Transfer matrix theory of leaky guided waves

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Abstract
We present a general transfer matrix approach for the propagation of guided waves in presence of inhomogeneities or « scatterers ». We particularly address the problem of the coupling with radiation modes leading to a leakage of the guided wave to the surrounding bulk medium at each scattering. Examples are surface acoustic waves, electromagnetic or acoustic excitations or evanescent electromagnetic waves near a boundary, guided waves in optical fibers... From symmetry and conservation laws, we obtain, in the case of symmetric scatterers, the general form of the transfer matrix in terms of four independent real parameters. For 1D-periodic lattices of identical scatterers, we show that leakage vanishes at the band edge : this coherent effect stems from the complete destructive interference between the converted radiations at each scatterer. This result demonstrates that coherent leakage is deeply different from a usual « dissipation » effect. Finally, we discuss the competition between Anderson localization and coherent leakage in the presence of disorder. Near the band edges and in the presence of disorder, the « attenuation length » due to the leakage is much larger than the localization length. We suggest an experimental situation where these effects could be observed