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The purely classical counterpart of the Scattering Probability Matrix (SPM)$\mid S_{n,m}\mid^2$ of the quantum scattering matrix $S$ is defined for 2Dquantum waveguides for an arbitrary number of propagating modes $M$. We comparethe quantum and classical structures of $\mid S_{n,m}\mid^2$ for a waveguidewith generic Hamiltonian chaos. It is shown that even for a moderate number ofchannels, knowledge of the classical structure of the SPM allows us to predictthe global structure of the quantum one and, hence, understand importantquantum transport properties of waveguides in terms of purely classicaldynamics. It is also shown that the SPM, being an intensity measure, can giveadditional dynamical information to that obtained by the Poincar\`{e} maps.Comment: 9 pages, 9 figure

Classical versus quantum structure of the scattering probability matrix: Chaotic waveguides