부산대학교 도서관

When a time-harmonic wave-train of infinite duration is scattered by fixed objects, a stationary diffraction pattern is produced. This three-dimensional pattern may be characterized by lines---here called dislocation lines in analogy with dislocations in imperfect crystals---on which the pattern amplitude is zero. If, however, the excitation is a quasimonochromatic pulse (that is, an amplitude modulated carrier wave), the pattern changes with time, and the dislocation lines move and sweep out surfaces called dislocation trajectories. In this paper, the authors study the relation between the stationary dislocation lines for monochromatic excitation and the moving lines of the pulse pattern. First, a two-dimensional model involving two interfering monochromatic plane waves is studied. The effects of shape and bandwidth of the pulse are described. Then a theory for pulses of small bandwidth is given. A perturbation expansion in terms of the pulse bandwidth is derived and used to compute such things as the dislocation trajectories in terms of information about the monochromatic wave diffraction pattern at frequencies near the centre frequency. Some examples are examined and a connection with Thom's catastrophe theory is made. The discussion is not always mathematically rigorous, but arguments are usually detailed and plausible. No practical applications of these ideas are described, but an earlier paper by Nye and M. V. Berry [Proc. Roy. Soc. London Ser. A 336 (1974), 165--190; MR0351263 (50 \#3752)] suggests a possible use for dislocation lines in remote sensing as markers in a wave field, because they are definite features that are recognizable even in the presence of noise.