Scalar wave propagation across a semi-infinite step or step-like discontinuity on any one boundary of the square lattice waveguides is considered within nearest-neighbour interaction approximation. An application of the Wiener–Hopf method does yield an exact solution of the discrete scattering problem, using which, as the main result of the paper, the transmission coefficients for energy flux are obtained. It is assumed that a wave mode is incident from either side of the step and the question addressed is what fraction of incident energy is transmitted across the atomic step discontinuity. A total of ten configurations are presented that arise due to various placements of discrete Dirichlet and Neumann boundary conditions on the waveguide. Numerical illustrations of a measure of ‘conductance’ are provided.

在最近邻相互作用逼近内，考虑了在方阵波导的任意一个边界上跨半无限阶跃或阶梯状不连续性的标量波传播。Wiener-Hopf方法的应用确实产生了离散散射问题的精确解，以此作为论文的主要结果，获得了能量通量的透射系数。假设波模式是从台阶的任一侧入射的，并且要解决的问题是入射能量的哪一部分在原子台阶的不连续点上传输。由于在波导上离散Dirichlet和Neumann边界条件的不同放置，总共出现了十种配置。提供了“电导”量度的数字说明。