Interference and Energy Conservation in Phased Antenna Arrays and Young’s Double Slit  Experiment

Abstract: The interest in creating and detecting electromagnetic waves carryingangular momentum in such a way that they form helical wavefronts,so called "twisted light'', has increased in recent decades.One possible way of generating such waves at radio frequenciesis to use a circular phased antenna array, where a larger relativephasing of the antenna elements corresponds to more twist of thewavefront per wavelength.However, analytical computations of the radiated power, and in turn theamountof emitted angular momentum, displays a quite rapid decrease with increasedphasing. This decrease in intensity may cause problems when alarge range of twisting is desired; for instance, as a means to encodeand transmit information. We have found that the decrease in radiatedpower does not haveany explicit relation to the beam being endowed with angular momentum.Instead, the decrease in emitted power can be explained byelectromagnetic couplingof the antenna elements in the array and that energy conservationholds, because an equal decrease in power is seen at the input of the array.We also show that a similar discrepancy is seen between the incomingand the total diffracted power in Young's classic double slit experiment,which, having only two slits, cannot provide any twisted light.The source of that discrepancy should be of a different origin.Although an explanation in terms of surface plasmons was recently givenin the literature, that is only applicable to metal screens. A general explanation of the problem therefore remains to be found.