Topological Photonic States And Their Interactions In Magneto-Optical Photonic Crystals

Photonic crystals(PCs)are the artificial microstructures composed of materials with different refractive indexes arranged in a certain period,and topology is a subject that studies the global properties of geometric figures or structures that can remain unchanged after continuously deforming.Recently,the concept of topology has been extended to photonics,which has opened up a new frontier field of topological photonics.It is found that topological photonic states(TPSs)possess the one-way property,and they are strongly robust against defects,obstacles and disorders on the transport path,because the imperfections can only lead to the change of local properties instead of global properties of topological PCs.Magnetooptical photonic crystal(MOPC)is the first system to observe the existence of TPSs,and is also one of the most powerful platforms to study the generation and interaction of TPSs and explore novel topological phenomena in photonics.This dissertation mainly focuses on the exploration of new states,new phenomena,new devices and new properties behind them in MOPCs.The specific research contents include following seven points:1.The concept of photonic Lorentz force and constructed the physical images of TPSs in MOPC systems is proposed.The energy flux,photon momentum and electromagnetic(EM)force equations in magnetized MO medium are deduced.It is found that the existence of offdiagonal elements in permeability tensor makes the emergence of imaginary parts of the energy flux,photon momentum and EM force equations,and the imaginary part of them is always perpendicular to their real part.By analogy with the electronic Lorentz force,the concept of photonic Lorentz force and the left-handed rule to judge the transport direction of EM waves is proposed.The formation mechanisms and physical images of energy flux vortex in infinite MO medium,asymmetric radiation and one-way edge state in semi-infinite MO medium,one-way windmill scattering in MO cylinder,and TPSs in MOPC are revealed.2.The EM wave scattering theory of MO cylinder is developed and the mathematical and physical origins of one-way windmill scattering is revealed.The EM wave scattering equation and energy flux equation of magnetized MO cylinder is deduced.It is found that the existence of non-diagonal elements leads to the symmetry breaking of the positive-and negative-order of Bessel function,causing the nonreciprocally scattering.Furthermore,the magnetization equation and polarized magnetic charge density equation are deduced,and it is found that there exist one-way polarized magnetic charges on the surface of magnetized MO cylinder,resulting in a one-way windmill scattering.As a result,the mathematical and physical originates of the one-way windmill scattering on a magnetized MO cylinder is revealed.Finally,the influences of the various radii of magnetized MO cylinder and the excitation frequencies and directions of incident plane waves on the one-way windmill scattering are discussed.3.The concept of antichiral TPSs are theoretically proposed and an experimental scheme to observe antichiral TPSs in microwave domain is designed.The existence of TPSs in nonmagnetized,uniformly magnetized and compound magnetized MOPCs is explored,and it is found that the compound magnetization can make the two pairs of degenerated Dirac points move down and up respectively and lead to the tilting of band structure.As a result,antichiral TPSs emerge at two parallel boundaries of MOPC.The electric field and energy flux distributions are calculated and the one-way property and the transport robustness of antichiral TPSs are demonstrated,and further the formation mechanism and physical image of them are revealed.Finally,a compact three-channel topological one-way waveguide by combining two antichiral MOPCs with the same magnetization is constructed,and a feasible experimental measurement scheme in a microwave domain is proposed.4.The existence of antichiral TPSs is experimentally observed and a tunable topological beam splitter is realized.According to the scheme designed in theory,a rectangular MOPC of a honeycomb lattice is manufactured.The existence of antichiral TPSs is experimentally observed,and the one-way property and the transmission robustness of antichiral TPSs are verified.It is found that antichiral TPSs only exist on two parallel zigzag edges,while the armchair edges cannot support any edge states.Finally,by combining two rectangular antichiral MOPCs with opposite magnetizations,a compact double-edge four-channel topological beam splitter is constructed,and the beam splitting ratio can be tuned by changing the incident angle of EM waves.5.The strongly coupling of two counter-propagating TPSs is studied and the slow light rainbow in a gradient magnetized waveguide is realized.The interaction of two counterpropagating TPSs in a MOPC waveguide is focused.It is found that by changing the waveguide width,the strongly coupling of two counter-propagating TPSs can be constructed,as a result,a closed energy loop is formed and a flat band supporting the dispersionless slow light states is realized.Furthermore,the magnetic tunability of slow light states is studied,and the broadband magnetically tunable dispersionless slow lights is realized,which can alleviate the contradiction between slow light and broadband.Finally,a gradient magnetized MOPC waveguide is constructed,and a broadband switchable topological slow light rainbow is realized.As a result,the different frequency components of incident wave packet can be slowed down and trapped in different positions in MOPC waveguide.6.The influence of the geometries of MOPC waveguide on the strongly coupling of two counter-propagating TPSs is studied and a slow light rainbow in a uniformly magnetized waveguide is realized.The influences of the waveguide geometries on the strongly coupling of two counter-propagating TPSs is explored.It is found that by modifying the cylinder radius and the waveguide width,a flat band possessing dispersionless slow light states at various frequencies can be realized.Furthermore,it is found that due to the existence of one-way edge states at the boundary of MOPC waveguide,the incident plane wave can remotely and nonreciprocally excite the slow light states in the MOPC waveguide.Finally,a uniformly magnetized compound MOPC waveguide is constructed,and a topological slow light rainbow with broadband magnetic tunability,high spatial resolution,low energy crosstalk and no signal distortion is realized.7.The strongly coupling of two co-propagating TPSs is studied and a topological slow light waveguide supporting the transport of dispersionless topological one-way slow light is realized.The interaction of two co-propagating TPSs in a MOPC waveguide is focused.It is found that by tuning the waveguide width,the strongly coupling of two co-propagating TPSs can be constructed and an eight-shaped energy loop is formed.As a result,the unique dispersion curve supporting the broadband dispersionless one-way slow light states is produced.Furthermore,the formation mechanism of odd-and even-TPSs in the waveguide is explored,and the slow light characteristics of them in the waveguides with different widths is discussed.Finally,a topological one-way waveguide is constructed,which can be used to demonstrate that a broadband electromagnetic pulse can bypass the metallic obstacle without any backscatterings and signal distortions.