Numerical Computation For Bound States In The Continuum In Photonic Crystals

Bound States in the Continuum(BIC)is one of the resonant states in photonic crystal waveguides.Compared with the other two resonant states,the frequency of BIC lies in the radiation field,but it does not couple with the radiation wave because the energy is bound inside the photonic crystals.The special properties of BIC make it widely used in optical devices such as filters and has become a hot issue in photonic crystal research.Numerical simulation is an important method to study the BIC phenomenon in photonic crystal waveguides.In this paper,based on electromagnetic wave theory and finite element method,the mathematical model and numerical simulation of BIC generation and regulation in twodimensional honeycomb photonic crystal are focused on.The band gap of photonic crystal is the basis of BIC generation.Firstly,a new two-dimensional honeycomb photonic crystal structure with a wide band gap is constructed based on the numerical analysis of the finite element method.Starting from the Maxwell equation of electromagnetic wave propagation in two-dimensional photonic crystals,the continuous variational problem of two-dimensional honeycomb photonic crystals is established based on the variational principle.For this eigenvalue problem,the energy band can be simulated with high efficiency by solving it with linear finite element discretization in the first Brillouin zone.Based on the numerical simulation method and the linear search algorithm,new twodimensional honeycomb photonic crystal structures with wide band gaps of various materials are designed.The numerical simulation results show that the simulation algorithm is correct and effective,the model and algorithm in this paper can provide algorithmic support for the design of two-dimensional honeycomb photonic crystal structures.Based on numerical simulation methods,the BIC phenomenon of different structured photonic crystals is further investigated.The existing theoretical and experimental results show that BIC is an isolated point above the light ray in the band structure of photonic crystal and is usually located between the two lowest energy bands,which is divided into-ΓBIC and off-Γ BIC,among which-Γ BIC exists only in symmetric structures.In this paper,both-Γ BIC and off-Γ BIC are found in singleperiodic columnar photonic crystals by numerical simulation,where-ΓBIC located at the origin of Brillouin zone is a standing wave and depends on the structural parameters and dielectric constant of the photonic crystal;In the photonic crystal flat waveguide,the off-Γ BIC which is not on the boundary of the Brillouin zone is actually also related to the symmetry of the structure,and the BIC vanishes when the symmetry of the structure is broken.Further,the tuning problem of BIC in a foveated photonic crystal flat plate is explored.The numerical simulation results show that the adjustment of the structural parameters can change the BIC position in the momentum space while maintaining the original energy band structure,thus achieving the regulation of the BIC.