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Second-order photonic topological insulators (SPTIs) featured with topological edge and corner states provide an intriguing way for steering light in integrated optics. However, existing SPTIs have narrow bulk gaps for tightly confining topological edge and corner states. In this paper, we propose a bi-directional evolutionary structural optimization (BESO) method to inversely engineer SPTIs in C3-symmetric lattices. At first, we maximize the first band gap of a photonic crystal (PC) enforced with C3 symmetry. Then, the topological phase transition is achieved by inverting the optimized PC. Highly localized topological edge and corner states are formed at the boundary and corner between the optimized PC and its inversion-symmetry partner. The bandwidth of the topological edge state for TE modes achieves 44.9%, exceeding two times of the current record. The robust of the topological corner states is further demonstrated. Our work provides a new route for designing SPTIs, paving the way towards their practical application.

A relatively newer generation of magnetic field sensors has found application in broadband electric current measurement. They are based on the magnetoresistance (MR) effect, remain linear for strong magnetic field stimulus, and can operate at a wide band of frequencies. This chapter explains the study of the effect of sensor size, and then designs a measurement system with small MR sensor head. A single magnetic sensor can be employed for large current measurement when placed in the close vicinity of a conductor. However, the magnetic field is complex in modern substations. Higher sensitivity limits the application of MR sensors in environments with nearby magnetic noise sources. A novel method for a wide range of electric current measurement with tunnel magnetoresistance sensors has been proposed to reduce the effect from an adjacent current‐carrying conductor, which is verified by numerical simulations, finite element analysis of the field, and laboratory experiments in the presence of strong magnetic disturbance.

Topology-driven nonlinear light-matter effects open up new paradigms for both topological photonics and nonlinear optics. Here, we propose to achieve high-efficiency second-harmonic generation in a second-order photonic topological insulator. Such system hosts highly localized topological corner states with large quality factors for both fundamental and second harmonic waves, which could be matched perfectly in frequency by simply tuning the structural parameters. Through the nonlinear interaction of the doubly resonant topological corner states, unprecedented frequency conversion efficiency is predicted. In addition, the robustness of the nonlinear process against defects is also demonstrated. Our work opens up new avenues toward topologically protected nonlinear frequency conversion using high-order photonic topological modes., Comment: 7 pages, 8 figures

With an auxiliary weak external magnetic field, we reexamine the fundamental thermodynamic function, Gibbs free energy $G(T,h)$, to study phase transitions in classical spin lattice models. A cross derivative, i.e., the second-order partial derivative of $G(T,h)$ with respect to both temperature and field, is calculated to precisely locate the critical temperature, which also reveals the nature of a transition. The strategy is efficient and universal, as exemplified by the five-state clock model, two-dimensional (2D) and 3D Ising models, and the $XY$ model, no matter if a transition is trivial or exotic with complex excitations. More importantly, other conjugate pairs could also be integrated into a similar cross derivative if necessary, which would greatly enrich our vision and means to investigate phase transitions both theoretically and experimentally.

Second-order phononic topological insulators (SPTIs) featured with topological edge and corner states offer promising ways for steering elastic waves. However, existing SPTIs were mainly designed with trial-and-error procedures, limiting the achievable width of topological bandgaps for tightly confining edge and corner states. Here, we develop a topology optimization approach for designing quantum spin Hall effect-based SPTIs. By simultaneously maximizing the powers emitted by the artificially selected body forces via topology optimization, the dipolar and quadrupolar modes are excited at the desirable frequencies. As a result, topologically nontrivial and trivial phononic crystals (PCs) with a record-breaking size of the overlapped bandgap (36.14%) are created. Thereafter, SPTIs arranged by hexagon and rhombus unit cells extracted from the optimized PCs are successfully created, validating the effectiveness of the optimization results. Additionally, the spatial decay of corner states is quantitatively characterized based on the complex band theory. Our work bridges topology optimization with SPTIs and, meanwhile, enriches the mechanism of corner states.

The propagation of evanescent waves inside phononic band gaps is important for the design of phononic crystals with desirable functionalities. This paper extends the bi-directional evolutionary structure optimization (BESO) method to the design of phononic crystals for maximizing spatial decay of evanescent waves. The optimization objective is to enlarge the minimum imaginary part of wave vectors at a specified frequency. The study is systematically conducted for both out-of-plane and in-plane waves at various frequencies. Numerical examples demonstrate that the proposed optimization algorithm is effective for designing phononic crystals with maximum spatial decay of evanescent waves. Various topological patterns of optimized phononic crystals are given. The results also show that the proposed optimization algorithm can successfully overcome difficulties in opening band gap at desirable frequencies, especially for the complete band gap and multiple band gaps.

