Platonic crystals are periodic structures which are designed to guide flexural wave energy through thin
elastic plates.
The term platonic crystal is formed by analogy to
photonic crystals,
phononic crystals, and
plasmonic crystals. The name emphasizes a thin plate formulation, which is governed by a fourth order
partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.
The function is often thought of as an "unknown" that solves the equation, similar to ho ...
, as opposed to a
second order equation which governs other types of crystals. There are also strong connections between platonic crystals and
metamaterials.
The study of platonic crystals is referred to as ''platonics'', and does not refer to the teachings of
Plato
Plato ( ; Greek language, Greek: , ; born BC, died 348/347 BC) was an ancient Greek philosopher of the Classical Greece, Classical period who is considered a foundational thinker in Western philosophy and an innovator of the writte ...
, or the
Platonic solid
In geometry, a Platonic solid is a Convex polytope, convex, regular polyhedron in three-dimensional space, three-dimensional Euclidean space. Being a regular polyhedron means that the face (geometry), faces are congruence (geometry), congruent (id ...
s. The term is now in common usage by multiple research groups in Australia, New Zealand, France, and the United Kingdom.
Applications
The types of platonic structures that have been examined include arrays of perforations,
arrays of pins,
arrays of point masses,
as well as periodic variations in the plate material itself.
Platonic crystals have been shown to exhibit a number of behaviours similar to photonic crystals, including
negative refraction
In optics, negative refraction is the Electromagnetism, electromagnetic phenomenon where light ray (optics), rays become refraction, refracted at an Interface (chemistry), interface that is opposite to their more commonly observed positive refrac ...
, beam splitting, and wave trapping.
They may also feature large
stopband
A stopband is a band of frequencies, between specified limits, through which a circuit, such as a filter or telephone circuit, does not allow signals to pass, or the attenuation is above the required stopband attenuation level. Depending on app ...
s where wave propagation is not possible through the crystal,
as well as cloaking near degenerate band surfaces.
Investigations into defective platonic crystals has also revealed strong energy localization effects within the defects, with high
quality factor
In physics and engineering, the quality factor or factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energy lost in ...
s.
Experimental work in platonics to date has shown promising results in cloaking
and flat lens focusing of flexural wave energy.
[{{citation, author1=M. Dubois , author2=M. Farhat , author3=E. Bossy , author4=S. Enoch , author5=S. Guenneau , author6=P. Sebbah , year = 2013 , title = Flat lens for time-domain focusing of elastic waves in thin plates , journal=Applied Physics Letters , volume=103 , issue=7 , pages=071915 , arxiv= 1303.3022 , bibcode=2013ApPhL.103g1915D , doi=10.1063/1.4818716 ]
References
Solid mechanics