Transparency at the interface between two isospectral crystals

TL;DR

This paper demonstrates how supersymmetric quantum mechanics can be used to design fully transparent interfaces between two isospectral one-dimensional crystals, enabling reflectionless wave propagation across the boundary.

Contribution

It introduces a novel method to create transparent interfaces between isospectral crystals using supersymmetric quantum mechanics techniques.

Findings

A fully transparent interface between isospectral crystals is theoretically constructed.

An explicit example connecting Mathieu and non-sinusoidal potentials is provided.

The approach enables reflectionless wave transmission at the interface.

Abstract

Reflection at an interface separating two different media is a rather universal phenomenon which arises because of wave mismatching at the interface. By means of supersymmetric quantum mechanics methods, it is shown that a fully transparent interface can be realized, connecting two isospectral but different one-dimensional crystals. An example of reflectionless interface is presented for the sinusoidal (Mathieu) crystal connected to a non-sinusoidal potential by a transparent domain wall.