Rotating Waves in the Laplace Domain for Angular Regions

In a recent work [1,2,3] this author showed that the diffraction by an impenetrable wedge having arbitrary aperture angle always reduces to a standard Wiener-Hopf factorization. However, he encountered some difficulties in ascertaining the coincidence of WienerHopf solutions with the ones obtained by the Malyuzhinets method. These difficulties are due to the use of two different spectral representations: the unilateral Fourier Transforms (or Laplace transforms) in the Wiener-Hopf technique and the Sommerfeld functions in the Malyuzhinets method. Moreover Sommerfeld integrals introduce the complex angular spectrum w, whereas the Fourier integrals introduce the complex wave numbers η . To simplify this comparison, it appeared more convenient to this author to formulate a Laplace approach in the angular spectrum w, without using Sommerfeld integrals. This can be accomplished with the introduction of the concept of the rotating waves. The main aim of the paper is the exposition of this theory. This author believes it is interesting for further understanding of the wave motion in angular regions. A second aim is to show the elegance of the rotating waves method. To this end the solution of the diffraction problem constituted by the diffraction of a plane wave by many isorefractive wedges is