Resonant Frequencies and High Modes in Layered Wave Guides

When a boundary between two sections of a multilayered wave guide becomes a pressure or particle‐velocity node, the sections can be treated independently and the intersections of their characteristic curves define two infinite lattices of points which give the quasi‐resonant and antiresonant propagation frequencies of the complete wave guide. The antiresonant lattice points also give the group velocity maxima corresponding to the frequencies for which the modes of the wave guide are strongly coupled to the characteristic modes of an individual layer or section of the guide. The resonant lattice points give the group velocity minima corresponding to a somewhat weaker coupling with the complementary section. In addition to clarifying the physics of guided waves in layered media, these lattices accelerate the numerical procedures and lead, in the case of high modes of propagation, to useful approximations and/or simplifications of the exact solutions.