley & Dr. M. Murphy

2. Contents Project Aim What is Optical Trapping?
Optical Forces & Optical Trapping Theory
Difference Between Classical & Fibre Based “Optical Tweezers”
Fibre Trapping at Low Insertion Angles; The Problem, Solution & the Resultant Change in Trap Dynamics
Experimental methods, Particle Tracking, Force Determination & Results
Conclusion

3. Project Aim To develop a 3D-single beam optical trap
To aid investigations of the mechanical properties of cells
Capable of easy integration with other microscopy applications for example AFM
Therefore some degree of portability required
Leading to the development of an optical fibre based configuration

4. What is Optical Trapping?

5. Optical Forces Forces generated up to 200 x 10-12 N
Scattering force - Due to reflection, points in the direction of the beams propagation
Gradient force - Due to refraction, points in the direction of the beams high intensity region

6. Optical Trapping Theory
Scattering force must be cancelled –
counter propagating beams
gravity
Single beam trapping
gradient force must be greater than scattering force
Achieved by strongly focusing the laser
Creating a high intensity Gaussian profile 1 2 3

7. Classical “Optical Tweezers”
First demonstrated by Arthur Ahskin in 1986
High NA microscope objective used for focusing the laser and imaging
Photo detectors for position detection
Multiple trapping sites
Particle transit in X and Y plane
Large surface are required

8. Single Tapered Fibre “Optical Tweezers”
Advantages
Reduced size and build costs
No position detection
Decoupled from the microscope
Capable of sample elevation
Disadvantages
Complexity increases for multiple trapping sites
Fibre tips manufactured to focus the light
Prone to damage

9. Fibre Trap “to be or not to be”?
Literature suggests optimum trapping forces found at fibre insertion angles between 45-55°
Oh dear major problem
AFM has a head above the sample chamber
Insertion angle no greater than 10°

10. Trapping at Low Insertion Angles
First Fibre tip (tip # 44) trapped at 45° Insertion angle
But not at 10°
Why is this? After all its just a beam of light incident upon a spherical object
Lead to investigations of the tip profile

11. Trapping at Low Insertion Angles
Taper profile was such that the particle had to be elevated
Requiring very high optical powers in excess of 600 mW
Lead to the development of new tips with different profiles
Requiring a longer taper and a smaller diameter tip

12. New Slim Models Created 3 new working tips # 92, 94 & 96
Successfully tested at 45°, 30° & 10° insertion angles
3D trapping occurring at optical powers ranging between ≈ mW
Tip # 96 trapping focal point beyond fibre end
Start Frame
End Frame

13. Change in trap Dynamics
At 10° insertion angle the introduction of a trapping range was observed
Particles within the range are trapped and repelled if beyond
The trapping range is tuneable, varying with tip profile
Ranges recorded between 6-13 µm

14. Experiment 1 Force Determination
Dynamic measurement method
Particle trapped, laser deactivated
Fibre tip moved in (–ve) x direction, Laser reactivated
High speed video records the particles position, as it is drawn into the trap
Repeated for various laser outputs, tips and insertion angles
Characterise the trap as a function of the optical power with respect to the trapping force

15. Experiment 2 Optical Force Field Mapping
Particles trapped from various points about the fibre tip
Knowing the optical trapping force for each trajectory will allow the mapping of the optical force field distribution
Providing information such as focal point, beam spot size, beam waist position and divergence angle

16. Particle Tracking
Particles trajectory is tracked using particle tracking image processing package developed in the IDL platform
Provides particle co-ordinate data in both pixel and µm formats
Allows the origin to be set at the fibre end

17. Force Determination
Fopt = Trapping force
η = Viscosity of the medium
r = Radius of the particle
S =Particles position
m = Mass of particle
Derivative of the particles position/time = acceleration
Second derivative of the particle position/time = velocity
Re = Reynolds number
ρ = Density of the medium
V = Maximum velocity
D = Particle diameter
η = Viscosity f the medium
Trapping force calculated using the stokes equation and Newton's second law
Calculated from the first and second derivatives of the particles position as a function of time
Inertia force can be ignored due to the Reynolds number (Re)<< 1

18. Results Tip number 92 Number of Frames Time Duration Seconds
Distance travelled
X Axis (µm)
Optical Power (mW)
Max Force 1
(Newton)
Max Force 2
858
1.716 6
52.35
e-12
e-12
379
0.758 7
121.94
e-13
e-12
208
0.416
196.49
e-12
163
0.326
289.62
e-12
e-12
138
0.276
5.75
378.92
e-12 69
0.138
5.5
467.6
e-12 64
0.128
6.5
539.43
e-12

19. Conclusion Project Aims Optical Trapping Forces
Basic Optical Trapping Theory
Differences Classical and Fibre Based Optical Traps
Low Insertion Angle Hurdles and Solutions
Novel Trap Dynamics Observation
Experimental Procedures
Particle Tracking & Force determination
Discussion of Initial Results

20. Thank You
Any Questions?