Band Engineering And Slow Light Characteristics Of Topological Photonic Crystals

Topology,as a mathematical concept to discuss a certain invariance under continuous deformation,was generalized to the discussion of condensed matter physics.Then the study of topological states of matter was extended to optical systems,and topological photonics based on topological band theory gradually became a new research field.Topological phenomena such as optical quantum Hall effect,optical quantum spin Hall effect and optical quantum valley Hall effect have been discovered in optical systems,which greatly promote the research and development of photonic topological insulators.Based on topological photonic crystals,unique optical transport and light field modulation characteristics can be realized,such as boundary transport characteristics that inhibit backscattering and defective immunity,selective transport characteristics dependent on spin orbits,and multi-dimensional light regulation.The energy band engineering based on topological photonic crystals can not only produce slow light with a large group index,but also increase the bandwidth,and at the same time have topological protection characteristics,such as robustness,unidirectional transmission,high-quality factor,etc.,which provides new ideas for the design of new photonic devices for future optical path integration devices.Next,we design the slow light waveguide structure based on the band engineering of various types of topological photonic crystals,and further study the slow light characteristics.First,we propose a topological slow light based on sandwich-structured photonic crystals.This heterogeneous structure consists of three photonic crystals with different topological phases,and two coupled topological edge states are generated in the bandgap species at the same time,which can produce the slow light mode of zero group velocity dispersion,considerable average group index,and normalized delay bandwidth product.Based on time domain simulation,the zero-group velocity dispersion transmission of Gaussian pulses is calculated.Second,we propose a method to realize topologically slow light by using a triplestructured photonic crystal based on the valley Hall effect.This heterostructure consists of a multilayer Dirac photonic crystal and two valley photonic crystals with different valley Chern numbers,the topological valley waveguide state can be obtained.Flat bands in the full bandgap can support topologically slow optical waveguide modes with a large group index(=100).The multi-layer structure in the middle allows the topological slow optical waveguide mode to support the transmission of high energy capacity,and the topological slow optical waveguide mode maintains the valley locking effect and can be immune to the influence from backscattering.Third,we theoretically propose a topological electromagnetic system based on topological non-trivial photonic crystal cavity defects.The cavity defect coupling mode is pseudospin polarization,which is achieved by weak coupling between topological cavity defects.Based on the tight combination approximation,the flat dispersion relationship of the coupling mode is obtained,which is suitable for decelerating light.The characteristics of slow light,including group exponential and group velocity dispersion,are discussed in detail.At the characteristic frequency of a single cavity defect,the group velocity dispersion of the coupling mode is zero.These states can be excited by using two spatially symmetrical line-source arrays that carry orbital angular momentum.The characteristics of unidirectional propagation and transmission by bending are demonstrated,and slow light transport is stable when defects are introduced into the photonic crystal structure.