Ray-wave correspondence in bent waveguides

Abstract

The present paper is concerned with wave propagation at high frequency in bent waveguides. The multimodal formalism proposed in earlier papers by the authors is shown to be suitable for investigating very high frequency problems. Then, following works made by Luna-Acosta et al. (G. Luna-Acosta, J.A. Méndez-Bermúdez, P. S˘eba, K.N. Pichugin, Classical versus quantum structure of the scattering probability matrix: chaotic waveguides, Phys. Rev. E 65 (2002) 046605; J.A. Méndez-Bermúdez, G. Luna-Acosta, P. P˘eba, K.N. Pichugin, Understanding quantum scattering properties in terms of purely classical dynamics: two-dimensional open chaotic billiards, Phys. Rev. E 66 (2002) 046207) for open quantum billiards, the ray-wave correspondence of the scattering matrix ( S matrix) is studied by first constructing a ray- S matrix and then comparing its structure with the structure of the wave- S matrix that is obtained with the exact multimodal formalism, for different geometries of curved waveguides. A great similarity between these two matrices is observed and it is shown that the scattering matrix constructed only by counting rays allows us to predict and understand numbers of the wave scattering properties in waveguides.