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Portable Optical Tweezers Kit Chapter 4: Principles of Optical Tweezers
Page 14 MTN012639-D02
3. When the focus is below the
sphere’s center, i.e.
𝑆/𝑅 ≤ 0
, scattering and gradient
force act in the same direction
. When the focus is above the sphere’s center,
i.e. 𝑆/𝑅 ≥ 0 , both forces point in opposite directions.
We also note that the absolute value of the gradient force is always higher than the
absolute value of the scattering force. This is the requirement for any stable optical
tweezers trap. The fundamental quantity to fulfill this requirement is the microscope
objective’s numerical aperture, which defines the angle of the focus which we will discuss
next.
Sometimes the focus is not above or
below the sphere’s center but along the y-axis
instead. Again, the reference axis goes through the sphere’s center, and we plot the
occurring forces as a function
of the focus’ distance
𝑆
to the sphere’s center in units of the
sphere’s radius.
Figure 8 shows the gradient force and the scattering force. Plotting the sum of both forces
would not make sense as they point in different directions (
𝐹
𝑠,𝑡𝑜𝑡
in Z direction and
𝐹
𝑔,𝑡𝑜𝑡
in
Y direction).
From Figure 8, we learn that:
1.
The general form of the curves is similar to the focus’ movement on the Z axis.
Only outside of the sphere the force decreases a little faster than compared to
the Z axis.
2. The maximal gradient force is larger than the maximal scattering force (absolute
values). This is the case when the parameters such as the numerical aperture
allow optical trapping.
3. The maximal gradient force are located just within the sphere, close to the
surface. The maximal value of the scattering force is found right on the surface.
Scattering and Gradient Force with the Focus Changed in Y
Direction
6
Gradient force,
𝐹
𝑔,𝑡𝑜𝑡
Scattering force, 𝐹
𝑠,𝑡𝑜𝑡
For
c
e [a.u.]
Location of the focus in units of the sphere radius
𝑅
(Y direction)