Bounds States In The Continuum And Topological Properties Of Relevant Systems Based On Near-field Coupling Mechanism

Near field refers to the non-radiation field generated in structures which can not propagate in the free space.Due to the imaginary wave vectors of the near field along the vertical direction of the material surface,the near field decays exponentially with the increasing distance to the material surface,and the near field is thus called evanescent field.For certain resonant structures such as metal wires and split ring resonators,the near field can be localized in a limit space with the scale much smaller than the working wavelength.Under the circumstances,the strong near field may have great potential in enhancing the interaction between matters,nonlinear effect,ultra-sensitive detection and ultra-high resolution optical microscope.The interaction based on the overlap of near fields from different components is called near-field coupling.Because of the high energy density constrated around the structures and exponentially attenuation of near field strength when it is away from the materials,the near-field coupling can be very strong and sensitive to the variation of coupling distance,which is different from the far-field coupling stemming from radiation coupling between two objects（The far-field coupling decays slowly with the increase of coupling distance.）.When designing electromagnetic systems in MHz or KHz bands,such as wireless power transfer（WPT）systems,metal detectors and magnetic shielding equipments,the far-field coupling between units can be neglected due to the low working frequency（When the dimension of the system is much smaller than the working wavelength,the radiation from the system is negligible.）,and the near-field coupling dominates for improving the system performance.Hence,we need to properly design the units（or meta-atoms）and modulate the near-field coupling among the meta-atoms to make the system work in an optimal state.Many intriguing physical phenomena can be realized based on near-field coupling mechanism,such as the Bound states in the continuum（BICs）found in the one-dimensional（1D）near-field coupling dimerized chains.BICs are energy states that fall within the continuum spectra but remain localized.In 1929,this concept was firstly raised by Von Neumann and Wigner.They mathematically designed a finite quantum potential well,from which electrons cannot escape due to the destructive interference between the transition paths.This concept has been extended to optical systems afterwards,where researchers have proposed various mechanisms to achieve BICs,such as symmetry incompatibility,destructive interference among radiation modes and the formation of localized resonant states in the transmission channels.Recently,BICs are also found in the 1D far-field coupled PT（Parity-time）symmetric systems with balanced gain and loss,where BICs are exactly the accidental eigenmodes with real eigen energies.However,little research of BICs in near-field coupled systems with gain and loss is reported.In addition to participating in the formation of BICs,we also investigate the impact of near-field coupling on the topological properties of far-field coupled systems.The concept of topological insulators first appeared in condensed physics where the researchers found that when an external magnetic field is introduced to break the time inversion symmetry of graphene,the electrons in graphene move in one direction along the material edge and are not affected by defects on the edge.This special state of electrons is called topologically protected edge state and the graphene in the magnetic field is called topological insulator.Later the concept of topological insulators was introduced into optics,and researchers have devoted massive efforts to study the topological insulators.A new material classification method is provided based on the topological invariant（e.g.,Z₂ topological insulators are distinguished by Winding numbers）of bulk function.Due to the mechanism of topological protection,non-trivial topological insulators are widely used in one-way energy transmission and defect-immune signal transmission.According to different coupling mechanisms,topological insulators can be simply divided into near-field coupling ones and far-field coupling ones.There are already many researches on these two kinds of topological insulators,but few works on hybrid coupling（Namely,near-field coupling and far-field coupling coexist in a system.）topological insulators are reported.Based on the reaserch background mentioned above,this dissertation makes the innovative exploration in the three following aspects:1.BICs in the near-field coupling systems with gain and loss and the characterization of BICs.2.Application of BICs in the near-field coupling systems for mid-range WPT.3.Modulation of near-field coupling on topological properties of far-field coupling system.In the second chapter of this dissertation,we theoretically consider two near-field coupled resonators with unbalanced gain and loss,respectively.An eigenmode with real eigen energy,namely BIC,is found under the PT symmetry broken phase.This special BICs results from the accidental appearance of the real eigenvalues with the evolution of systematic parameters（e.g.,the gain or the loss）.Unlike the general BICs,the amplitude of two resonators when working at BIC is not equal due to the unbalanced gain and loss.The relative amplitude of the two resonators is relevant to the ratio of gain and loss.We can thus modulate the eigen field distribution by adjusting the ratio of gain and loss.Then,we experimentally realize this model by utilizing coupled resonant coils and develop a method to characterize the BIC in this system.This model has potential applications in WPT and Wireless sensing.In Chapter 3,we design a system for mid-range WPT based on the coupled resonators model with unbalanced gain and loss proposed in Chapter 2.WPT has been a research hotpot in recent years and WPT systems based on magnetic coupled resonant coils are already used to charge mobile devices,electric vehicles and human implant devices.Mid-range WPT refers to that the energy transmission distance is several to ten times larger than the size of the transmitters and receivers,and it has certain specific applications,such as charging the tiny devices implanted in the human body.The near-field coupling between the receivers and the transmitters is weak due to the long energy transmission distance.Hence,the receivers can be regarded as perturbations to the transmitters.The working states of the transmitters can be designed as BICs to enhance the local magnetic field and high energy transmission efficiency thus can be obtained.In chapter 4,we investigate the topological transition of 1D far-field coupling dimerized chain with the introduction of near-field coupling.Firstly,we develop the Bloch theory based on coupled-mode theory and transfer matrix method to describe this hybrid model.Then we theoretically study the impact of the near-field coupling on the band structures of the 1D dimerized chain.In the case of unchanged far-field coupling conditions,the system will also undergo topological phase transition with the increase of near-field strength accompanying with the appearance of flat band and indirect band gap.It is intriguing that the indirect band gap is not discovered in the model with only near-field coupling or far-field coupling.We also calculate the Zak phase of each band to quantitatively describe the topological properties of the pass bands.Finally,based on the microstrip transmission lines,we achieved a 1D hybrid-coupled dimerized chain where near-field coupling and far-field coupling can be modulated independently.By pairing quasi-1D dimerized chains with different near-field coupling strengths but identical far-field coupling conditions,we experimentally observe the topological interface state,hence topological phase transition of the 1D model induced by near-field coupling is demonstrated.Our model provides a platform for the study of multi-channel couplings among units.Finally,in chapter 5,we make a brief summary of the overall works in this dissertation and propose several prospects for the future work.