Propagation of peculiar heterogeneous waves

Abstract

Waves whose amplitudes become null at infinity are searched. The problem is reduced to the research of solutions of a two partial derivatives equations system. For the cartesian components of fields it proceeds the orthogonality condition of the isophase and the equiamplitude surfaces and the conditions of equality between the wave vector modulus and the propagation constant of the medium. The waves, the longitudinal components, isophases and equiamplitudes of which, have the same revolving axis, are studied in the case where the phase is proportional to the course. The waves, the equiamplitudes of which are orthogonal to plane isophases, have a constant in the whole space wave vector. More, if, the equiamplitudes are plane the solution are the plane and uniform heterogeneous waves (the plane and homogeneous waves are a peculiar case). If the cylindrical components, equiamplitudes are circular cylinders and if their isophases are plane, there are solutions with finite amplitude everywhere and null amplitude in any direction except the one of the propagation. They give a representation of a parellel light beam. A method to elaborate such a beam is suggested. Two of those beams, of the same frequency, which follow the same way, conduct to the interferences specifical to heterogeneous waves.