… The restoring force (F x ) acting on the particle points towards the trap centre with a magnitude
that is proportional (through constant k x , the trap stiffness) to the particle's displacement (…

… Bold letters refer to vector quantities while their non bold version with the subscripts i, j
and k stand for their three Cartesian coordinates each subscript varying from 1 to 3. …

… and a linearly polarized incident plane wave propagating along x axis with wave vector k=k,0,0
and having electric field components EIB =EIA=0,0,E0 expikx . Their substitution into Eq. …

We use a Laguerre–Gaussian laser mode within an optical tweezers arrangement to demonstrate
the transfer of the orbital angular momentum of a laser mode to a trapped particle. The …

… As the waves propagate a distance Δz, they undergo a phase shift k z Δz, where k z is the
wavevector … For this to happen, the phase shift k z Δz must be the same for all the plane wave …

The response of a microscopic dielectric object to an applied light field can profoundly affect
its kinetic motion 1 . A classic example of this is an optical trap, which can hold a particle in a …

… (where R is the radius of the imaging lens) which, from (3), can be estimated as (k/kr)R,
when we consider the beam close to the optic axis. Durnin et al. [3] also found that the on-axis …

… where x is the transverse coordinate, z the propagation distance, x 0 a characteristic
transverse length scale, and k = 2π n/λ is the wavevector with n the index of refraction and λ the …

… exp ( i k z z)J l (k r r) exp ( i lφ) , where J l is the lth-order Bessel function, and k z and k r are
… of the free-space wavevector, such that k=2πn/λ= k z 2 +k r 2 . The zeroth-order beam has a …

We demonstrate controlled rotation of optically trapped objects in a spiral interference pattern.
This pattern is generated by interfering an annular shaped laser beam with a reference …