Abstract
The propagation of waves in square lattice strips, as waveguides, with discrete analogues of hard and soft outer boundaries is considered in the presence of a bifurcating lattice row which is either soft or hard. By an application of the discrete Fourier transform, the related boundary value problem, for both types of the bifurcated waveguides, is formulated as a discrete Wiener--Hopf equation. The exact solution of the latter is found in the form of a contour integral on the unit circle in complex plane. Closed form expressions for the approximate solution in the far-field are provided using the normal mode expansion. A general expression for the reflectance and transmittance is obtained; the sum, in the absence of dissipation, is established as unity. It is shown that the limiting wave field, as the waveguide width tends to infinity, coincides with that on an infinite lattice; the proof is presented in the dissipative case. The discrete paradigm of the bifurcated waveguides, introduced in the paper, has natural applications in engineering and science.
Published Version
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