Progress and realization platforms of dynamic topological photonics

Dynamic topological photonics is a novel research field, combining the time-domain optics and topological physics.In this review, the recent progress and realization platforms of dynamic topological photonics have been well introduced.The definition, measurement methods and the evolution process of the dynamic topological photonics are demonstrated to better understand the physical diagram. This review is meant to bring the readers a different perspective on topological photonics, grasp the advanced progress of dynamic topology, and inspire ideas about future prospects.

Reconfigurable(4, 6^(2)) and(4, 8^(2)) Archimedean plasma photonic crystals in dielectric barrier discharge

Archimedean photonic crystal has become a research area of great interest due to its various unique properties. Here, we experimentally demonstrate the realization of reconfigurable(4, 6^(2))and(4, 8^(2)) Archimedean plasma photonic crystals(APPCs) by use of dielectric barrier discharges in air. Dynamical control on both the macrostructures including the lattice symmetry and the crystal orientation, and the microstructures including the fine structures of scattering elements has been achieved. The formation mechanisms of APPCs are studied by time-resolved measurements together with numerical simulations. Large omnidirectional band gaps of APPCs have been obtained. The tunable topology of APPCs may offer new opportunities for fabricating multi-functional and highly-integrated microwave devices.

Excitation of defect modes from the extended photonic band-gap structures of 1D photonic lattices

This paper stuides numerically the model equation in a one dimensional defective photonic lattice by modifying the potential function to a periodic function. It is found that defect modes （DMs） can be regarded as Bloch modes which are excited from the extended photonie band-gap structure at Bloch wave-numbers with kx = 0. The DMs for both positive and negative defects are considered in this method.

The interaction of in-band and in-gap lattice soliton trains in optically induced two-dimensional photonic lattices

We demonstrate the coherent interactions of lattice soliton trains, including in-band solitons （IBSs） and gap soliton trains （GSTs）, in optically induced two-dimensional photonic lattices with self-defocusing nonlinearity. It is revealed that the π-staggered phase structures of the lattice soliton trains will lead to anomalous interactions. Solely by changing their initial separations, the transition between attractive and repulsive interaction forces or reversion of the energy transfer can be obtained. The ‘negative refraction＇ effect of the soliton trains on the interaction is also discussed. Moreover, two interacting IBSs can merge into one GST when attraction or energy transfer happens.

Spatial solitons in photonic lattices with large-scale defects

We address the existence, stability and propagation dynamics of solitons supported by large-scale defects surrounded by the harmonic photonic lattices imprinted in the defocusing saturable nonlinear medium. Several families of soliton solutions, including flat-topped, dipole-like, and multipole-like solitons, can be supported by the defected lattices with different heights of defects. The width of existence domain of solitons is determined solely by the saturable parameter. The existence domains of various types of solitons can be shifted by the variations of defect size, lattice depth and soliton order. Solitons in the model are stable in a wide parameter window, provided that the propagation constant exceeds a critical value, which is in sharp contrast to the case where the soliton trains is supported by periodic lattices imprinted in defocusing saturable nonlinear medium. We also find stable solitons in the semi-infinite gap which rarely occur in the defocusing media.

A novel optical beam splitter based on photonic crystal with hybrid lattices

A novel optical beam splitter constructed on the basis of photonic crystal（PC） with hybrid lattices is proposed in this paper.The band gap of square-lattice PC is so designed that the incident light is divided into several branch beams.Triangular-lattice graded-index PCs are combined for focusing each branch.Computational calculations are carried out on the basis of finite-different time-domain algorithm to prove the feasibility of our design.The waveguide is unnecessary in the design.Thus the device has functions of both splitting and focusing beams.Size of the divided beam at site of full-width at half-maximum is of the order of λ/2.The designed splitter has the advantages that it has a small volume and can be integrated by conventional semiconductor manufacturing process

Beam control in tri-core photonic lattices

We report on theoretical investigations of beam control in one-dimensional tri-core photonic lattices （PLs）. Linear splitting is illustrated in tri-core PLs; the effect of defect strength on the splitting is discussed in depth for single-wavelength light. We reveal that splitting disappears when the defect strength trends to zero, while reoccurring under nonlinearity. Multi-color splitting and active control are also proposed in such photonic structures.

Localization and Steering of Light in One-Dimensional Parity-Time Symmetric Photonic Lattices

We theoretically study the propagation dynamics of input light in one-dimensional mixed linear-nonlinear photonic lattices with a complex parity-time symmetric potential. Numerical computation shows simultaneous localization and steering of the optical beam due to the asymmetric scatter and interplay between Kerr-type nonlinearity and PT symmetry. This may provide a feasible measure for manipulation light in optical communications, integrated optics and so on.

