THORLABS EDU-OT2 User Manual page 9

Portable Optical Tweezers Kit
where �� is the electrical susceptibility, ��
the bead. The potential energy ��
⃗
electrical field �� is ��
��, the energy density in the bead is defined by:
The occurrence of the gradient force, which is a force component that is directed in the
direction of the intensity gradient of the incident electrical field, can be explained when one
observes this potential energy �� of the bead in the electrical field. Equation (2) states that
�� is proportional to ��
thus to intensity �� ∝ |�� ⃗ |
incident field is proportional to the gradient of the potential energy ∇�� and therefore
proportional to the intensity gradient ∇��. The following equations describe the gradient
force:
Here, �� is the polarizability of the dipoles and �� is the relationship of the refraction index
of the particles, ��
medium, ��
(water in our case).
��
The destabilizing scattering force component is explained by the scattering of the incident
light at the particle. The force action is created by the absorption and isotropic re-emission
of the light by the bead. As �� ≪ ��, the conditions are fulfilled for Rayleigh scattering. The
resulting force can be stated as follows:
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∑
�� = ��
��
��
of one of the point dipoles with dipole moment �� in the
��
⃗
= −�� �� . Because there are �� point dipoles in a bead with the volume
��
�� ⋅ ��
��
�� = = −
��
⃗
. Therefore, according to equation (3), �� is proportional to |�� ⃗ |
2
of the incident field. The force exerted on the particle by the
��
��������
�� = ��
(polystyrene in our case) to the refraction index of the surrounding
��
��
��������������������
128 ��
�� =
Chapter 4: Principles of Optical Tweezers
��
⃗
= ⋅ �� ⋅ �� = �� ⋅ ��
��
is the electrical constant, and �� is the volume of
0
��
⋅ �� ⃗ = −�� ⃗ ⋅ �� ⃗
⋅ ��
⏟
��
�� ⃗
2 �� ��
= ∇��
2
�� ��
��
2
�� − 1
2 3
�� ( )
��
2
�� + 2
��
��
�� =
��
��
�� ��
��
= ⋅ ��
��
2
5 6 2
�� �� − 1
( )
4 2
3 �� �� + 2
⃗
⋅ ��
0
MTN012639-D02
(2)
(3)
2
and
(4)
(5)
(6)
(7)
(8)