  Optical micro-manipulation and trapping of micro-particles delivers a
mechanical system in direct interaction with a beam of light. In this
interaction, the optical properties such as polarisation, beam profile and
wavelength of the trapping beam are important. Different beams are associated
with different momentum transfer, trap stiffness and stabilisation properties,
for example. One method to determine the best beam profile is through the use
of the optical eigenmode approach. To use this method, we employ Mie scattering
theory which enables the exact determination of the scattered field as a
function of the incident field. More precisely, this approach allows us to
calculate the Hermitian relationship between the incident field and the optical
forces acting on the scattering objects. This Hermitian relationship defines
also a set of orthogonal optical eigenmodes which deliver a natural basis to
describe momentum transfer in light-matter interactions. This relationship
defines also a set of orthogonal optical eigenmodes. Using these modes it is
possible to define, for each numerical aperture, particle size or geometry, the
optimal trapping beam.
