THORLABS EDU-OT2, Руководство пользователя

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Portable Optical Tweezers Kit Chapter 4: Principles of Optical Tweezers
Page 12 MTN012639-D02
Next, the forces need to be summed. For that, we start by observing Figure 6. A partial
beam with distance
𝑟
to the symmetry axis of the whole beam falls on the sphere under
an angle 𝜃 . As discussed above, we can split the resulting force in two perpendicular
components,
𝐹
𝑠
and
𝐹
𝑔
. For clarity, we can now add another partial beam, namely the one
mirrored on the symmetry axis
, denoted “mirror beam”. As sketched in Figure 6, this partial
beam
falls on the sphere on the other side and results in “mirrored” force vectors
𝐹
𝑠,𝑚𝑖𝑟𝑟𝑜𝑟
and
𝐹
𝑔,𝑚𝑖𝑟𝑟𝑜𝑟
in the right part of the sphere (which were not drawn to avoid an overcrowded
figure).
The Contribution of One Ray to the Total Force
5,6
When you consider all of the partial beams with the same condition around the symmetry
axis, it immediately becomes clear that all force components in X and Y direction vanish
and only resulting force components along the Z axis remain.
These can be written as
𝐹
𝑔,𝑧
= −𝐹
𝑔
∙ sin 𝜙 = −𝐹
𝑔
∙
𝑟
√𝑟
2
+ 𝑙
2
(22)
𝐹
𝑠,𝑧
= 𝐹
𝑠
∙ cos 𝜙 = 𝐹
𝑠
∙
𝑙
√𝑟
2
+ 𝑙
2
(23)
where
𝐹
𝑔,𝑧
is pointing in the negative Z direction and is, therefore, negative. Hence, each
infinitesimal force contributing to the total force is given by
𝑑𝐹 = 𝐹
𝑠
∙ cos 𝜙 − 𝐹
𝑔
∙ sin 𝜙
(24)
6
Adapted from A. Langendörfer:”Aufbau einer Optischen Pinzette für das Landesmuseum für
Technik und Arbeit in Mannheim“, wissenshaftliche Arbeit, KIT, Karlsruhe, 2009