Chapter 9: Optical Tweezers Flashcards
What are optical tweezers?
Instruments that use the momentum transfer of photons to trap small particles. The trapped particles can then be manipulated using several different techniques and the forces acting on them can be measured.
How small are the forces that optical tweezers can measure?
1-100 pN
Optical tweezers are capable of manipulating single molecules with ________ precision.
Nanometer
What are the applications of optical tweezers?
- Examining properties of DNA
- Observing activity and effects of binding proteins acting on DNA
- Viewing molecular motors
(Determining energy required for these processes and interactions)
Describe the basic premise of optical traps
Optical tweezers are used to trap dielectric microspheres (beads) made of polystyrene by using strongly focused laser light of a specific wavelength which transfers momentum to the microspheres. This produces a force, known as radiation pressure, which pushes the microsphere in the direction of the incident beam.
Give the equation for the magnitude of momentum for a single photon
|p| = magnitude of momentum
h = Planck’s constant
λ = wavelength
The force that arises from momentum transfer of a single laser ray is proportional to the _____ of the ray divided by the ________ of the medium.
Power
Velocity (speed of light/refractive index)
How is the total momentum transferred to a microsphere estimated?
By modelling the bead as a plane mirror on which the light is incident. A calculation can then be done for the momentum transferred by an incident photon.
k = 2π/λ
ħ = h/2π
ω = angular frequency
E = photon energy
Give the equation from the force exerted by a laser beam on a microsphere at a rate of N photons per second
(Following Newton II)
F = force
P_beam = beam power
v = velocity
What is the typical power of optical tweezers?
A few milliwatts
What are the two types of optical trapping and what are their differences?
- Rayleigh regime where the sphere has a diameter much smaller than the wavelength of the laser.
- Geometrical optics regime where the laser has a wavelength much shorter than the sphere diameter.
How can biological molecules be manipulated by optical tweezers?
They are attached by linkers to the polystyrene beads.
Briefly outline the Rayleigh regime
As the microsphere diameter is a lot smaller than the wavelength of the laser, it is assumed that it is exposed to a relatively constant oscillating electric field from the light. Hence, the dielectric material becomes polarised so it acts as a single point electric dipole. This interaction produces a gradient force which is parallel to the gradient of the intensity so the bead will always be pushed to the position of highest intensity, however, the gradient force is counteracted by a scattering force.
For the Rayleigh regime, give the equation that relates the oscillating electric field to the electric point dipole
Give the equation for the force acting on the electric point dipole (from the dielectric material following the Rayleigh regime)
F_g = gradient force
U = potential energy
p(r, t) = electric point dipole
E(r, t) = oscillating electric field
Derive the equation for the average gradient force in the Rayleigh regime
Give the equation for the average gradient force in the Rayleigh regime
F_g = gradient force
n = refractive index
ε_0 = permittivity of a vacuum
α = polarisability
I(r) = beam intensity
What is the scattering force in the Rayleigh regime?
A force that arises due to the bead oscillating synchronously after the harmonically oscillating electric field that radiates in all directions. This changes the magnitude and direction of the energy flux, changing the momentum of the photons.
Give the equation for the scattering force in the Rayleigh regime
What is the Poynting vector?
The vector cross product between the electric field, E(r, t), and the magnetic field, H(r, t), in the electromagnetic wave. It is given by S(r, t) and represents the instantaneous energy flux crossing a unit area per unit time in the beam propagation direction.
The averaged Poynting vector over time gives the ______ of the beam.
Intensity
What is the equation that relates the Poynting vector and intensity?
Give the equation for scattering force in terms of the intensity
For efficient trapping, the gradient force must be ______ than the scattering force which can be done by having a very tight focus of the laser beam because this ________ the intensity gradient.
Bigger
Steepens
Briefly outline the geometric optics regime
The diameter of the polystyrene microsphere is much greater than the wavelength of the laser beam so the refraction of individual beams is considered. If the microsphere is displaced from the focal point of the laser, refraction occurs so the laser wave vector and momentum also change due to conservation of momentum. This provides a restoring force that keeps the bead in the focal point.
The restoring force for the geometrical optics regime is proportional to the ______ ______ ___ ______ ____ ___ ___ _____ _____. Hence, it can be described similarly to the ______ _____ equation.
Distance between the sphere centre and the focal point
Spring force
Give the equation for the restoring force in the geometrical optics regime
F = restoring force
k = trap stiffness constant
x = displacement
What is the accuracy of the geometrical optic regime for a micron-sized sphere?
10nm
The lower the trap stiffness, the _____ the resolution of the force.
Lower
How can optical tweezers be calibrated?
The viscous drag force, F = 6πηrv, must first be calibrated. The velocity is found by surrounding the bead in an oscillating fluid of fixed amplitude and frequency then measuring velocity as v = ωx_0 cos(ωt). This can be done for several different signals and a graph of force against signal can be plotted to find the calibration factor (gradient).
Derive the calibration factor of optical tweezers
