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Most natural and artificial materials have crystalline structures from which abundant topological phases emerge1–6. However, the bulk–edge correspondence—which has been widely used in experiments to determine the band topology from edge properties—is inadequate in discerning various topological crystalline phases7–16, leading to challenges in the experimental classification of the large family of topological crystalline materials4–6. It has been theoretically predicted that disclinations—ubiquitous crystallographic defects—can provide an effective probe of crystalline topology beyond edges17–19, but this has not yet been confirmed in experiments. Here we report an experimental demonstration of bulk–disclination correspondence, which manifests as fractional spectral charge and robust bound states at the disclinations. The fractional disclination charge originates from the symmetry-protected bulk charge patterns—a fundamental property of many topological crystalline insulators (TCIs). Furthermore, the robust bound states at disclinations emerge as a secondary, but directly observable, property of TCIs. Using reconfigurable photonic crystals as photonic TCIs with higher-order topology, we observe these hallmark features via pump–probe and near-field detection measurements. It is shown that both the fractional charge and the localized states emerge at the disclination in the TCI phase but vanish in the trivial phase. This experimental demonstration of bulk–disclination correspondence reveals a fundamental phenomenon and a paradigm for exploring topological materials. It is experimentally shown that topological states exist at crystallographic defects in the bulk and that disclination defects trap fractional charges characteristic of topological crystalline insulators.

We proposed a promising method to achieve phase modulation utilizing photonic crystal (PC). The broken parity and time-reversal symmetries induce intrinsic nonreciprocity. The supported one-way phase velocity which has a close relationship with biased magnetic field (BMF). Different from the most metasurfaces, only one structure is required to realize electromagnetic wave spatial distributions by adjusting each cell’s BMF. As an application, a deflector with only one column shows obviously nonreciprocity accompanied with magnetically tunable deflection angle. We further designed a flat lens and an axicon under different applied BMF distributions. Such phase modulation by PC provides a new flexible way to realize phase modulation, which can reduce difficulties in design and fabrication.

Topological insulators have unconventional gapless edge states where disorder-induced back-scattering is suppressed. In photonics, such edge states lead to unidirectional waveguides which are useful for integrated photonic circuitry. Cavity modes, another type of fundamental component in photonic chips, however, are not protected by band topology because of their lower dimensions. Here we demonstrate that concurrent wavevector space and real-space topology, dubbed as dual-topology, can lead to light-trapping in lower dimensions. The resultant photonic-bound state emerges as a Jackiw–Rebbi soliton mode localized on a dislocation in a two-dimensional photonic crystal, as proposed theoretically and discovered experimentally. Such a strongly confined cavity mode is found to be robust against perturbations. Our study unveils a mechanism for topological light-trapping in lower dimensions, which is invaluable for fundamental physics and various applications in photonics., Although topological confinement of waves to the edges is common, lower-dimensional wave confinement is scarce. Here, Li et al. demonstrate that concurrent wavevector and real-space topology can lead to a topologically protected zero-dimensional cavity mode in a two-dimensional photonic crystal.

We demonstrated a good unidirectional transmission (UT) with high transmission efficiency without breaking time-reversal symmetry both theoretically and experimentally. By adjusting the topological structure and designing the component of all-dielectric photonic crystal, an accidental degenerated Dirac point is built at Γ point. We obtained simultaneous zero permittivity and zero permeability. Truncating the PC into a bow-tie shape, we observed a total reflection in one direction but a total transmission in the opposite direction. The good agreement between the theoretical and experimental data verifies such model supports a good UT even considering the material's loss. Due to the PC's scale invariance, this kind of UT can be conveniently exploited into terahertz or optical frequency, providing a great promising application to optical communication and optical circuit.

We experimentally presented electromagnetic one-way transmission in 2D magnetic photonic crystal (MPC) with only 1 Oe remnant magnetism. Such nonreciprocal edge state is independent on the degenerated point but extends from the bulk mode instead. We proved the edge state exists in both PEC and PMC boundary conditions. Distinguished from those under fully saturated magnetization, the nonreciprocal transmission in this paper requires very low, even near-zero biased magnetic field, which is flexible to implement and opens up a new avenue in nonreciprocal device design.

We propose a zero phase delay waveguide simply utilizing two parity-time (PT) photonic crystals (PCs) magnetized in opposite directions. Based on the bulk one-way phase velocity of the PCs, electromagnetic wave incident normally on such a waveguide experiences reverse phase change, which makes the outgoing wave have the same phase with the incident wave, i.e. zero phase delay. By adjusting the filling ratio of the two PCs, we can feasibly realize zero phase delay in a wide frequency range, which provides potential for practical applications.