Study on ceramic photonic bandgap structure with three-dimensional diamond lattice

A novel process, which was based on powder injection molding, was investigated for the fabrication of ceramic photonic bandgap structure with three-dimensional diamond lattice. The SiO2-TiO2 ceramic powder was mixed with a water-soluble agent to produce slurry. The slurry was then injected into an epoxy mold with inverse diamond lattice, fabricated by the stereolitographic rapid prototyping process. To increase the density of the green compact, cold isostatic pressing was applied on the unit. Using thermal debinding, the water-soluble agent and the epoxy were extracted at 360 and 650 K, respectively. Sintering was immediately done at 950 K for 5 h and the desired three-dimensional ceramic structure was obtained. The calculated band diagram for this structure indicated the existence of an absolute photonic bandgap for all wave vectors. At 14.7-18.5 GHz, a complete band gap was located with a maximum attenuation of 30 dB at 17 GHz, when transmission was measured in the 〈100〉 direction between 10 and 20 GHz.

Germanium Based Two-Dimensional Photonic Crystals: The Hexagonal and Honeycomb Lattices

The properties of two-dimensional (2D) photonic crystals (PCs) composed of germanium (Ge) are discussed. We investigate polarization-dependent photonic band diagrams (transverse electric and transverse magnetic polarizations), gap maps, surface plots, contour maps, etc. for 2D PCs with Ge rods in air and vice versa for two different lattices geometries, namely hexagonal and honeycomb lattices. The obtained graphs for the four possible combinations are presented in this paper. All the graphs depict clear photonic band gaps. The conditions for the largest TE and TM band gaps are described. The honeycomb lattice of Ge rods in air background offers a large complete photonic band gap Δω/ωm greater than 8% (for rod radius of r = 0.2 μm). Using these data, new Ge based photonic devices can be fabricated to confine, control and manipulate light in a more useful way.

Analysis of the Effect of Air Hole Diameter and Lattice Pitch in Optical Properties for Hexagonal Photonic Crystal Fiber

We have investigated the different optical properties such as confinement loss, waveguide dispersion of a five rings hexagonal photonic crystal fiber under varied air hole diameter (d), lattice pitch (Λ), and air hole diameter to lattice pitch ratio for three different materials fused quartz glass, borosilicate glass and sapphire glass. We observed low confinement loss and high negative dispersion at higher d/Λ. Achieving high d/Λ can be done in two ways: increasing the air hole diameter or decreasing the lattice pitch. It has been observed, increasing the air hole diameter has significant effect over reducing lattice pitch in achieving low confinement loss. On the other hand, decreasing the lattice pitch over increasing the air hole diameter has significant effect in achieving high negative dispersion. It has also been found that, effective refractive index (neff) decreases significantly when lattice pitch decreases.

Tailoring topological corner states in photonic crystals by near-and far-field coupling effects

We explore the behaviors of optically coupled topological corner states in supercell arrays composed of photonic crystal rods,where each supercell is a second-order topological insulator.Our findings indicate that the coupled corner states possess nondegenerate eigenfrequencies at theΓpoint,with coupled dipole corner states excited resonantly by incident plane waves and displaying a polarization-independent characteristic.The resonance properties of coupled dipole corner states can be effectively modulated via evanescently near-field coupling,while multipole decomposition shows that they are primarily dominated by electric quadrupole moment and magnetic dipole moment.Furthermore,we demonstrate that these coupled corner states can form surface lattice resonances driven by diffractively far-field coupling,leading to a dramatic increase in the quality factor.This work introduces more optical approaches to tailoring photonic topological states,and holds potential applications in mid-infrared topological micro-nano devices.

Talbot effect in anti-PT symmetric synthetic photonic lattices

We investigated the Talbot effect in an anti-parity-time(PT)symmetric synthetic photonic lattice composed of two coupled fiber loops.We calculated the band structures and found that with an increase in the gain-loss parameter,the band transitions from a real spectrum to a complex spectrum.We study the influence of phase in the Hermitian operator on the Talbot effect,and the Talbot effect disappears when the period of the input field is N>8.Further study shows that the variation of Talbot distance can also be modulated by non-Hermitian coefficients of gain and loss.This work may find significant applications in pulse repetition-rate multiplication,temporal invisibility,and tunable intensity amplifiers.

