Field patterns: A new type of wave with infinitely degenerate band structure. (20th February 2018)

• Record Type: Journal Article
• Authors: Mattei, Ornella; Milton, Graeme W.
• Is Part Of: Europhysics letters. Volume 120:Number 5(2017:Dec.)
• Publication Date: 2018-02-20
• Subjects: 42.25.Bs -- 81.05.Zx -- 77.84.Lf; Physics -- Periodicals; Electronic journals; 530.05
• DOI: 10.1209/0295-5075/120/54003
• Languages: English
• ISSNs: 0295-5075

Abstract

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) (Milton G. W. and Mattei O., Proc. R. Soc. A, 473 (2017) 20160819; Mattei O. and Milton G. W., New J. Phys., 19 (2017) 093022). 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. In this letter, by applying Bloch-Floquet theory, we show 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. Each generalized function is concentrated on a specific field pattern, each parameterized 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.