Volume 120, Number 5, December 2017
|Number of page(s)||6|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||20 February 2018|
Field patterns: A new type of wave with infinitely degenerate band structure
Department of Mathematics, University of Utah - Salt Lake City, UT 84112, USA
Received: 25 September 2017
Accepted: 31 January 2018
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.
PACS: 42.25.Bs – Wave propagation, transmission and absorption / 81.05.Zx – New materials: theory, design, and fabrication / 77.84.Lf – Composite materials
© EPLA, 2018
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