title: Hopf-Ranãda linked and knotted light beam solution viewed as a null electromagnetic field.
abstract: The Hopf-Ranãda linked and knotted light beam solution, which has been interpreted physically and extended analytically by Irvine and Bouwmeester recently, is viewed in this Letter as a null electromagnetic field. It is shown, in particular, that the Hopf-Ranãda solution is a variant of a luminal null electromagnetic wave due originally to Robinson and Troutman and reported by Bialynicki-Birula recently. This analogy is motivated by means of a method due to Whittaker and Bateman, and a relationship to well-known scalar luminal localized waves is examined.
authors.affiliation: The Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University,Blacksburg, Virginia 24060, USA. besieris@vt.edu
authors.forename: Ioannis M
authors.initials: IM
authors.lastname: Besieris
authors.forename: Amr M
authors.initials: AM
authors.lastname: Shaarawi