Research On Non-Hermitian Terahertz Topological Photonic Crystals

Terahertz（THz）wave is an electromagnetic wave that falls between microwave and infrared radiation.Its frequency is higher than microwaves and lower than infrared.In recent years,with the advancement of experimental technology and the proposal of various efficient methods for generating Terahertz waves,this frequency range has gradually become a hot research area in the international academic community.At the same time,Terahertz technology is an important technical means to achieve the 6G system（sixth-generation system）,as it can solve the problem of spectrum resource allocation and utilization in 6G communication and provide great assistance for the development of the next generation of wireless interconnect technology.The development of 6G technology depends on efficient and compact photonic chips,which pose high demands on the propagation of light waves.The discovery of topological insulators is one of the most important advances in condensed matter physics in recent years.Their physical properties are not affected by small disturbances,and they have bulk insulation,edge transmission,and backscatter suppression properties.This is a new paradigm of light wave propagation,and its combination with Terahertz technology can undoubtedly greatly promote the development of next-generation communication technology.This article focuses on the research of topological insulators in the Terahertz frequency range,and constructs a nano silicon carbide（Si C）particle square lattice array structure.This structure is also a type of photonic crystal,which has the potential to operate in the sub-wavelength range,and achieves topological effects based on phonon polaritons by coupling between Si C particles.In contrast,the coupling in metallic materials is based on localized surface plasmon polaritons.However,their topological properties can be characterized using a theory called the coupled dipole method.Therefore,they are collectively referred to as dipolar arrays.The main research content and innovation points are1.Using lattice sums techniques to rigorously consider the full dipole-dipole interaction of the Si C square lattice structure,the bulk band,projected band,and open boundary spectrum are calculated.The long-range coupling makes the degenerate second and third bands shifted out of the zero-energy band gap due to C₄ symmetry and time-reversal symmetry protection,and robust corner states appear in the band gap.In contrast,the traditional 2D SSH（two-dimensional Su-Schrieffer-Heeger）model,which only considers nearest-neighbor coupling,can not open a zero-energy band gap and does not have robust corner states in the band gap.As the coupling coefficient is a complex number,the proposed system is non-Hermitian,and the bulk polarization of the system is calculated,accurately capturing the system’s topological phase transition.2.The constructed lattice sums techniques can be used for various two-dimensional periodic dipolar array structures,which is a mathematical extension of the full coupling method for one-dimensional structures.It can be used to explore the topological properties of different full coupling dipolar arrays and also provide a relatively accurate theoretical tool for exploring the topological properties of dipolar arrays in experiments.