Optical trapping of carbon nanotubes and graphene

We study optical trapping of nanotubes and graphene. We extract the distribution of both centre-of-mass and angular fuctuations from three-dimensional tracking of these optically trapped carbon nanostructures. The optical force and torque constants are measured from auto and cross-correlation of the tracking signals. We demonstrate that nanotubes enable nanometer spatial, and femto-Newton force resolution in photonic force microscopy by accurately measuring the radiation pressure in a double frequency optical tweezers. Finally, we integrate optical trapping with Raman and photoluminescence spectroscopy demonstrating the use of a Raman and photoluminescence tweezers by investigating the spectroscopy of nanotubes and graphene fakes in solution. Experimental results are compared with calculations based on electromagnetic scattering theory. © 2011 by the Author(s); licensee Accademia Peloritana dei Pericolanti, Messina, Italy.

A Newton algorithm for invariant subspace computation with large basins of attraction

We study the global behaviour of a Newton algorithm on the Grassmann manifold for invariant subspace computation. It is shown that the basins of attraction of the invariant subspaces may collapse in case of small eigenvalue gaps. A Levenberg-Marquardt-like modification of the algorithm with low numerical cost is proposed. A simple strategy for choosing the parameter is shown to dramatically enlarge the basins of attraction of the invariant subspaces while preserving the fast local convergence.