Research On Bound States In The Continuum In Non-hermitian Optical Systems

Bound states in the continuum(BICs)are a special kind of spatially localized states with energy above the potential well but they are localized in space and square-integrable.BICs were originally proposed in a quantum system in 1929 by von Neumann and Wigner.However,their model is very difficult to realize experimentally since a complex local potential is needed be constructed accurately.On the other hand,the existence of localized state with E > V can be achieved by destructive interference between multiple resonance states.Interference between multiple resonance modes is a genceric phenomenon in classical wave systems,making the concept of BICs widely extended to optical or electromagnetic systems.Especially in recent years,with the rapid advancement of micro-and nano-fabrication technology,nanophotonic materials can mold the flow of photons due to the structures comparable to or even much smeller than the scale of wavelength.This render it possible to observe BICs in experiments.Researches on BICs in optical systems give rise to rich new physics,such as topological vortices,multipole singularities and coherent perfect reflections.In this thesis,the BICs in the optical branch are studied in a Su-Schrieffer-Heeger(SSH)chain,and even observed experimentally in a one-dimensional microwave system.Furthermore,the behavior of BICs under a parity-time(PT)-symmetric perturbation are studied for the first time.The results show that each of these BICs always splits into a pair of new type BIC(which we call pt-BIC)and lasing threshold mode when a PT-symmetric perturbation is introduced.This phenomenon is generic and verified in SSH chains,photonic-crystal fibers and photonic crystal slabs.The existence of pt-BICs clearly reveals the new physics arising from the interplay between the BIC and PT-symmetry.The details of this article are listed as follows:First,based on the coupled dipole equation,we have constructed the first analytically solvable model for BICs.According to the condition of destructive interference of lattice A and B in the SSH chain,we have found all the symmetry-protected BIC and accidental BICs in momentum space,and then we have obtained a complete phase diagram for accidental BICs.Two accidental BICs merge with the symmetry-protected BIC on the critical surface in the parameter space.To obtain a merging BIC,researchers need to find the quality factor with a higher divergence rate than an isolated BIC,which often requires tedious numerical search.We directly given the critical surface of merging BIC,which can pave the way for the research of BICs.Finally,we have extended the theory to the microwave regime and verified the existence of BIC experimentally in a one-dimensional system by measuring the propagation length of the resonance mode near the BIC.Second,in the SSH chain,each unit cell hosting two particles,one on sublattice A,and one on sublattice B.The PT-symmetric gain and loss can be added to particles A and B,respectively.In this thesis,we studied the effects of PT-symmetric perturbation on BICs for the first time.We have revealed a novel phenomenon: PT-symmetry induces mode splitting,rather than mode merging.One BIC mode splits into two modes,one is a new type of BIC(pt-BIC),and the other is a mode at the lasing threshold.The radiation loss at the lasing threshold is exactly balanced by the net gain of the particles.These PT symmetry-induced BICs have real eigenfrequencies and do not radiate to the far field,but they can be excited by waves coming from the far field.This is completely different from ordinary BICs that cannot be excited by external plane waves.In addition,we have proved that the Q-factor divergence rate for the pt-BICs is half of that of the ordinary ones.In fact,a pair of pt-BIC and lasing threshold mode corresponds to the right and left eigenvectors of the non-Hermitian matrix involving gain and loss,which suggests that the phenomena revealed here is generic for other PT-symmetric system supporting BICs.Finally,a PT-symmetric perturbation has been introduced into a photonic crystal slab that supports BIC.We shown that a pt-BIC will arise from each ordinary BIC together with the creation of rings of lasing threshold modes with the pt-BICs embedded in these rings.Different from previous works of BICs,the Q-factor divergence rate of a pt-BIC is reduced and anisotropic in momentum space.Also,pt-BICs do not have to be on high symmetry lines of the Brillouin zone,and they can be tuned to almost an arbitrary position in Brillouin zone.This striking property should be attributed to the PT symmetry.Pt-BICs also can be characterized by topological charges of polarization vortices of far-field radiation and can be created or annihilated with the total charge conserved.A unified picture on the pt-BICs and the associated lasing threshold modes is given based on the temporal coupled mode theory.Based on the prototypical SSH system,the existence of BIC has been verified theoretically and experimentally.A new type of pt-BIC and mode-splitting phenomenon,as well as other associated novel phenomena,are discovered when a PT-symmetric perturbation is introduced into the system supporting BICs.Our results manifest that the new physics of the subtle interplay between PT symmetry and BICs go beyond the exceptional point(EP)physics that has captured the attention of many researchers in the past few decades.Thus,our results point to some new directions for the exploration in the field of PT symmetry and non-Hermitian systems.At the same time,the bound state which can be excited by the far field(pt-BIC)also provides new possibilities for the application of BIC in laser and ultra-sensitive detection.