Non-Hermitian Skin Effect In Photonic Microring Resonator Arrays

The ability to precisely steer the flow of light is critical for the next generation of photonic integration,which is newly developed by the recent progress of topological photonics.The photonic topological insulator is an analogy of the motion of electrons in a crystal protected by system topology.Based on the topological degree of freedom,topologically protected optical and integrated photonic devices can be realized,allowing for robust and backscattering-immune photon transmission that provides a promising approach to solve the problems of crosstalk and disorder-induced scattering losses.Gain and loss are ubiquitous and easy to implement in optical systems.Based on the concept of non-Hermitian physics,the degree of freedom for topological photonics is extended to the complex domain,providing a way to realizing novel topological modes and phases.Topological transmission generally relies on topological edge states,whose number and emergence are predicted by the bulk-boundary correspondence.However,when a system is applied with non-Hermitian asymmetric couplings,the skin effect appears with all modes accumulated at the system boundary,dramatically breaking the traditional bulkboundary correspondence determined by Bloch states.At present,the researches of the nonHermitian skin effect mainly focus on the basic Su-Schrieffer-Heeger(SSH)model which is implemented in the discrete optical systems,including fiber loops and quantum walk.The abundant content in non-Bloch topological photonics with skin effect is still waiting for further exploration.In this thesis,we theoretically present the realization of non-Hermitian asymmetric coupling in coupled ring resonators and construct several different non-Bloch topological insulators,such as square-root and quadrupole ones.The skin effect and non-Bloch bulkboundary correspondence are investigated in these systems featured with continuous wave dynamics.Subsequently,the skin effect is utilized to steer the light flow and applied to design novel integrated photonic devices.The work is presented as follows:(1)Derived by the transfer matrix method and verified by full vector simulation,the tight-binding model of the asymmetric coupling in the coupled ring resonator arrays is obtained.The asymmetric coupling is realized by integrating the same amount of gain and loss into the two half perimeters of linking rings that effectively couple two adjacent site rings.The coupling configuration is deduced by the transfer matrix method.The result is verified based on the full-vector algorithm,providing an effective tool to investigate the non-Bloch topological model in the coupled ring resonators.(2)We investigate the non-Hermitian skin effect and non-Bloch bulk-boundary correspondence in a ring resonator array which can be mapped into the square root of a Su-Schrieffer-Heeger(SSH)model with non-Hermitian asymmetric coupling,in which a robust edge mode transmission with multi-frequency channels and oneway transmission of skin modes can be realized.Such a square-root topological insulator inherits the properties from its parent Hamiltonian,sharing the same phase transition points and exhibiting non-Bloch features as well.A full-wave simulation for coupled ring resonator array is demonstrated.By comparing the energy spectrum and mode distribution under periodic and open boundary conditions of the two micro-ring structures,the non-Bloch bulk-boundary correspondence is verified.Non-Hermitian unidirectional transmission of pseudospin bulk state has a wider bandwidth and may find potential applications in light trapping,lasers,and filters.(3)We implement a non-Hermitian quadrupole topological insulator in a twodimensional microring resonantor array,achieving the localization properties of the second-order topological modes,skin-topological modes and second-order skin modes.We theoretically investigate the energy bands and topological invariants in this topological configuration.Furthermore,the distribution and transmission spectrum of different kind of modes are obtained through a full-wave simulation in the microring resonator array.Localization property is investigated with the implementation of different interfaces.In addition,we propose a scheme to realize the non-Hermitian quadrupole topological insulator in a passive silicon waveguide system,which is easier to implement experimentally.The construction of a non-Hermitian quadrupole topological insulator in the two-dimensional microring resonator can be used to realize high-quality and low-volume cavities accompanied with robustness,promising the integration and miniaturization of photonic devices,and may find applications in lasers and broadband light trapping.(4)We propose a topological configuration based on ring resoantors where synthetic gauge fields for photons provide a versatile approach to generate and control the non-Hermitian skin effect.By utilizing indirectly coupled ring arrays with longrange couplings for interference and on-site gain and loss for non-Hermiticity,we find that the skin effect appears once the gauge field is not an integer multiple ofπ.In addition to tunable localization direction,the skin modes display anisotropic behaviors with frequencydependent decay length,which can be explained by the split subregion of generalized Brillouin zone(GBZ)and an effective model under adiabatic elimination.Through numerical simulation,we can also demonstrate exotic features in propagation effects enabled by the skin effect,including asymmetric transmission and reconfigurable accumulation interface.The proposal is not directly dependent on non-Hermitian asymmetric coupling and thus is compatible with current experimental technology,which can be further generated to other photonic systems such as waveguide arrays.Our study paves the way to dynamically steer skin modes,which may find applications in laser,optical switch,and signal processing.