Geometrical Optics Approach In The Mie Regime R - THORLABS EDU-OT2 User Manual

Portable Optical Tweezers Kit
Here, �� is the speed of light in vacuum and �� is the incident intensity and �� is the scattering
cross-section of the incident light. It is important to note that the scattering force is
proportional to the intensity and points in the beam direction.
Geometrical Optics Approach in the Mie Regime R >> 
4.2.
This ray optical approach deals with the second possible extreme case. Here, we will
assume that the radius of the bead is much larger than the wavelength of the incident
laser. In this range, the conditions of geometric (ray) optics are fulfilled and one can think
of the laser beam as a bundle of rays. Typically, this assumption is valid for beads with a
radius �� that is greater than ∼ 10��. The basics of the theoretical derivation of the gradient
and scattering force in accordance with this model can be found in a work by Ashkin
The particle properties of light must now be taken into account, namely that light can
transfer momentum to an object in the form of photons. The force action of a beam on a
particle can be explained using Newton's second law: the force on a particle is exactly
equal to the change in the momentum of the particle over time:
The following equation describes the change in momentum
medium with a refractive index ��
Here, ��(��) is the intensity distribution in the beam cross-section. Often, a Gaussian profile
is used, in which the intensity decreases in a Gaussian distribution from the center of the
beam outward. This is also the case in our setup.
If a beam with the power ��
reflected and part of it will reach the interior of the sphere through transmission (see Figure
2). For the power of these two partial beams, the following is in effect:
Here, �� is the reflectivity and �� is the transmissivity. The transmitted beam transports
��
momentum into the sphere in accordance with the equation (10).
4
Ashkin A., Forces of a single-beam gradient laser trap on a dielectric sphere in the ray
optics regime. In: Biophys. J. 61 (1992) 2, 569-582
Rev B, July 8, 2019
����
�� =
����
:
��
���� ��
��
= �� =
��������
���� ��
hits a sphere at an angle of ��, part of the beam will be
��������
�� = ��
�������� ��������
�� = ��
���������� ��������
Chapter 4: Principles of Optical Tweezers
����
of a beam over time in a
����
��
��
( )
�� �� ����
��
⋅ ��
��
⋅ ��
4
.
(9)
(10)
(11)
(12)
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