Transmission of waves across atomic step discontinuities in discrete nanoribbon structures

Abstract

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.

Phase recovery from phaseless scattering data for discrete Schrödinger operators

“…Propositions 2.6 and 2.7 are proved in section 5. Formulas similar to (30), (31) can be also given for s 12 := f + (k, 1), where k = − arccos(E/2).…”

“…In quantum mechanics, according to the Born principle, the complex values of wave functions ψ + and scattering amplitude f + do not have direct physical interpretations, whereas the absolute values of these functions admit probabilistic interpretation and can be measured directly in physical experiments. For example, in the problem of electronic transport through interfaces, naturally described in terms of transmission and reflection, following the Landauer-Büttiker approach [25,26], the scattering amplitudes (the probability amplitude) decide the conductance in the linear response regime; see, for example, [27][28][29][30] for an application to transport in waveguides where the forward problem of discrete Schrödinger equation has been solved exactly.…”

Scattering of surface waves by inhomogeneities in crystalline structures

“…, where which are reminiscent of the expressions of the reflectance and transmittance in waveguides [42,43]. To obtain above expressions (6.12) from (4.6), recall (2.11), (6.7), and it is useful to note…”