THORLABS EDU-OT3, User Manual

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Portable Optical Tweezers Kit Chapter 3: Principles of Optical Tweezers
Rev B, February 15, 2022
Page 9
direction, which is upwards in Figure 2. The factor
𝑄𝑄
𝑡𝑡
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
𝑦𝑦 −
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:
𝐹𝐹
𝑆𝑆
> 𝐹𝐹
𝑡𝑡
(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
𝑟𝑟
between the partial beam and the symmetry
axis of the whole beam, ranging from 0 to
𝑟𝑟
𝑚𝑚𝑚𝑚𝑚𝑚
, and (ii) over its angular coordinate
𝛽𝛽
,
ranging from 0 to 2
𝜋𝜋
.
Figure 4 shows how the coordinates
𝑟𝑟
and
𝛽𝛽
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