Novel Optical Properties And Non-Reciprocity In Photonic Lattices

In recent years,the engineering and research on the nature of artificial microstructural materials have not only focused on foundation subjects such as physics and chemistry,but also attracted attentions of the researchers in energy science,material science,information science,life science and other interdiscipline.With the development of nano-fabrication and characterization technology,a large number of artificial microstructures have been presented and fabricated in the past 30 years,such as photonic crystals,optical metamaterials and so on.Due to the periodic distribution of electromagnetic parameters in space,the propagation of electromagnetic waves in these artificial microstructures exhibits a great deal of novel physical properties.By engineering the dispersion relations and band structure of these periodic materials,people can control the state of electromagnetic waves just like controlling electrons in crystals,and a series of photonic devices have been realized such as waveguides,cavities,optical modulator and so on,which are superior to traditional counterparts.At the same time,some extraordinary optical effects such as negative refraction,zero refraction and super-aggregation have also been demonstrated.These achievements generat new ideas and opportunities to mold the flow of photons and realize controllable interaction between light and matters.Usually,optical microstructures refer to artificial materials which own different characteristics of the excitation and propagation caused by modulation of refractive index in optical materials.The most typical case of structures include waveguide arrays,photonic crystals and their corresponding optical microcavities.In this thesis,several photonic lattices such as waveguide arrays and photonic crystal cavities are presented.By introducing non-Hermitian coupling and space-time control of dielectric constants,some novel effects of light waves in localization,coupling and transmission processes have been investigated theoretically and numerically.The research contents include the following aspects:1.In the introduction,we first give a brief discribtion of the physical concepts,characteristics and applications of photonic crystals.On this basis,we discuss parity-time symmetric photonics,namely the new effects in the presence of gain or loss and the influence on property of related devices.In addition,we introduce the non-reciprocity phenomenon in photonic systems,that is,light wave propagating in the medium shows different behavior in opposite directions.We mainly review the principles and methods of realizing nonreciprocal optical effects.2.Waveguide arrays are photonic lattices owning periodic transverse refractive index distribution and no refractive index modulation in the direction of light propagation.Due to mode overlap and coupling between adjacent waveguides,light waves can exhibit completely different transmission characteristics from continuous medium systems.We construct a four-waveguide system to consider the propagation of light via non-Hermitian coupling.By modulating the coupling between waveguides with complex potential energy function,the Hamiltonian of the system turns into a non-Hermitian form.We discuss the eigenvalue of the system by the coupled mode theory systematically.Unlike Hermitian systems,three kinds of will appear while introducing a non-Hermitian coupling term into the waveguide-waveguide system.Among those exceptional points,four-order exceptional points are called higher-order exceptional points and exceptional points formed by the degeneration of two or three eigenstates are called second-order exceptional points and third-order exceptional points,respectively.The reasons for the diversity of exceptional points in this non-Hermitian four-waveguide system are revealed.The systems with higher order exceptional point have higher sensitivity than those with low order exceptional point.In particular,the evolution of different order exceptional points depending on different parameters such as waveguide propagation constants,coupling strength between waveguides and non-Hermitian coupling coefficient(describing the strength of non-Hermitian coupling)is discussed.It reveals that the higher-order exceptional points are degeneracy of the lower order exceptional points.In addition,the distribution of light field near the exceptional points and the total energy of the system are presented by simulation calculation.Those results show that the energy of the system is conserved when the non-Hermitian coefficient is relatively small.With the increase of the non-Hermitian coefficient,the eigenvalues of the system become imaginary,and the energy of the system changes to unconserved state.The research of the generation and properties of exceptional points in non-Hermitian coupled waveguides system can provide a new way for further exploring the complex topological structure with higher order exceptional points.3.Su-Schrieffer-Heeger(SSH)model(one-dimensional polyacetylene model)is a one-dimensional dimer chain structure used to describe the interlaced distribution of electron coupling strength on the chain.The main characteristic of the mode distribution in SSH model is that there are two topological phases which depends on different coupling strength.The nontrivial topology of the lattice implies that it has edge states on the boundaries,while the tricial toplogy of the lattice do not has.Recently,one pair of gain and loss has been introduced into SSH photonic lattices to construct the non-Hermitian SSH lattice chains,and the optical topological properties of the system have been studied.By analogy with this model,we construct a one-dimensional SSH photonic lattice via non-Hermitian coupling theoretically,i.e.introducing one pair conjugate non-Hermitian coupling terms into the coupling interaction between specific lattices in the photonic lattice chain,and discussing the evolution of the eigenstates of the system with non-Hermitian coupling.Under open boundary conditions,we consider the energy eigenvalues of the system and discuss the transition behavior of SSH mode from topologically nontrivial phases to trivial phases induced by non-Hermitian coupling.At the same time,we also consider the influence of the odevity of lattices on the topological properties of SSH lattice chains.We find that when one pair of conjugate non-Hermitian coupling are introduced at ends of the photonic lattice chain,only when the lattice number of the photonic lattice chain is odd,the energy eigenvalue of the system will split twice(second critical point)with the increase of the non-Hermitian coupling.It is completely different from the traditional non-Hermitian SSH lattice chain in which the generation of second critical value does not depend on the odevity of lattices.4.We demonstrate a novel method to realize nonreciprocal optical isolation and wavelength conversion via a cascaded system for the first time.For simplicity,we design a cascaded system consisted by three photonic crystal cavities.Rabi oscillation is generated to transfer energy between two cavities with the same mode.We explore the process of system energy changed by space-time dynamic tuning.Then the action of dynamic tuning is performed to adjust the mode to couple with a third cavity.Due to the mismatch of optical modes,nonreciprocal optical isolation is realized by this cascaded system.The magnitude of wavelength conversion in the process of dynamic tuning depends on the magnitude of refractive index,while the change of the refractive index is very limited under external light,heat or electricity.So at the same time,our system breaks the refractive index limitation of the wavelength conversion.With the method of wavelet transform,the time domain and frequency domain information in each cavity are given,and the dynamic process of energy and frequency varying during time in each cavity is also presented.The concept of breaking the refractive index limit can be explained by the signals and system theory.Our system can be extended to other kind of cascaded systems with different cavities,provide a new way for non-reciprocal manipulation of photons in optical communications and nano-photonic devices.