A novel broadband concave paper antenna is proposed for low cost and conformal applications. The new design is a three-dimensional monopole antenna. Owing to the concave flexible paper substrate, the proposed antenna is easy to integrate with the packing case or the communication product. The broadband antenna can be used in the applications covering the 0.903–2.63 GHz band, such as 2G, 3G, and WLAN. Its gain is 3.8 dBi at 0.915 GHz, 3.5 dBi at 1.0 GHz, 2.8 dBi at 1.8 GHz, and 4.8 dBi at 2.45 GHz. Experiments validate the simulated results of our antenna.

A practical method was proposed to implement the directional antenna by self-biased magnetic photonic crystals (MPC). By studying the influence of the shell’s boundary shapes and the source’s position on the antenna radiation, we designed an antenna with a good directional radiation performance by utilizing MPC in hexagonal lattice to fill a left-handed material (LHM) shell with a special shape. The implementation provides a practical way of LHM in the antenna applications.

Considering the combined effects of the intensity scintillation and the beam wander in the satellite-to-ground laser uplink communication system, the bit error rate (BER) performance of three modulation schemes – on–off keying (OOK), binary phase-shifted keying (BPSK), quadrature phase-shifted keying (QPSK) are investigated. In comparison with the condition in which the atmospheric turbulence is not taken into consideration, conclusions that atmospheric turbulence severely degrades the performance of the system are drawn. Based on the simulation results, the advantages of BPSK are analyzed in contrast with OOK and QPSK. Specially, when transmission power is 4 W, performance of OOK shows 18 dB impairment while performance of QPSK shows 3 dB impairment compared with BPSK under the atmospheric fluctuation. Further compared to QPSK, BPSK owns lower BER and simpler process. Considered the feasibility in communication systems, BPSK should be the most reasonable modulation scheme which can decrease the BER of systems without increasing the transmitter power among these three modulation schemes. Besides, optimum divergence angle, optimum beam radius and appropriate receiver diameter are also analyzed, which is significant in practical applications.

One-way light has attracted much attention recently. They have wide range of applications, such as optical isolators and optical diodes. At present, two approaches can be used to realize the one-way light. One is one-way surface waves, which come from chiral edge states of photonic crystals [1, 2]. The other is one-way body waves, which may originate from the parity-time symmetry of a system [3, 4]. Here, we theoretically demonstrate that by breaking parity and time-reversal symmetries at the same time electromagnetic waves can self-collimate and propagate unidirectional in photonic crystals fabricated by semi-cylindrical ferrite rods in magnetized states. Self-collimated one-way body wave presents at certain unit cell configurations of the photonic crystal, and the one-way wave beam shows robustness in some way to certain kind of disorders in the wave channel. We find the propagation direction of the self-collimated one-way wave beams can be tuned using a bias magnetic field. Therefore, we can bend the self-collimated one-way body wave, which can be considered as a curved waveguide. Further, by applying the bias magnetic field in a complex configuration, the self-collimated one-way wave beam can be bent into arbitrary trajectories within the photonic crystal, providing a new avenue for controlling wave beams.

Electromagnetic (EM) topological states [1, 2] have been drawing lots of attentions in both physical and engineering field for their good performance in optical isolator, circulator, etc‥ As a resemblance of signal carrier in modern communication, the excited EM chiral edge state (CES) is immune to the impurity of transmission path without any backward scattering, providing a potential for future transoceanic communication with no require of repeaters of amplifiers. Mimicking modulation and demodulation of FDM, in this work we realize a resemble function in photonic system by constructing multi-mode CES. Different from most of the presented work with only one CES mode, in this paper we design and experimentally observed a two-mode CES. Such multi-mode CES resembles frequency division multiplexing (FDM). If we consider real space position in PC as the time and the wave vector as frequency. By designing a magnetic photonic crystal (MPC) with square lattice, we obtained eight Dirac points existing at non-high symmetry point in Brillioun zone due to mirror symmetry [3] by keeping time-reversal symmetry. It is demonstrated all Dirac points are unbuckled to open a full gap in the effect of bias magnetic field. Once the MPC is truncated by metal cladding, two-mode edge states appear inside the gap as shown. At an operating frequency, two EM waves are excited with different wavelengths (wavevector) but the same transmission direction. The experimental data verify such two-mode edge states are unidirectional and robust against the scatterings from disorders of various kinds. By introducing the Fast Fourier Transform (FFT) algorithm in EM system, we successfully obtain the band structure of CES basing on the field profile measured. Later, imitating the demodulation in communication engineering, we theoretically propose a method to eliminate one of modes by introducing two feed with same magnitude and phase but located at different positions.

