Thoughtful comments on 'Bessel beams and signal propagation'

In this Letter we present thoughtful comments on the paper 'Bessel beams an d signal propagation' showing that the main claims of that paper are wrong. Moreover, we take the opportunity to show the nontrivial and indeed surpri sing result that a scalar pulse (i.e., a wave train of compact support in t he time domain) that is solution of the homogeneous wave equation (vector ( (E) over right arrow, (B) over right arrow) pulse that is solution of Maxwe ll equations) is such that its wave front in some cases does travel with sp eed greater than c, the speed of light. In order for a pulse to possess a f ront that travels with speed c, an additional condition must be satisfied, namely the pulse must have finite energy. When this condition is fulfilled the pulse still can show peaks propagating with superluminal (or subluminal ) velocities, but now its wave front travels at speed c. These results are important because they explain several experimental results obtained in rec ent experiments, where superluminal velocities have been observed, without implying in any breakdown of the principle of relativity. (C) 2001 Elsevier Science B.V. All rights reserved.