Study Of Bound State In Continuous And Topological Edge State Of Photonic Crystal Structure

Photonic crystals and sub-wavelength structure involve the energy band gap that commonly used in the optical field.With the control of the band gap,which can easily exert the powerful optical properties of photonic crystals,such as specific frequency light transmission,photon energy localization,high-sensitivity light sensing and so on.As a special photonic crystal,grating provides a research platform for most researchers with its periodicity and excellent structure.Because of the symmetry of grating,a new concept,bound state（BIC）in continuous is mentioned.The concept of BIC is introduced by quantum physics in recent years,excellent light local confinement,strong light limitation and specific light frequency selection can be realized through artificial structural adjustment.However,the traditional single grating structure restricts the higher dimensions research and further development of the devices in BIC field.The main work of this paper combine simple grating with multilayers film and optimize the shape of grating,which realize the further expansion of grating structure,and provides help and reference for the development of optical BIC state.In addition,the beam selection of photonic crystal band gap is designed,and a rotating cylinder structure is also designed skillfully.With the unique band gap of photonic crystals,the gradient topological edge state optical transmission is realized,and the application of multi-channel wavelength division multiplexer is achieved by combination.The current works are as follows:1.A complex structure composed of grating and multilayer film structure is proposed,and the energy band’s characteristics of the structure are analyzed to find the position of BIC.Due to the influence of multilayer film,a higher Q factor can be obtained in the complex structure than the simple grating.Based on the transfer matrix theory,the propagation process of waves in complex structures and the change of Q value are analyzed.In addition,due to the interference by two channels,one channel is a broadband channel that caused by Fabry-Perot resonance,and the other channel is narrowband channel that caused by guided mode resonance.The reflection spectrum presents a series of asymmetrical lines.We define an asymmetrical parameterδto control the structure characteristics,and finding the effect produced by BIC.When theδgradually decreases to zero,the quasi-BIC is transformed into BIC through the asymmetric Fano line.Therefore,due to the influence of high Q factor and quasi-BIC,Goos-H?nchen shift with high sensitivity is realized.2.Firstly,the symmetric rectangular grating structure is considered.When cutting off a corner of the rectangular grating,the quasi-BIC Fano line can be observed in the spectrum,and the breaking of plane symmetry is realized.After that,the Fano linewidth can be further reduced by changing the inclination of another rectangular grating in the period.In the momentum space,the change of structure means that the topological charge is split from q=1to half charge q=1/2.We analyze the guided mode resonance（GMR）excitation of the grating structure,and discuss the relationship between the dispersion in the waveguide layer and the BIC in the energy band,which proves the correctness of the BIC excited by the structure theoretically.In addition,with the change of asymmetric parameters M₁ and M₂,the asymmetric line shape presented by the spectrum gradually optimize and finally disappear,realizing the process of BIC turn into quasi-BIC.Due to the ultra-high Q factor of quasi-BIC,a large GH shift is realized,and a sensor with higher sensitivity is realized.3.Based on a photonic crystal unit,a multi-channel wavelength division multiplexer in two-dimensional photonic crystals（PCs）with different rotation angles is proposed.The optical transmission of topological edge state is realized with the difference of 2D Zak phase.With the proposed rotation parameterδ,different channels are arranged in gradient.Different channels are combined with each other that can realize a photonic crystal plate with higher degree of freedom.Compared with the previously designed edge-state optical transmission plate,the integrated photonic crystal plate has higher selectivity and more ingenious port transmission.In theory,optical selectivity at any frequency can be achieved,thus generating richer expansion.Finally,the structural material design and experimental operation are achieved,and the experimental results are agree well with the theoretical simulation results.In this work,the optical transmission of 9.34,9.67,10.12 and 10.94GHz channels have been realized,and the propagation efficiency is very high.