Quasicrystalline structures and uses thereof
This invention relates generally to the field of quasicrystalline structures. In preferred embodiments, the stopgap structure is more spherically symmetric than periodic structures facilitating the formation of stopgaps in nearly all directions because of higher rotational symmetries. 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 pre-selected range of wavelengths propagating in multiple directions.
1. The method of using a quasicrystalline composition of matter to produce a device, said method comprising:
a) providing a quasicrystalline composition comprising dielectric material elements;
b) arranging said material elements such that said quasicrystalline composition has at least a five-fold symmetry axis and not a six-fold symmetry axis; and
c) selecting said material elements such that said composition is a dielectric heterostructure that exhibits a photonic band structure of corresponding symmetry, forbidden in crystals and characterized by a complete band gap, so as to produce a device comprising said quasicrystalline composition.
2. The method of claim 1 , wherein said device comprising said quasicrystalline composition emits radiations substantially only within the visible spectrum to create a lamp.
3. The method of claim 1 , wherein said device comprising said quasicrystalline composition reflects at least a portion of a band of radiation frequencies incident thereon or propagating therein to create a quasicrystalline photonic reflector.
4. The method of claim 3 , wherein at least a portion of said propagating band passes through said device comprising said quasicrystalline composition.
5. The method of claim 4 , wherein said device comprising said quasicrystalline composition comprises a compact optical circuit.
6. The method of claim 1 , where said device comprises an array of quasicrystals, wherein each of said quasicrystals is selected to cover a specific range of frequencies such that, collectively, said frequencies comprise a broadband antenna.
7. The method of claim 6 , wherein said quasicrystals are attached together to form a substrate such that said substrate exhibits a photonic bandgap whose bandwidth varies as a function of location of said quasicrystals on the substrate.
8. The method of claim 1 , further comprising the step of introducing a structural defect by removing or positioning said material elements such that said device traps at least a portion of the electromagnetic radiation incident thereon.
9. The method of claim 8 , wherein said device traps said radiation at all angles of incidence.
10. The method of claim 8 , wherein said trapped radiation resonates within said structural defect to create a dielectric resonator.
11. The method of claim 1 , wherein said arranging of material elements comprises generating first and second quasicrystalline patterns, each pattern comprising locations, said material elements comprising a plurality of refractive indices, wherein said plurality of refractive indices have a plurality of maximum values and a plurality of minimum values, and wherein said maximum values are at locations in said first pattern and said minimum values are at locations in said second pattern.
12. The method of claim 11 , wherein said plurality of refractive indices further comprises a plurality of intermediate values at locations in a third pattern that is quasicrystalline.
13. The method of claim 11 , wherein said first pattern is quasicrystalline in three-dimensional space.
14. The method of claim 11 , wherein said first pattern is icosahedral.