D
2) relative to the central symmetric axis between the two fibers (at
Df
2 ) was
calculated. The error in the position of the object can be better than 0.5µm
dependent on the number of frames. As the error of the position is directly correlated to the number of frames that are analysed as well as how often the objects are moved for short static measurements the error can be estimated to be 0.5µm while for long dynamic measurements it can increase to 2µm
in extreme cases. This error is related to the pattern matching convolution algorithm. As all consecutive frames are correlated to the initial image, here for example drift in the imaging setup can induce an image blur and increase the error over time. Although the algorithm is 2D rotation invariant it does not account for variation in 3D which can occur when cells are trapped. At this point I am well equipped to do first initial measurements with the fibre trap.
2.3
Fibre trap design considerations
Designing a fibre trap one may initially believe that a multi mode fibre is preferable to a single mode, as light coupling is more efficient and alignment easier. Therefore I compared a multi mode with a single mode fibre trap in their ability to trap CHO cells as well as spheres.
For the multi mode fibre (cladding diameter = 125µm, core diameter = 50µm, NA = 0.2) a 20× microscope objective (NA = 0.4, focal length = 9mm, working distance = 1.7mm and entrance aperture = 6mm) was used. The following mode profile, shown in figure 2.4 (left) was obtained with this fibre and shows a speckle pattern. The different path length of the modes within the multi mode fibre causes this speckled pattern due to the interfer- ence of the modes at the fibre output. A super-Gaussian is fitted to aid the eye for comparison, the measured spot size4 was 45-50µm.
With the single mode fibre (mode field diameter at 1060nm = 6.2±0.5µm
and NA = 0.14) a 10× microscope objective (NA = 0.25, focal length = 16.5mm, working distance = 5.5mm and aperture = 7.5mm) was used to couple into each fibre. A Gaussian mode was obtained with this fibre (shown in figure 2.4 (right)), the spot size was 6.6µm. From the Gaussian fit5 the
beam waist w0 was calculated to
√
2∗2.43 = 3.43µm at a wavelength of 1070nm for both measurements. These parameters are reasonably close to
4Diameter of the spot image on the fibre surface. 5I=A∗exp(−(r/w
i)2) withwi =w0/
√ 2)
Figure 2.4: Left: Multi mode fibre profile with a 6thorder super-Gaussian fit. Right: Single mode
fibre profile with a Gaussian fit. Inset shows the corresponding intensity near field pattern, not to scale.
3.1±0.25µm (including the error) given by the manufacturer6 and will be
used in the theoretical simulations presented in the following chapters. In both traps arrays of up to three Chinese Hamster Ovary (CHO) cells were observed. If a two CHO cell array is moved7 the volume occupied in a multi
mode trap is far bigger than in a single mode trap due to the bigger emis- sion cone of the multi mode fibre. The super-Gaussian fit of the multi mode line profile in figure 2.4 contains 6 regular Gaussian curves, due to the mode structure it is not a full cone where the trapped cells occupy preferably the maxima. Figure 2.5 shows the position trajectory points red and blue for each CHO cell between the two fibers while being displaced several times over more than 2000 measurements.
Comparing both graphs shows that the y position spreads over less than 1µm
for the single mode and 7µm for the multi mode fibre. Trapping within a single mode fibre in the transverse propagation plane is therefore well defined due to the sharper intensity peak as compared to a multi mode fibre with a wide emission cone. Specifically the multi mode fibre trap has an approxi- mately 7 times bigger trapping volume than a single mode fibre trap, which can be useful for guiding or cell handling applications in biophotonics [10]. Spheres can also be trapped in a multi mode fibre trap, polymer spheres up to 100µmcan be bound in a chain [10], as they do not exhibit array forma- tion. If smaller silica spheres of about 5.17µm are placed in the trap then
6Given as mode field diameter (MFD) where intensity has decreased to 1/e2 which is
equal to spotsize and 2×w0 [35].
2.3. FIBRE TRAP DESIGN CONSIDERATIONS
Figure 2.5: Comparison of the z and y positions of a two CHO cell arrays in a multi mode fibre trap with 32µmseparationD(left) and single mode fibre trap with 54µmcell separationD(right). Red and blue crosses show the position for each of the cells while being displaced over several frames. 15µmis the approx. diameter of the individual cells with a constant fibre separation of 120µmand 100mW trapping power for both traps. Although the cell diameter is constant the cells in the single mode trap exhibit a larger separation leading to non overlapping tracking trajectories.
multiple trapping positions can be observed, this is shown in figure 2.6.
Figure 2.6: 5.17µmspheres in a multi mode fibre trap. 1) One sphere is captured in a single intensity peak and guided to the left. 2) Four spheres are trapped at positions where intensity maxima overlap. Two collapsed arrays are formed, with the arrays being at different positions in xyz.
These arrangements are not well defined and happen randomly. Spheres are guided past each other as they are guided within one intensity maximum and trapping only occurs if two maxima overlap.
Attempts were made to get a coherently illuminated beam profile for the multi mode fibre by wrapping the fibre around a post of 6mm in diameter. The beam profile improved only marginally and a speckled pattern was still observed.
Here I conclude that multi mode fibre can be used to trap sizes larger than 10µmand open up the possibility to form 3 dimensional sphere chains within overlapping mode maxima. Also they give the possibility to utilise multi mode fibre coupled high power diodes as a cheaper alternative to a laser to fibre coupling setup. At this point further experiments were only conducted with the single mode fibre trap to obtain stable trapping along the beam propagation axis with strong confinement in the xy-plane, thereby limiting array formation to one dimension.