Field patterns: a new type of wave with infinitely degenerate band structure

TL;DR

This paper introduces a new wave type called field pattern waves in space-time composites with PT-symmetry, revealing infinitely degenerate dispersion relations and structured propagation patterns.

Contribution

It demonstrates the existence of infinitely degenerate dispersion diagrams in field pattern materials and characterizes the associated wave basis functions.

Findings

Dispersion diagrams are infinitely degenerate.

Wave dynamics decompose into independent patterns.

Field patterns concentrate disturbances predictably.

Abstract

Field pattern materials (FP-materials) are space-time composites with PT-symmetry in which the one-dimensional- spatial distribution of the constituents changes in time in such a special manner to give rise to a new type of waves, which we call field pattern waves (FP-waves) [G. W. Milton and O. Mattei, Proc. R. Soc. A 473, 20160819 (2017), O. Mattei and G. W. Milton, arXiv:1705.00539 (2017)]. Specifically, due to the special periodic space-time geometry of these materials, when an instantaneous disturbance propagates through the system, the branching of the characteristic lines at the space-time interfaces between phases does not lead to a chaotic cascade of disturbances but concentrates on an orderly pattern of disturbances: this is the field pattern. By applying Bloch-Floquet theory we find that the dispersion diagrams associated with these FP-materials are infinitely degenerate: associated with each point on the dispersion diagram is an infinite space of Bloch functions, a basis for which are generalized functions each concentrated on a field pattern, paramaterized by a variable that we call the launch parameter. The dynamics separates into independent dynamics on the different field patterns, each with the same dispersion relation.