Wave propagation in periodic networks of thin fibers

TL;DR

This paper develops a one-dimensional approximation for wave propagation in thin fiber networks, focusing on boundary conditions at branch points, with applications to interferometers and wave packet control.

Contribution

It introduces a novel approach to describe boundary conditions at branching points in thin fiber networks, enabling analysis of wave behavior in complex structures.

Findings

Parameters for transparency of wave packets identified

Method applicable to Mach-Zehnder interferometers on chips

Framework for controlling wave packet speed and transmission

Abstract

We will discuss a one-dimensional approximation for the problem of wave propagation in networks of thin fibers. The main objective here is to describe the boundary (gluing) conditions at branching points of the limiting one-dimensional graph. The results will be applied to Mach-Zehnder interferometers on chips and to periodic chains of the interferometers. The latter allows us to find parameters which guarantee the transparency and slowing down of wave packets.