Study On Topological Phases And Topological Phase Transitions In Electromagnetic Metamaterials

The concept of topological phases in photonics has fundamentally changed people’s understanding of the phase of matter and aroused extensive research interest of researchers.Compared with photonic crystals or phononic crystals,the realization of topological phases in electromagnetic metamaterials does not depend on the strict periodic structure.At present,many novel physical phenomena have been realized by using electromagnetic metamaterials,such as negative refraction,super-resolution imaging,electromagnetic cloaking,and so on.However,the research on realizing topological phases and exploring topological phase transitions based on electromagnetic metamaterials is very limited.In this thesis,we take electromagnetic metamaterials as the research object,and deeply explore the topological phases and topological phase transitions in several different types electromagnetic metamaterials,and to provide references for the optical field regulation.The main research contents and results are as follows:Systematically studies topological phase transitions and anomalous bulk-edge correspondences in magnetized plasma.The topological phase diagram in magnetized plasma is drawn,and the critical point of topological phase transition is given.The topological phase transition from a closed ellipsoidal equal frequency surface to an open type I or type II hyperbolic equal frequency surface is studied.A novel optical isolator based on the topological surface state to leakage mode is designed by using magnetized plasma.The physical mechanism of anomalous bulk-edge correspondence in magnetized plasma is revealed,by properly considering the spatial cutoff,the nonphysical response under large wave number is avoided and the anomalous bulk-edge correspondence is corrected.When the bulk-edge correspondence is restored,a new dual-band topological protected edge state is found.The topological characteristics of the dual-band system are proved by the stable propagation of the edge wave around the defect.The topological wave-division function of the dual-band edge state is realized by designing a four-channel.The topological phases and multiple unidirectional surface waves in gyroelectric metamaterials are studied.In gyroelectric metamaterials,when the hyperbolic-like and double semi-ellipsoid-like bands are simultaneously gapped by the vacuum state,the gyroelectric metamaterials can support multiple unidirectional surface waves with a small Chern number(C =1).The degeneracy of multiple unidirectional surface waves in double semi-ellipsoid-like gyroelectric metamaterials is analyzed by numerical calculation,and it is proved that the propagation direction of surface waves is determined by its own ellipticity.It is further proved that the topological characteristics of surface waves still exist in the system after considering dispersion in gyroelectric metamaterials.The topological phases and optics filtering effect in gyrotropic metamaterials are studied.Through analytical and numerical calculations,it can be seen that the gapless surface state not only appears in the common band gap between the metamaterials and the vacuum state,but also can exist in the infinitely extended wave vector space.The gapless surface state decays rapidly along the normal direction of the interface and has high field localization characteristics.When the electromagnetic duality symmetry of the material system is broken,the gyrotropic metamaterials that can support the gapped surface state are further studied.Although there is a gap in the surface state,the surface wave can still stably bypass the sharp defects.The physical mechanism of optics filtering effect is revealed in gyrotropic metamaterials.Numerical simulation demonstrates that the optical filtering effect can be regarded as the characteristic of the existence of the gapped surface state.By changing the electromagnetic parameters of the covering material,the bandwidth controllable optics filtering effect can be realized.Various forms of topological phases and topological phase transitions in chiral metamaterials are studied.The physical mechanism of topological phase transitions in chiral metamaterials is revealed,and it is proved that there are edge states or Fermi arcs in different topological phases.In the local/lossless chiral metamaterials,the topological phase transition is closely related to the Weyl point.The topological phase transition from the Weyl semimetal phase to the trivial phase is studied,and the connection characteristics of edge states and Fermi arcs in the material system are given.When the nonlocal effect is considered,the topological phase transitions occur between the I/II Weyl semimetal phase and the trivial phase.Further,considering the influence of material loss on the system,the chiral metamaterials undergoe topological phase transition under specific loss.