Laser light with a Laguerre-Gaussian amplitude distribution is found to have a well-defined orbital angular momentum. An astigmatic optical system may be used to transform a high-order Laguerre-Gaussian mode into a high-order Hermite-Gaussian mode reversibly. An experiment is proposed to measure the mechanical torque induced by the transfer of orbital angular momentum associated with such a transformation.PACS number(s): 42.50.Vk

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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 present an efficient method for probing the orbital angular momentum of optical vortices of arbitrary sizes. This method, based on a multipoint interferometer, has its most important application in measuring the orbital angular momentum of light from astronomical sources, opening the way to interesting new astrophysics. We demonstrate its viability by measuring the orbital angular momentum of Laguerre-Gaussian laser beams.

A B S T R A C TWe present a deep multicolour CCD mosaic of the Coma cluster (Abell 1656), covering 5.2 deg 2 in the B and r bands, and 1.3 deg 2 in the U band. This large, homogeneous data set provides a valuable low-redshift comparison sample for studies of galaxies in distant clusters. In this paper we present our survey, and study the dependence of the galaxy luminosity function (LF) on passband and radial distance from the cluster centre. The U-, B-and r-band LFs of the complete sample cannot be represented by single Schechter functions. For the central area, r , 245 h 21 . The LF becomes steeper at larger radial distances from the cluster centre. The effect is most pronounced in the U band. This result is consistent with the presence of a star-forming dwarf population at a large distance from the cluster centre, which may be in the process of being accreted by the cluster. The shapes of the LFs of the NGC 4839 group support a scenario in which the group has already passed through the centre.

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