One-way transmission and negative refraction are the exotic wave properties founded in photonic crystals which attract a great attention due to their promising applications in photonic devices. How to integrate such two phenomena in one material or device is interesting and valuable. In this work, we theoretically and experimentally demonstrate that one-way electromagnetic space wave can be realized by means of two-dimensional magnetic photonic crystals. Simultaneously breaking the time-reversal and parity symmetries of the magnetic photonic crystals designed, we observe oblique incident space wave propagating one-way in the magnetic photonic crystals with positive or negative refraction occurring at interfaces, which can be manipulated upon the incident angle and operating frequency. Our work may offer a potential platform to realize some exotic photoelectronic and microwave devices such as one-way imaging and one-way cloaking.

We experimentally observed a photonic Chern insulator with large Chern number. Two nontrivial chiral edge states have been distinguished. By introducing two excitation probes and changing their positions, we successfully eliminate one of the modes.

To achieve a unidirectional transmission waveguide with miniature dimensions and flexible geometry, we propose a self-guided unidirectional waveguide composed of a chain of gyromagnetic rods. Two configurations of the waveguides were demonstrated. One is of a zigzag chain form, the other is a straight-line chain. These two types of waveguides have very wide one-way edge mode bandwidths. The simulated and experimental results illustrate their extraordinary wideband one-way transmission characteristics. They can also be expected to function as flexible platforms for practical applications because of their thin transverse dimensions and robustness to bending.

At the zigzag edge of a magnetic photonic crystal with honeycomb lattice, the nonreciprocal surface modes (NSMs) could appear below the magnetic surface plasmon (MSP) frequency. The NSMs possess very flat slopes outside the light line, which is strikingly different from the nearly linear dispersion curve just above the MSP frequency and results in strong confinement and enhancement of the electromagnetic field. Particularly, an enhancement over 100 times in magnetic field is achieved because of the strong magnetic response arising from the MSP resonance. In addition, the branch of double-valued NSM dispersion curve provides zero group velocity away from the Brillouin zone boundary.

We present an experimental demonstration of self-guiding electromagnetic edge states existing along the zigzag edge of a honeycomb magnetic photonic crystal. These edge states are shown to possess unidirectional propagation characteristics that are robust against various types of defects and obstacles. In particular, they allow for the unidirectional transport of electromagnetic energy without requiring an ancillary cladding layer.

There exist two types of electromagnetic (EM) one-way edge states in magnetic photonic crystal (MPC). One is associated with photonic band gap (PBG) relevant to Bragg scattering, while the other is associated with PBG originating from magnetic surface plasmon resonance. Both support robust unidirectional wave transmission, but each with relatively limited operating bandwidth. By optimizing the lattice spacing and filling ratio of MPC as well as tuning the external static biasing magnetic field, we are able to fuse the two types of EM one-way edge states together and therefore achieve broadband one-way transmission. The operating bandwidth could be about 4 GHz in a microwave regime; this is much larger than that based on either type, providing a way towards the practical applications of unidirectional wave propagation.

In a ground-to-satellite communication system with a preset EDFA, the EDFA's performance will be affected by space environment. With 250 Gy radiation, the EDFA's gain decreases by 2 dB from 19.97 dB at 20 °C. The BER increases by 2.5 orders of magnitude from 10(-10), and increases more with more radiation. The situation aggravates when the temperature rises by 73 °C. The laser's divergence-angle and transmitter radius have optimal values to make the lowest BER and increasing receiver diameter makes lower BERs, so setting these parameters with appropriate values will compensate the degradation caused by EDFA.

To better understand the resonance modes caused by the interelement couplings in the building block of metamaterials, we propose a circuit model for the hybrid resonance modes of paired split ring resonators. The model identifies the electromagnetic coupling between the paired rings by electric and magnetic coupling networks and well explains the variation of hybrid resonance modes with respect to the distance and the twist angle between the rings. The predictions of our model are further proved by experiments.

We experimentally demonstrate that electromagnetic waves in the waveguide comprising gyromagnetic photonic crystals (GMPCs) and a metal cladding are robust one-way slow waves in the frequency range of the chiral edge states of GMPC. Measured with phase shift technique in microwave regime, the group velocity of the wave could be one order of magnitude smaller than the speed of light with group index up to 15.6. The one-way wave with much slower group velocity is shown by retailoring the waveguide further. This waveguide provides a potential way to realize robust slow-light transmission lines in electromagnetic or optical systems.