@article {2091, title = {Sparse and composite coherent lattices. (With commentary)}, journal = {Physical Review A}, volume = {71}, year = {2005}, month = {2005 Jun 20}, pages = {063406}, abstract = {

A method is described that yields a series of (D+1)-element wave-vector sets giving rise to (D=2 or 3)-dimensional coherent sparse lattices of any desired Bravais symmetry and primitive cell shape, but of increasing period relative to the excitation wavelength. By applying lattice symmetry operations to any of these sets, composite lattices of N\>D+1 waves are constructed, having increased spatial frequency content but unchanged crystal group symmetry and periodicity. Optical lattices of widely spaced excitation maxima of diffraction-limited confinement and controllable polarization can thereby be created, possibly useful for quan- tum optics, lithography, or multifocal microscopy.

Commentary: Develops a formalism to find a set of wavevectors that create a periodic optical lattice of any desired Bravais symmetry by the mutual interference of the corresponding plane waves. Discovers two new classes of optical lattices, sparse and composite, that together permit the creation of widely spaced, tightly confined excitation maxima in 3D potentially suitable for high speed volumetric live cell imaging. The implementation of this idea was derailed by our exclusive focus on PALM at the time, and many of its goals have since been reached with our Bessel beam plane illumination microscope. Nevertheless, sparse and composite optical lattices may prove useful in atomic physics or for the fabrication of 3D nanostructures.

}, author = {Betzig, E} }