Design study of APS-U-type hybrid-MBA lattice for mid-energy DLSR

In recent years,a new generation of storage ring-based light sources,known as diffraction-limited storage rings(DLSRs),whose emittance approaches the diffraction limit for the range of X-ray wavelengths of interest to the scientific community,has garnered significant attention worldwide.Researchers have begun to design and build DLSRs.Among various DLSR proposals,the hybrid multibend achromat(H-MBA)lattice enables sextupole strengths to be maintained at a reasonable level when minimizing the emittance;hence,it has been adopted in many DLSR designs.Based on the H-7BA lattice,the design of the Advanced Photon Source Upgrade Project(APS-U)can effectively reduce emittance by replacing six quadrupoles with anti-bends.Herein,we discuss the feasibility of designing an APS-U-type H-MBA lattice for the Southern Advanced Photon Source,a mid-energy DLSR light source with ultralow emittance that has been proposed to be built adjacent to the China Spallation Neutron Source.Both linear and nonlinear dynamics are optimized to obtain a detailed design of this type of lattice.The emittance is minimized,while a sufficiently large dynamic aperture(DA)and momentum acceptance(MA)are maintained.A design comprising 36 APS-U type H-7BAs,with an energy of 3 GeV and a circumference of 972 m,is achieved.The horizontal natural emittance is 20 pm·rad,with a horizontal DA of 5.8 mm,a vertical DA of 4.5 mm,and an MA of 4%,as well as a long longitudinal damping time of 120 ms.Subsequently,a few modifications are performed based on the APS-U-type lattice to reduce the maximum value of damping time from 120 to 44 ms while maintaining other performance parameters at the same level.

Vector Lattice Vortex Solitons

Two-dimensional vector vortex solitons in harmonic optical lattices are investigated. The stability properties of such solitons are closely connected to the lattice depth V0. For small V0, vector vortex solitons with the total zero-angular momentum are more stable than those with the total nonzero-angular momentum, while for large V0, this case is inversed. If V0 is large enough, both the types of such solitons are stable.

Simultaneous creation of multiple vortex-antivortex pairs in momentum space in photonic lattices

Engineering of the orbital angular momentum(OAM)of light due to interaction with photonic lattices reveals rich physics and motivates potential applications.We report the experimental creation of regularly distributed quantized vortex arrays in momentum space by probing the honeycomb and hexagonal photonic lattices with a single focused Gaussian beam.For the honeycomb lattice,the vortices are associated with Dirac points.However,we show that the resulting spatial patterns of vortices are strongly defined by the symmetry of the wave packet evolving in the photonic lattices and not by their topological properties.Our findings reveal the underlying physics by connecting the symmetry and OAM conversion and provide a simple and efficient method to create regularly distributed multiple vortices from unstructured light.

一维三格点光格子中拓扑振荡及拓扑非对称边缘态

为了全面认识奇数格点原胞中拓扑保护对于光束稳定传输的重要性,系统研究了一维三格点光格子模型中的光传输特性。利用能带理论和耦合模方程,对模型进行了模拟和仿真,发现两种在经典的两格点模型中不存在的具有拓扑保护的光传输行为,即具有拓扑保护的类拉比振荡光传输和具有拓扑保护的非对称传输,揭示了这两类光传输现象的物理机制,深入解析了光束振荡的本质,并验证了这两类光传输行为的鲁棒性,强调了光学系统在不同条件下的稳定性和可靠性。该研究可为利用奇数格点原胞中拓扑性质操纵光传输的潜在应用提供启示,并为新型拓扑光学器件的设计提供新的思路。

Absolute band gaps of a two-dimensional triangular-lattice dielectric photonic crystal with different shapes

Absolute band gaps of a two-dimensional triangular-lattice photonic crystal are calculated with the finite-difference time-domain method in this paper.Through calculating the photonic band structures of the triangular-lattice photonic crystal consisting of Ge rods immersed in air with different shapes,it is found that a large absolute band gap of 0.098 (2c/a) can be obtained for the structures with hollow triangular Ge rods immersed in air,corresponding to 19.8% of the middle frequency.The influence of the different factors on the width of the absolute band gaps is also discussed.

Multiple super-resolution imaging in the second band of gradient lattice spacing photonic crystal flat lens

Based on the triangular lattice two-dimensional photonic crystal(PC), the lattice spacing along the transverse direction to propagation is altered, and a gradient PC(GPC) flat lens is designed. The band structures and equal frequency curves of the GPC are calculated;then, the imaging mechanism and feasibility are analyzed. The imaging characteristics of the GPC flat lens are investigated. It is observed that the GPC can achieve multiple types of super-resolution imaging for the point source. This GPC lens is allowed to be applied to imaging and other fields such as filtering and sensing.

Self-trapping and oscillation of quadruple beams in high band gap of 2D photonic lattices

through single-site excitation. By changing the initial to the lattices, periodic oscillations of the localized quadruple state becomes a rotating doubly charged undergo charge-flipping when the rotating direction is orientation of the incident quadruple beam related quadruple mode may be obtained. The localized optical vortex （DCV） during rotation and should reversed.