We predict that nanoparticles of octupolar symmetry (nano-triangles
and nano-tetrahedra), whose orientation cannot be affected by means
of linear optics, subjected to a coherent mixture of fundamental and
second harmonic fields will rotate and orient controlled by the relative
phase between these fields. This is due to the generation of the
second-harmonic polarization and its interaction with the
second-harmonic field. We have described this effect quantitatively
for triangular and
tetrahedral clusters of metal nanospheres where it can be observed
experimentally and used in applications.
As an efficient nanolens, we propose a self-similar linear chain of several metal nanospheres with progressively decreasing sizes and separations. To describe such systems, we develop the multipole spectral expansion method. Optically excited, such a nanolens develops the nanofocus (``hottest spot'') in the gap between the smallest nanospheres, where the local fields are enhanced by orders of magnitude due to multiplicative, cascade effect of its geometry and high $Q$-factor of surface plasmon resonance. The spectral maximum of the enhancement is in the near-ultraviolet, shifting toward the red as the separation between the spheres decreases. We also introduce surface plasmon amplification by stimulated emission of radiation (spaser) in nanolenses. Predominantly amplified are the dark, odd-parity eigenmodes, which do not suffer dipole-radiative losses and produce coherent, local optical fields comparable in strength to atomic fields, with minimal far-field radiation.
The proposed systems can be used for nanooptical detection, Raman characterization, nonlinear spectroscopy, nano-manipulation of single molecules or nanoparticles, and other applications.