THORLABS EDU-OT2 User Manual page 16

Portable Optical Tweezers Kit
The total force ��
������
��
, where
��,������
and
In Figure 7, we plotted the gradient force, the scattering force and the resulting total force
as a function of the focus position �� relative to the radius �� of the sphere. The direction is
the Z axis, meaning that the plot shows the behavior when the focus is moved through the
center of the sphere from bottom to top. The curves were calculated with the above
equations with a set of typical parameters since we only want to discuss the curve's
general form. Therefore, the forces are given in arbitrary units (a.u.). On the horizontal
axis, "+1" corresponds to the focus position on the sphere's outer surface right above the
sphere's center while "-1" corresponds to the lower surface below the center.
Location of the focus in units of the sphere radius �� (Z direction)
From Figure 7, we learn that
The gradient force always points towards the focus. For example, when ��/�� ≥ 0,
1.
the focus is above the sphere's center. Then ��
the sphere upwards into the focus.
2. The scattering force always points in the direction of propagation of the incident
beam, in this case downwards. Note that ��
Rev B, July 8, 2019
is the sum of the total scattering force ��
��
������
�� = ∫ ∫ ��
��,������
0
��
������
�� = ∫ ∫ −��
��,������
0
Overview of All Forces When Focus is Changed in Z-Direction
Chapter 4: Principles of Optical Tweezers
2��
∙ cos ������������
��
0
2��
∙ sin ������������
��
0
Gradient force, ��
Scattering force, ��
Total force, ��
��
≥ 0 in the entire range of the plot.
��
and the total gradient force
��,������
��,������
��,������
������
≤ 0 and the gradient force pushes
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