Supplementary Information
Non-contact fiber-optical trapping of motile bacteria: dynamics
observation and energy estimation
Hongbao Xin, Qingyuan Liu, and Baojun Li*
State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and
Engineering, Sun Yat-Sen University, Guangzhou 510275, China
*
Email: stslbj@outlook.com
1. Design of the modified tapered fiber
To design a modified tapered fiber which can realizes the non-contact trapping of
bacterium, the focus of the light beam output from the fiber should be away from the fiber tip.
We have tried tapered optical fibers with different shapes. Because the diameter of the tapered
fiber is about several microns, much larger than the wavelength of the input light (980 nm),
the focus of the light beam can be estimated using simple ray optics. The refraction of
incident light follows refraction law, given by
n1sinθ1 = n2sinθ2,
(1)
where n1 = 1.445 and n2 = 1.39 are the refractive indices of the fiber and water, respectively,
and θ1 and θ2 are the incident angle and refracting angle, respectively.
Figure S1a shows the focus estimation of light beam output from an optical fiber with a
gradually tapered end. The incident angle of a ray with a distance of 1.15 µm to the fiber axis
is θ1 = 74º, and the refracting angle θ2 is then 88º, resulting a focus with a distance of D1 =
0.45 µm to the fiber tip. Similarly, for an optical fiber with an abruptly tapered end (the shape
and size of the abruptly tapered region is the same as that of the modified tapered fiber
designed in our simulation) as shown in Fig. S1b, the estimated focus is with a distance of D2
= 6.8 µm to the fiber tip, larger than D1. For the modified tapered fiber designed in our
simulation, both the abruptly tapered region and the protruding tip can extend the beam focus
to a larger distance. The end of the protruding tip can be regarded as a displacement (0.75 µm)
of the end of the abruptly tapered region with the same size along the fiber axis, as shown in
the dashed blue and red regions in Fig. S1c. And thus the focus of the light incident at the end
is further extended with a distance of 0.75 µm. Overall, the modified tapered fiber with an
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abruptly tapered region and a protruding tip can generate a beam focus away from the fiber tip
with a distance much larger than that generated by a gradually tapered fiber.
Figure S1 Focus estimation using ray optics, the blue box indicated the tapered end
of the fibers. (a) For an optical fiber with a gradually tapered end, the estimated focus
for two rays with a distance of 1.15 µm to the fiber axis is with a distance of D1 =
0.45 µm to the fiber tip. (b) For an optical fiber with an abruptly tapered end, D2 =
6.8 µm. (c) For the modified tapered fiber with an abruptly tapered region and a
protruding tip, the focus is further extended with a distance of ΔD2 = 0.75 µm to that
of the fiber in Fig. S1b.
2. Simulation details
In the simulation, the layout of the modified tapered fiber is the same as that designed in
Fig. 1a. The bacterium, here we used E. coli, is assumed to be a rod (length: 1.7 µm; diameter:
500 nm) with hemispherical caps. The refractive indices of the modified tapered fiber, E. coli,
and water are set to be 1.445, 1.39, and 1.33, respectively. Figure S2a shows the 3D model
used in the simulation while Fig. S2b shows the 2D cross-section view of the model in xy
2
plane.
Figure S2 Models of the simulation. m-TF: modified tapered fiber. (a) 3D model of
the simulation. (b) 2D cross-section view of the model in x-y plane.
3. Examples of simulated energy distribution and force calculation for E. coli with
different locations
In the simulation, E. coli bacterium was located with different locations, and force was
then calculated. Some typical examples of the simulated energy density distribution and
calculated optical force for the bacterium with different locations are shown in Fig. S3. Figure
S3a shows the simulated energy density distribution for the bacterium located with a distance
of 5.1 µm to the modified tapered fiber tip in x direction and 0.5 µm to the modified tapered
fiber axis in y direction, the calculated Fy is –146.2 pN/W. Thus for the bacterium beside the
axis, it will be trapped to the axis by Fy. Figs. S3b, c and d show the distributions for the
bacterium along the axis with distances of 2.35, 8.35, and 15.35 µm, respectively. The
respective Fx are 21.3, –24.0, and 6.4 pN/W. Thus the bacterium will be driven away, trapped,
and driven away, respectively.