Topological photonics revolutionizes some of the traditional approaches to light propagation and manipulation, and it provides unprecedented means for developing novel photonic devices. Recently discovered higher-order topological phases go beyond the conventional bulk-edge correspondence for photonic crystals and introduce novel opportunities for topological protection. Here, we introduce an intelligent numerical approach for inverse design of higher-order photonic topological insulators with great flexibility for controlling both topological edge and topological corner states. In particular, we consider the second-order photonic topological insulator and design several structures supporting both edge and corner states at different frequencies. By carefully programming these structures, we suggest a novel approach for topological routing of the edge and corner states by changing the operational frequency. Our finding paves the way to integrated topological photonic devices with novel functionalities., 12 pages, 5 figures

For the realization of topologically protected wave propagation, engineering artificial structures of topological insulators (TIs) inspired by quantum mechanics has attracted extensive attention over the last few years. However, the existing structures commonly compose of a regular shape of inclusions for the limited arrangements in the unit cell. This paper develops a topology optimization approach for designing novel structures of acoustic TIs. With the mechanism of acoustic TIs based on the quantum spin Hall effect (QSHE), topology optimization first seeks sonic crystals (SCs) with double Dirac cones of dipolar and quadrupolar modes. Then, topology optimization creates topological trivial and non-trivial SCs by breaking the double Dirac cones, which freely assemble into acoustic TIs. The optimized structures exhibit the typical functionalities of acoustic TIs, the robust propagation and spin-locked unidirectional transmission of topological edge states, verifying the effectiveness of the proposed approach.

Vibrations propagating underground may have harmful effects on adjacent buildings and human health. Recently, the notion of phononic crystals has been introduced and applied to isolate vibrations below the ground. In this paper, considering the viscoelastic material model, the complex band diagrams are suggested to analyse the transportation of vibrations in the composite foundation consist of soil and different underground structures. In the complex band diagram, the minimum imaginary part of the wave vectors is taken as the index to measure the ability of the pile group to weaken vibrations. Several types of underground barriers, including circular piles, continuous walls, and multi-layer piles, are analysed. The result shows that multi-layer piles can induce local resonance and achieve an attenuation zone at the low-frequency level. The attenuation effect of periodic barriers is then verified by transmission models. The results show that the complex band diagrams can quantitatively evaluate the isolation effect of periodic barriers, which is beyond the capability of classic band diagrams.

Higher-order topological insulators (TIs) develop the conventional bulk-boundary correspondence theory and increase the interest in searching innovative topological materials. To realize a higher-order TI with a wide passband of one-dimensional (1D) and two-dimensional (2D) transportation modes, we design three-dimensional non-trivial and trivial sonic crystals whose combination mimics the Su–Schrieffer–Heeger model. The topological boundary states can be found at the interfaces, including the zero-dimensional corner state, 1D hinge state, and 2D surface state. The fabricated sample with the bent two-dimensional and one-dimensional acoustic channels exhibits the multidimensional sound propagation and verifies the mode transition among the complete bandgap, hinge mode, and surface mode. The bandwidth of the single-mode hinge state achieves a large relative bandwidth of 9.1% in which sound transports one-dimensionally without significant leak into the surfaces or the bulk. The higher-order topological states in the study pave the way for sound manipulation in multiple dimensions.

Accurate information about electric current is a key parameter in smart grid. Non-contact measurements are desirable and state of the art. One notable problem with the non-contact current measurement is that they are based on the relationship of electric current and the magnetic field generated by the current, which is susceptible to the superposition of unwanted magnetic field on the magnetic field under measurement. In this paper, a novel adaptive filter with three-sensor array to reduce the effect of the unwanted magnetic field, is proposed. Testing is performed to quantify the consequence of cross talk in alternating current measurement by means of numerical simulations and finite element analysis (FEA) method. The proposed method demonstrates that when the peak value of the current under measurement is from 500 A to 1000 A with interference current changing in a certain range, error between the processed magnetic field and magnetic field under measurement is less than 3 % in numerical simulations and less than 4 % FEA simulations.

One drawback of contactless current measurement by magnetic sensor is that its detected results can be easily affected by the superposition of the external magnetic interference. Damping the effect of the noise is complex and delicate without the knowledge of the interference. The usage of magnetic shielding is one potent way to compensate the shortcoming. However, complete magnetic shielding fails to provide the shielding for the shielding only happens within the material. Therefore, in this paper, a separated double-layer structure with the gap is proposed for large current measurement with strong magnetic noise from random places. The ambition is to keep the targeted magnetic field within the shielding stable even when exposed to strong magnetic interference environment. Parameters of the designed structure are investigated and the validation of the structure is confirmed by finite element analysis method when the magnitude of the current under measurement ranging up to 1000 A. From FEA method, when the interference is at arbitrary places around the conductor, the standard deviation without and with noise is less than 0.13, authenticating the efficacy of this shielding structure.

A spherical and large-velocity-gradient model is adopted for the theoretical calculations of NGC 7027, AFGL 2688 and IRC+10216, whose emissions of CO far-infrared lines are comparatively strong. The statistical equilibrium calculations cover 107 energy levels. The upper energy limit is 4863 cm(-1) above the energy level with v = 0 and J = 0. There are altogether 107 energy levels with v = 0, J = 0 - 50; v = 1, J = 0 - 37 and v = 2, J = 0 - 17. The relative flux distributions of the CO lines, as functions of the upper rotational quantum number J, of the line, may be a good probe to examine the physical conditions of the region in which the CO line emissions arise. The CO far-infrared lines of IRC + 10216 are excited mainly by the central star, while for NGC 7027 and AFGL 2688 by the shocked warm and dense gases. The excitation mechanism is also discussed for other observed objects by using ISO. The CO spectra in the wavelength range 67-186 mu m are important probes for detecting objects with kinetic temperatures of several hundred degrees, i.e. the envelopes of carbon- or oxygen-rich stars, planetary nebulae, young stellar objects and star-forming complexes.