Discrete matrix Schrodinger equation equivalents of discrete two-component matrix wave systems

Abstract

Multichannel discrete lossless two-component wave systems describe physical scattering for multiple coupled transmission lines, for elastic media, and for electromagnetic wave propagation in layered media. Such a wave system is transformed into an equivalent discrete matrix Schrodinger equation that includes the effects of transmission losses and transmission scattering. These effects are not included in the continuous Schrodinger equation, so that discretisation of the latter omits significant effects. Applications include fast algorithms for synthesis and inversion of the reflection responses of multichannel scattering media. These algorithms require roughly half as many matrix multiplications as previous algorithms that employ the multichannel two-component wave system.