Xiangbo Yang

The two-dimensional optical waveguide network (OWN) proposed in this work not only supports Dirac cones at the Brillouin zone center and their high-symmetry points but also enables the formation of fractal quantized Dirac cones. By leveraging the inherent topological translational periodicity, we have derived analytical relationships that govern the frequencies, the number, and the taper angles of the network’s quantized Dirac cones. Moreover, we demonstrate that the fundamental properties of these Dirac cones are solely determined by two parameters ( p and q ). This discovery enables unprecedented on-demand control over Dirac cone characteristics through simple parameter tuning. Furthermore, when approaching the Dirac cone frequencies, the system exhibits two typical photonic behaviors: pseudo-diffusion phenomenon and defect-immune transmission. The essence of this phenomenon lies in the topologically protected transport capability conferred by Dirac cones with fractional-order eigenvalues, which enables robust optical transmission in defective environments. Unlike the topological transport mechanisms in traditional systems such as graphene, metamaterials, and photonic/phononic crystals, the unique fractional topological control transport mechanism in this square photonic network is fundamentally distinct from the physical nature of traditional integer-order topological protection.

Quasi-bound states in the continuum (quasi-BIC) with high quality factors and strong localized fields represent a highly competitive mechanism achieving high-performance sensors. Recently, metasurfaces with various meta-atom geometries have been designed to excite sharp quasi-BIC resonances for sensing applications. However, there is currently no systematic theory guiding the design of these structures. Perturbation theory was initially proposed to explain shifts in resonant modes of resonators due to changes in the external environment. We introduce this theory into the analysis of quasi-BIC modes, identify the parameter directly related to sensitivity ( S ), and demonstrate that optimizing the structure to ensure the excited mode field satisfies the boundary conditions can effectively enhance this parameter. Directed by perturbation theory and boundary conditions, we propose a high-performance metasurface sensor design method with significantly enhanced mode S . Specific cases are presented in this work, where the designed metasurfaces achieve significantly improved S of 805.97 nm/RIU and 1041.26 nm/RIU, exceeding the highest values reported in existing literature, and realizes an extremely high figure of merit. This approach can be applied to the analysis of different modes, providing a theoretical method and technical support for the development of high-performance sensors.

To explore the distribution of characteristic frequencies and the propagation properties of eigenmodes in topological networks at the zero-energy level, we design optical waveguide networks with two typical topologies: Möbius network and Klein network, inspired by the Möbius strip and Klein bottle, respectively. We investigate the degeneracy at characteristic frequencies and the propagation properties of the eigenmodes of these networks, both theoretically and experimentally. We discovered an intriguing eigenpropagation in the Möbius network and multiple degenerate eigenmodes in the Klein network, analyzing the propagation characteristics and distribution patterns of electromagnetic waves within them. In our experiments, we utilize coaxial cables as one-dimensional waveguides to construct transmission line networks for the two networks. We observe the distinct transmission paths of the Möbius network’s eigenmode and the two degenerate eigenmodes of the Klein network. Our findings provide a theoretical foundation for new optical modal transmission devices and novel nanoarrays, with potential implications for theoretical and experimental research in other quantum systems and topological networks.

By their powerful talent in manipulating optical parameters, metasurfaces demonstrate great ability in the generation of the vortex beams. Until now, vortex beam generators constructed by metasurfaces mostly lack tunability, which reduces the scope of their applications. Here, spin-decoupled moiré metalenses composed of two cascaded all-dielectric metasurfaces are designed. Utilizing mathematical derivation and numerical simulation, dual vortices with variable topological charge can be generated under the incidence of orthogonal circularly polarized light by tuning the mutual rotation between the two cascaded metasurfaces. Meanwhile, vector vortex beams can be produced by superposition of dual focused vortices under the linearly polarized light illumination and whose vector polarized states can also be manipulated by mutual rotation. This work provides a flexible design strategy for continuous manipulation of singular beams, which have potential applications in optical communication, microparticle manipulation, and super-resolution imaging.

We study a photonic band gap (PBG) material consisting of multiple waveguides. The multiconnected waveguides provide different paths for direct wave interference within the material. Using coaxial cables as waveguides, we are able to tune the PBG of the material. Using direct destructive interference between different paths of the waveguides, we experimentally observe a kind of PBG which is quite different from the traditional PBG that is caused by scattering in dielectrics with inhomogeneous refractive indices. Particularly, this newly observed PBG has an extremely strong wave attenuation, making electromagnetic (EM) waves in the PBG cannot even pass through one unit cell under certain conditions. We also systematically investigate the transmission of EM waves in our PBG materials and discuss the mechanism of band gap formation. Our results provide a new insight to develop new band gap materials for photons and phonons.

It is a highly significant area of research to investigate how to effectively enhance the focusing ability of abruptly auto-focusing beams (AAFBs) while extending the focal length. We introduce a dual-region parabolic trajectory offset modulation to auto-focusing ring Pearcey beams (RPBs), presenting a novel, to the best of our knowlege, approach to extend the focal length while greatly enhancing their auto-focusing capabilities. Unlike directly introducing a linear chirp, which inevitably shortens the focal length to enhance the auto-focusing ability and allows only single focusing in the RPBs, our scheme can achieve a multi-focusing effect. Furthermore, we have experimentally generated such a beam, verifying our theoretical predictions. Our findings offer promising possibilities for generating optical bottles, trapping multiple particles periodically, and enhancing free-space optical communication capabilities.

We theoretically and experimentally study a photonic band gap (PBG) material made of coaxial cables. The coaxial cables are waveguides for the electromagnetic waves and provide paths for direct wave interference within the material. Using multiconnected coaxial cables to form a unit cell, we realize PBGs via (i) direct interference between the waveguides within each cell and (ii) scattering among different cells. We systematically investigate the transmission of EM waves in our PBG materials and discuss the mechanism of band gap formation. We observe experimentally for the first time the wide band gap with strong attenuation caused by direct destructive interference.

In this paper, we investigate the singular multi-wavelength and multi-waveband transparencies generated by PT-symmetric dumbbell optical waveguide networks composed of two materials, and obtain the number regularity for the transparency wavelengths of one-unit-cell system and the general relationships for the transmission and reflection coefficients of multi-unit-cell systems. Consequently, three types of exact transparencies produced by multi-unit-cell systems are found based on the aforementioned formulas: (i)exact multi-wavelength unidirectional or bidirectional transparency as the same as those of one-unit-cell system; (ii)exact multi-wavelength bidirectional transparency at which one-unit-cell system cannot produce exact transparency, generated by adjusting the number of unit cells; (iii)exact multi-wavelength bidirectional transparency at which one-unit-cell system produces exact transparency, also generated by adjusting the number of unit cells. It provides theoretical foundations for developing highly sensitive and multi-wavelength optical filters. On the other hand, we also discover that multi-unit-cell systems can create approximate multi-waveband bidirectional transparencies by adjusting the number of unit cells, which provides scientific support for developing high-performance optical stealth devices.