Why are they afraid to publish an experiment which can show the distribution of angular momentum in a cross-section of a light beam?
The distribution of angular momentum in a cross-section of a circularly polarized light beam is unknown now.
Allen L. et al. wrote: "The local value of the ratio of angular momentum to energy changes from place to place in a light beam" , “A different amount of angular momentum might be expected to be transferred at different position in the wavefront” , “At a particular local point the z-component of angular momentum flux divided by energy flux does not yield a simple value” .
Simmonds and Guttmann wrote: “The skin region [of the beam] is the only in which the z-component of angular momentum does not vanish.” 
An experiment was suggested, which can show the distribution of angular momentum in a cross-section of a light beam . But the following journals rejected the corresponding paper (see ) without reviewing: all Physical Review, all IOP journals (EPL, NJP, JOPA), Elsevier (OC, PLA), OSA (OL, AO), Taylor (JMO, IJO), FOOP, CLEO/IQEC-conference.
Only Acta Physica Polonica (Prof. Witold Dobrowolski) wrote (after 5-month thinking): “The proposed experiment is useless; its result is easily predicted. Everything is based on misunderstanding. The author assumes that the absorption of photons occurs locally (where the energy density is the biggest). In fact, the process of absorption is nonlocal (best illustration: absorption of extended radiation by a small atom). Both energy and total angular momentum are local, although the splitting of the angular momentum into its orbital and spinorial parts is nonlocal”.
As you see, Prof. Witold Dobrowolski is a braggart. In reality, Professor can predict nothing about the angular momentum.
 Allen L., Padgett M. J., Babiker M. in Wolf E. (Ed.) Progress in Optics XXXIX. – Amsterdam, Elsevier, 1999, p.300.
 Allen L., Padgett M. J., “The Poynting vector in Laguerre-Gaussian beams and the interpretation of their angular momentum density,” Opt. Commun. 184, 67-71 (2000).
 Allen L., M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian modes,” Phys. Rev. A45, 8185-8189 (1992)
 Simmonds J. W., M. J. Guttmann, States, Waves and Photons (Addison-Wesley, Reading, MA, 1970)
 http://mai.ru/publications/index.php?ID=8926 (June 30, 2009)
 Khrapko R.I. Experiment concerning electrodynamics’ nonlocality http://khrapkori.wmsite.ru/ftpgetfile.php?id=46&module=files