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Figure S3 Simulated optical energy density distribution and calculated optical force
for bacterium with different locations.
4. Modified tapered fiber fabrication process
The modified tapered fiber was fabricated through a two-step method as shown in Fig. S4.
Step I: a single-mode optical fiber with a diameter of 125 µm (Fig. S4a) was fabricated into a
taper fiber with a nano-tip through a flame-heating technique; the diameter of the nano-tip is
about 400 nm (Fig. S4b). Step II: the nano-tip was pulled off and modified. And finally, a
modified tapered fiber was fabricated as shown in Fig. S4c.
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Figure S4 Three typical optical microscope images showing the modified tapered
fiber fabrication process. (a) A single-mode optical fiber was used. (b) A tapered fiber
(TF) with a nano-tip was fabricated. (c) A modified tapered fiber was fabricated.
5. 2D moving of a trapped E. coli bacterium
The trapped E. coli bacterium can be flexibly manipulated in 3D by manipulating the
modified tapered fiber, which is fixed by the six-axis manipulator (SAM). Thus the trapped
bacterium can then be delivered to a designated location for further study. Figure S5, as an
example, shows the 2D back-and-forth moving of a trapped E. coli bacterium with an optical
power of 50 mW launched into the modified tapered fiber. Figure S5a shows the
back-and-forth moving in y direction. At t1 = 0 s, a bacterium was trapped with a gap of 1.3
µm to the modified tapered fiber tip (Fig. S5aI). At t1 = 1 s, by moving the modified tapered
fiber in +y direction, the bacterium was moved with a distance of 7.5 µm in +y direction (Fig.
S5aII), with an average moving velocity of about 7.5 µm/s. At t1 = 4 s, by moving back the
modified tapered fiber in –y direction, the trapped bacterium was also moved with a distance
of 14.2 µm in –y direction (Fig. S5aIII), with an average moving velocity of about 4.7 µm/s.
Figure S5b shows the back-and-forth moving of the trapped bacterium in x direction. At t2 = 0
s, the bacterium was trapped with a gap of 1.3 µm to the modified tapered fiber tip (Fig. S5bI).
At t2 = 5 s, by moving the modified tapered fiber in –x direction, the bacterium was also
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moved with a distance of 7.4 µm in –x direction (Fig. S5bII), with an average moving velocity
of about 1.5 µm/s. At t2 = 12 s, by moving the modified tapered fiber in +x direction, the
trapped bacterium was also moved with a distance of 23.8 µm in +x direction (Fig. S5bIII),
with an average moving velocity of about 3.4 µm/s.
Figure S5 Optical microscope images of 2D moving of a trapped E. coli bacterium.
(a) Back-and-forth moving of the bacterium (yellow arrow indicated) in y direction,
the red and blue arrows indicate the input laser and the moving direction of the
trapped bacterium, the white dashed lines in II and III indicated the locations of the
bacterium in I and II, respectively. (b) Back-and-forth moving of the bacterium
(yellow arrow indicated) in x direction, the red and blue arrows indicate the input
laser and the moving direction of the trapped bacterium, the white dashed lines in II
and III indicated the locations of the bacterium in I and II, respectively.
6. Legends for Supplementary Movies
Movie S1. Details of the non-contact trapping and struggling process of a single E.
coli bacterium with an optical power of 48 mW launched into the modified tapered
fiber.
Movie S2. Details of the dynamics of a single E. coli bacterium with an optical power
of 11.5 mW launched into the modified tapered fiber. After the energy released, the
bacterium escaped from the trapping.
Movie S3. Details of the dynamics of a single E. coli bacterium with an optical power
of 17.5 mW launched into the modified tapered fiber. After the energy released, the
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bacterium escaped from the trapping with 1 struggling round.
Movie S4. Details of the dynamics of a single E. coli bacterium with an optical power
of 38.5 mW launched into the modified tapered fiber. After the energy released, the
bacterium escaped from the trapping with 8 struggling rounds.
Movie S5. Details of the dynamics of a single E. coli bacterium with an optical power
of 53.5 mW launched into the modified tapered fiber. After the energy released, the
bacterium was continuously struggling in the trapping well. At t = 90 s, the laser was
turned off and the bacterium swam away with an average velocity of 18.3 µm/s.
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