Photonic crystal: Difference between revisions

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Photonic crystals are composed of periodic [[dielectric]], metallo-dielectric—or even [[superconductor]] microstructures or [[nanostructure]]s that affect [[electromagnetic waves|electromagnetic wave]] propagation in the same way that the [[bloch wave|periodic potential]] in a [[semiconductor]] crystal affects the propagation of [[electrons]], determining allowed and forbidden electronic [[energy bands]]. Photonic crystals contain regularly repeating regions of high and low [[refractive index]]. Light waves may propagate through this structure or propagation may be disallowed, depending on their wavelength. Wavelengths that may propagate in a given direction are called ''[[Normal modes|modes]]'', and the ranges of wavelengths which propagate are called ''bands''. Disallowed bands of [[wavelength]]s are called ''photonic [[band gap]]s''. This gives rise to distinct optical phenomena, such as inhibition of [[spontaneous emission]],<ref name=Yablonovitch1987/> high-reflecting omni-directional mirrors, and low-loss-[[waveguide|waveguiding]]. The bandgap of photonic crystals can be understood as the destructive [[Wave interference|interference]] of multiple reflections of light propagating in the crystal at each interface between layers of high- and low- refractive index regions, akin to the bandgaps of electrons in solids.
 
There are two strategies for opening up the complete photonic band gap. The first one is to increase the refractive index contrast for the band gap in each direction becomes wider and the second one is to make the [[Brillouin zone]] more similar to sphere.<ref name=Yablonovitch1991>{{cite journal |doi=10.1103/PhysRevLett.67.2295 |pmid=10044390 |title=Photonic band structure: The face-centered-cubic case employing nonspherical atoms |journal=Physical Review Letters |volume=67 |issue=17 |pages=2295–2298 |year=1991 |last1=Yablonovitch |first1=E |last2=Gmitter |first2=T |last3=Leung |first3=K |bibcode=1991PhRvL..67.2295Y |doi-access=free }}</ref> However, the former is limited by the available technologies and materials and the latter is restricted by the [[crystallographic restriction theorem]]. For this reason, the photonic crystals with a complete band gap demonstrated to date have [[Cubic crystal system |face-centered cubic]] lattice with the the most spherical Brillouin zone and made of high-refractive-index semiconductor materials. Another approach is to exploit quasicrystalline structures with no crystallography limits. A complete photonic bandgap was reported for low-index polymer quasicrystalline samples manufactured by 3D printing.<ref>{{cite journal|author= Maiwald, L.|title= Control over Light Emission in Low-Refractive-Index Artificial Materials Inspired by Reciprocal Design |journal= Advanced Optical Materials |pages= 2100785 |year=2022|doi=10.1002/adom.202100785 |display-authors=etal|volume=10}}</ref>
 
The periodicity of the photonic crystal structure must be around or greater than half the wavelength (in the medium) of the light waves in order for interference effects to be exhibited. [[Visible light]] ranges in wavelength between about 400 nm (violet) to about 700 nm (red) and the resulting wavelength inside a material requires dividing that by the average [[index of refraction]]. The repeating regions of high and low dielectric constant must, therefore, be fabricated at this scale. In one dimension, this is routinely accomplished using the techniques of [[thin-film deposition]].