Comment on "Coherent acceleration by subcycle laser pulses"

Comment on " Coherent Acceleration by Subcycle Laser Pulses " Rau et al. [1] remark that, if a " unipolarlike " electromagnetic pulse existed, it could be used to transfer large amounts of energy to a charged particle that it overtakes in vacuum and far from any other material. An earlier work by Lai [2] made essentially the same point. Rau et al. then argue that there exists a solution to Maxwell's equations that has the desired unipolarlike form, at least in an interesting limit. However, this cannot be, according to a rather simple argument. See also [3]. Any physical source of electromagnetic waves is bounded, so that source appears pointlike when viewed from a great enough distance. Then, energy conservation requires that the pulse energy density fall off as 1͞r 2 , for distance r measured from some characteristic point within the source. Since the energy density is proportional to the square of the electromagnetic fields, we have the well-known result that the radiation fields from a bounded source fall off as 1͞r far from the source. This is in contrast to the static fields, which must fall off at least as quickly at 1͞r 2 , far from a bounded source. Now, consider the possibility of a unipolarlike pulse, i.e., one for which the electric field components E i ͑r, t͒ have only one sign at a fixed observation point r far from the source. Then, the time integral of at least one component of such a pulse would be nonzero: Z E i ͑r, t͒ dt fi 0. would have a nonzero value at zero frequency, E i ͑r, v ෇ 0͒ fi 0. However, the quantity E i ͑r, v ෇ 0͒ would then be a static solution to Maxwell's equation, and so must fall off similar to 1͞r 2. This contradicts the hypothesis that E i ͑r, t͒ represented an electromagnetic pulse from a bounded source, which must fall off as 1͞r. Thus, a bounded source cannot emit a unipolar electromagnetic pulse. This result does not hold for one-dimensional electromagnetic waves, such as plane waves, which, strictly speaking, can be generated only by an unbounded source. A well-known pedagogic example [4] is based on this case. If a charged particle were accelerated in only one direction , the associated radiation would be unipolar. However, unless the time integral of the acceleration is zero, the particle …