We present a method to efficiently sort orbital angular momentum (OAM) states of light using two static optical elements. The optical elements perform a Cartesian to log-polar coordinate transformation, converting the helically phased light beam corresponding to OAM states into a beam with a transverse phase gradient. A subsequent lens then focuses each input OAM state to a different lateral position. We demonstrate the concept experimentally by using two spatial light modulators to create the desired optical elements, applying it to the separation of eleven OAM states.

We probe the rotational diffusion of a perylene dye in supercooled glycerol, 5-25 K above the glass-transition temperature (T g ‫؍‬ 190 K) at the ensemble and the single-molecule level. The singlemolecule results point to a broad distribution of local viscosities that vary by a factor of five or more for different individual fluorophores at a given temperature. By following the same single molecules at various temperatures, we find that the distribution of local viscosities itself broadens upon approaching T g. This spatial heterogeneity is found to relax extremely slowly, persisting over hours or even days. These results convey a picture of heterogeneous liquid pockets separated by solid-like walls, which exist already well above the viscosimetric glass transition.fluorescence ͉ glass transition ͉ anisotropy ͉ correlation G lycerol is an archetypal molecular glass former. Although glycerol crystals can be grown from solution, the pure liquid readily supercools because of its high viscosity [10 3 times that of water at room temperature (1)], which is caused by the formation of a highly branched network of intermolecular hydrogen bonds. The viscosity of supercooled glycerol increases by 10 orders of magnitude between 291.8 K, the melting temperature of crystalline glycerol, and its viscosimetric glass-transition temperature T g ϭ 190 K. Throughout this range of temperatures, macroscopic rheology measurements seem consistent with the expected behavior of a Newtonian liquid, although they also reveal highly nonexponential kinetics (1-3).The necessity for cooperative motion at larger and larger scales on approaching the glass transition was recognized a long time ago by Adam and Gibbs (4). In their view, glass formation arises from dynamical arrest of cooperative domains, and their spread in sizes leads to an overall nonexponential relaxation. Indeed, spatially inhomogeneous dynamics (5) have been observed with a variety of techniques in many glass formers, including simple liquids (6-10) and polymers (11-15). Inhomogeneities have been found in the particular case of supercooled glycerol by dielectric hole burning (16), NMR (17), x-ray (18), light scattering (19), and stimulated Brillouin gain spectroscopy experiments (20, 21). These observations have to be reconciled with the common view of a supercooled liquid, which is supposed to remain a normal ergodic liquid until the glass transition. Heterogeneous regions with different relaxation dynamics are therefore expected to exchange with one another to restore ergodicity, by processes called environmental exchanges (6,9,10,12,(14)(15)(16). The typical mechanisms, length scales, and time scales of environmental exchanges remain largely unclear. NMR and dielectric relaxation point to times comparable to the molecular rotation times (16,22), whereas light scattering and fluorescence show inhomogeneities with exceedingly slow relaxation (9,12,(19)(20)(21).Single-molecule fluorescence is a well established method for studying rotational diffusion (23-26). Linear dichroism...

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