On prototypical wave transmission across a junction of waveguides with honeycomb structure

• Published in: Zeitschrift für angewandte Mathematik und Physik Vol. 69; no. 1; pp. 1 - 27
• Main Author: Sharma, Basant Lal
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.02.2018; Springer Nature B.V
• Subjects: Chebyshev approximation; Closed form solutions; Construction standards; Engineering; Exact solutions; Honeycomb construction; Lattice sites; Lattices; Mathematical Methods in Physics; Phonons; Scattering; Theoretical and Applied Mechanics; Tubes; 74A50; 74A60; Nanotube; Nanoribbon; 74S20; Hexagonal; Out-of-plane; Chebyshev; Secondary 81U30; Graphene; Primary 74J05; 39A14; Conductance
• ISSN: 0044-2275; 1420-9039
• DOI: 10.1007/s00033-018-0909-x

An exact expression for the scattering matrix associated with a junction generated by partial unzipping along the zigzag direction of armchair tubes is presented. The assumed simple, but representative, model, for scalar wave transmission can be interpreted in terms of the transport of the out-of-plane phonons in the ribbon-side vis-a-vis the radial phonons in the tubular-side of junction, based on the nearest-neighbor interactions between lattice sites. The exact solution for the ‘bondlength’ in ‘broken’ versus intact bonds can be constructed via a standard application of the Wiener–Hopf technique. The amplitude distribution of outgoing phonons, far away from the junction on either side of it, is obtained in closed form by the mode-matching method; eventually, this leads to the provision of the scattering matrix. As the main result of the paper, a succinct and closed form expression for the accompanying reflection and transmission coefficients is provided along with a detailed derivation using the Chebyshev polynomials. Applications of the analysis presented in this paper include linear wave transmission in nanotubes, nanoribbons, and monolayers of honeycomb lattices containing carbon-like units.