Optical tweezers for undergraduates: Theoretical analysis and experiments
Spherical aberration in optical tweezers. (a) Idealized situation without spherical aberration. (b) Real situation in most experimental setups. The focus is degraded due to the laser refraction at the glass-water interface of the sample, decreasing the trapping efficiency.
Two rays (wave vectors and ) from the beam are represented, refracting at a bead localized below the focus. The rays exert forces and when refracted on the bead surface. The resulting gradient force points to the laser focus.
Two rays (wave vectors and ) from the beam are represented, refracting at a bead localized above the focus. The rays exert forces and when refracted on the bead surface. The resulting gradient force also points to the laser focus in this case.
An incident ray undergoing multiple internal reflections and refractions on a bead.
Coordinate reference frame employed in the calculations.
Change in variables in the aberration-free case.
Change in variables in the general situation, including spherical aberration.
Schematic of the method used to calculate .
Plot of the force versus the displacement along the direction for an oil bead with , considering spherical aberration. The graph is linear, which means that the trap stiffness is constant.
Transverse trap stiffness divided by the local power as a function of bead radius: experimental data (circles), geometrical optics model considering spherical aberration (squares), and geometrical optics aberration-free model (triangles).
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