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 7
Reflection and Transmission of an Incident Partial Beam on the Inside and
Outside Surfaces of a Sample Bead with a Refractive Index Higher than the
Immersion Medium
Inside the sphere, the beam is reflected and transmitted numerous times. Part of the beam
is repeatedly reflected on the sphere's internal wall and remains in the sphere, while the
rest exits the sphere again through transmission. The beams which exit the sphere again
were thus subject to a change in momentum
𝑑𝑑𝑝𝑝
𝑑𝑑𝑡𝑡
. The force on the sphere is equal to the
momentum per unit time that remains in the sphere, based on equation (9). Now, the force
on the sphere is once again divided into two components: a component in the direction of
the incident beam (corresponds to the Z direction) and a perpendicular component
(corresponds to the Y axis). This results in the following for both forces:
𝐹𝐹
𝑡𝑡
≔ 𝐹𝐹
𝑧𝑧
= 𝑛𝑛
𝑚𝑚
𝑃𝑃
𝐵𝐵𝑆𝑆𝐺𝐺𝑚𝑚
𝑐𝑐
𝑄𝑄
𝑡𝑡
(13)
with the Q factor
𝑄𝑄
𝑡𝑡
= 1 + 𝑅𝑅
𝑟𝑟
cos
(
2 𝜃𝜃
)
−
𝑇𝑇
2
(
cos
(
2 𝜃𝜃 − 2 𝑡𝑡
)
+ 𝑅𝑅
𝑟𝑟
cos
(
2 𝜃𝜃
))
1 + 𝑅𝑅
𝑟𝑟
2
+ 2 𝑅𝑅
𝑟𝑟
cos
(
2 𝑡𝑡
)
(14)
and
𝐹𝐹
𝑆𝑆
≡
𝐹𝐹
𝑦𝑦
= 𝑛𝑛
𝑚𝑚
𝑃𝑃
𝐵𝐵𝑆𝑆𝐺𝐺𝑚𝑚
𝑐𝑐
𝑄𝑄
𝑆𝑆
(15)
with the Q factor