Quasicrystalline structures and uses thereof
This invention relates generally to the field of quasicrystalline structures. In preferred embodiments, the structure is heterostructure comprising dielectric materials arranged in two-dimensional space such that the overall structure is more rotationally symmetric than periodic structures. Symmetry may be five-fold or greater than six-fold. Such higher rotational symmetries provide stopgaps in nearly all directions. More particularly, the invention relates to the use of quasicrystalline structures for optical, mechanical, electrical and magnetic purposes. In some embodiments, the invention relates to manipulating, controlling, modulating and directing waves including electromagnetic, sound, spin, and surface waves, for a pre-selected range of wavelengths propagating in multiple directions.
1. A quasicrystalline composition of matter comprising a heterostructure, said heterostructure comprising a quasicrystalline arrangement of dielectric materials in a two-dimensional space, wherein said arrangement has at least a five-fold symmetry axis and not a six-fold symmetry axis and wherein said composition exhibits a photonic band structure in said two-dimensional space, said band structure having corresponding symmetry, which symmetry is forbidden in crystals, and which band structure comprises a complete two-dimensional band gap.
2. The composition of matter of claim 1 wherein said heterostructure comprises at least two dielectric materials.
3. The composition of matter of claim 1 wherein the quasicrystalline arrangement includes higher point group symmetry than said crystals.
4. The composition of matter of claim 1 wherein said complete bandgap is circularly symmetric.
5. A method of making the quasicrystal composition of claim 1 , the method comprising arranging at least two different dielectric elements or materials in a quasiperiodically ordered pattern in a two-dimensional space, said pattern having a preselected rotational symmetry forbidden in a crystalline material to create a composition that exhibits a photonic band structure having a corresponding rotational symmetry, which band structure comprises a complete band gap in two dimensions.
6. The method of claim 5 , wherein said pattern comprises structural defects introduced by removing or positioning particles or elements in the quasicrystal in a manner to thereby control the optical and physical properties of said quasicrystal.