THORLABS EDU-OT2, Руководство пользователя

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Portable Optical Tweezers Kit Chapter 4: Principles of Optical Tweezers
Page 10 MTN012639-D02
Figure 3 shows the values of the two
𝑄 −
factors, depending upon the angle of incidence
𝜃
when the focus is located slightly above the surface of the sphere. One can see here
𝑄
𝑔
is negative through almost the entire range, meaning the force acts in the negative Y
direction, which is upwards in Figure 2. The factor
𝑄
𝑠
is always positive. The Z-component
of the force therefore always points in the beam direction. If the beam were not to hit in the
upper half of the sphere, but rather in the lower half, one can easily conclude for reasons
of symmetry that the direction of the
𝑦 −
component would reverse, the direction of the Z-
component would remain the same.
In short: The sphere always moves into the focus or the point of highest intensity. In order
to ultimately achieve a stable optical trap, the following must be true:
𝐹
𝑔
> 𝐹
𝑠
(18)
In the following, we’ll discuss these forces in more detail.
Total force on the sphere
To obtain the total force acting on the sphere, we have to sum over all partial beams that
hit it.
For that, we integrate (i) over the distance
𝑟
between the partial beam and the symmetry
axis of the whole beam, ranging from 0 to
𝑟
𝑚𝑎𝑥
, and (ii) over its angular coordinate 𝛽 ,
ranging from 0 to 2

.
Figure 4 shows how the coordinates
𝑟 and 𝛽
of a partial beam (in red) are defined. The
dashed line stands symbolically for the
sphere the laser is focused on.
Coordinates of a Partial Beam