The situation becomes even more unusual when the superluminal source also accelerates. Fig. 2b shows a superluminal source moving in a circle; here, the acceleration is centripetal [4, 12]. The Huygens wavelets now form a Cerenkov envelope consisting of an asymmetric two- ˇ sheet structure. It is relatively simple to show that an observer within the envelope will see an odd number (3, 5, 7. . . ) of images of the source (i.e., an odd number of retarded times), the exact number depending on the source speed [3]. The most remarkable effect, however, occurs where the two sheets meet tangentially on a cusp curve (Fig. 2b); an observer at this point will receive instantaneously contributions from an extended period of source time [2, 4, 12]. This unique effect, demonstrated experimentally by the machine shown in Fig. 1 [1, 2], represents focusing of radiation in the time domain to produce a concentration of electromagnetic energy. The initial work indicates that this temporal focusing has possible applications in radar [8] and long-range, low-power, secure communications. A related effect occurs when a source undergoes linear acceleration (Fig. 2c); here, there is an extreme concentration of emitted radiation caused by temporal focusing in a ring around the source’s path [13]. Our studies suggest directed energy applications for such a source.