The Band Engineering And Applications Of Photonic Crystals

In recent years,photonic crystals have attracted a lot of interest.As the unit cell is configurable,photonic crystals have a large degree of structural freedom.With a lot of unique and practical physical properties,such as photonic band gap and topological indexes,photonic crystals have a lot of potential applications.Based on the band engineering method,we investigate the band engineering method and some new applications of two-dimensional photonic crystals.The major contents of this paper can be summarized as follows:1.Based on a band engineering method,we create a full-k-space flat band in two-dimensional photonic crystals.The full-k-space coverage represents a unique mechanism for achieving flat dispersions,which does not depend on high permittivity contrast or localized modes.The wave functions of the eigenstates distributed in air instead of in the dielectrics.With such a flat band,we demonstrate unique applications in ultra-sensitive detections.2.In complex photonic crystals,we investigate Dirac-like conical dispersions at the Brillouin zone center.The complex-unit-cell design provides extra degrees of freedom to engineer the normalized frequency of the Dirac-like point in a broad frequency regime.The unique double zero index properties associated with the Dirac-like point are well preserved in complex photonic crystals.By engineering the frequency of the Dirac-like point in different photonic crystals,different transmission behaviors can be achieved,such as total reflection and negative refraction.3.We investigate the angular selection of incident electromagnetic waves with two-dimensional photonic crystals.Such a design utilizes the Dirac conical dispersion at the Brillouin zone boundary.At the frequency of the Dirac point,the transmittance can reach unity at a particular incident angle associated with the Dirac dispersion.For all other incident angles the electromagnetic waves are reflected due to the existence of band gap.The position of the Dirac point at the Brillouin zone boundary can be engineered,and so does the selected angle.The angular selection is almost independent of the refractive index of the background medium,and can be achieved in both the transmission geometry and the reflection geometry.4.We investigate valleytronics in a two-dimensional square photonic lattice.When mirror symmetry is broken,different chiral photonic crystals can be created,while Dirac points at the Brillouin zone boundary are gapped.In the common band gap,topologically protected edge states are induced by nontrivial valley Chern number at the interface between two photonic crystals with opposite chirality.We demonstrate one-way propagation and the selection of edge states at the interface with a partial field orthogonal method.