Abstract:Topologically protected one-way transportation of sound, mimicking the topological properties of the condensed matter, has received greatly attentions. Thus far, the topological phases and the topological edge states of sound are yielded in the vicinity of the Dirac cones fixed at the high symmetric points of the Brillouin zone. Here, we present a new type of the phononic topological insulator in the square lattice with position-variational Dirac cones along the high symmetric lines. The emergence of such Dira… Show more
“…9). Similar to the earlier structure the edge states that arise are topologically nontrivial and gapless 22 .Figure 9 C 4 v even-parity interfacial mode — Left and right columns, panels (a,b), pertain to the orange over blue and blue over orange stackings, respectively. Top panels show eigensolutions obtained from Fourier-Hermite method.…”
Section: Resultssupporting
confidence: 67%
“…The parametric variation afforded to us, and encompassed in the variable , merely increases or decreases the slope thereby increasing or decreasing the distance between N and the Dirac point. Note that the Dirac cone occurs along the spatial symmetry path, σ h , of the structure due to the opposite parities of the bands; band repulsion occurs along the N path 22 thereby resulting in a partial band gap along N . If , then the partial gap along N isolates the Dirac cone along a portion of the IBZ path, NX .…”
Section: Resultsmentioning
confidence: 99%
“…Fortunately, the advent of topological insulators in quantum mechanics 9,10 , and their translation into classical systems, has led to waveguides that are more broadband and robust than previous designs 11–15 and ultimately to robust networks 16–20 ; however, the vast majority of the topological energy-splitters are based upon graphene-like hexagonal structures and hence restricted to a two-way partitioning of energy. Herein we rectify this with an intelligently engineered three-way topological energy-splitter, the geometrical design of which is based upon the square lattice 21,22 .…”
Strategically combining four structured domains creates the first ever three-way topological energy-splitter; remarkably, this is only possible using a square, or rectangular, lattice, and not the graphene-like structures more commonly used in valleytronics. To achieve this effect, the two mirror symmetries, present within all fully-symmetric square structures, are broken; this leads to two nondistinct interfaces upon which valley-Hall states reside. These interfaces are related to each other via the time-reversal operator and it is this subtlety that allows us to ignite the third outgoing lead. The geometrical construction of our structured medium allows for the three-way splitter to be adiabatically converted into a wave steerer around sharp bends. Due to the tunability of the energies directionality by geometry, our results have far-reaching implications for applications such as beam-splitters, switches and filters across wave physics.
“…9). Similar to the earlier structure the edge states that arise are topologically nontrivial and gapless 22 .Figure 9 C 4 v even-parity interfacial mode — Left and right columns, panels (a,b), pertain to the orange over blue and blue over orange stackings, respectively. Top panels show eigensolutions obtained from Fourier-Hermite method.…”
Section: Resultssupporting
confidence: 67%
“…The parametric variation afforded to us, and encompassed in the variable , merely increases or decreases the slope thereby increasing or decreasing the distance between N and the Dirac point. Note that the Dirac cone occurs along the spatial symmetry path, σ h , of the structure due to the opposite parities of the bands; band repulsion occurs along the N path 22 thereby resulting in a partial band gap along N . If , then the partial gap along N isolates the Dirac cone along a portion of the IBZ path, NX .…”
Section: Resultsmentioning
confidence: 99%
“…Fortunately, the advent of topological insulators in quantum mechanics 9,10 , and their translation into classical systems, has led to waveguides that are more broadband and robust than previous designs 11–15 and ultimately to robust networks 16–20 ; however, the vast majority of the topological energy-splitters are based upon graphene-like hexagonal structures and hence restricted to a two-way partitioning of energy. Herein we rectify this with an intelligently engineered three-way topological energy-splitter, the geometrical design of which is based upon the square lattice 21,22 .…”
Strategically combining four structured domains creates the first ever three-way topological energy-splitter; remarkably, this is only possible using a square, or rectangular, lattice, and not the graphene-like structures more commonly used in valleytronics. To achieve this effect, the two mirror symmetries, present within all fully-symmetric square structures, are broken; this leads to two nondistinct interfaces upon which valley-Hall states reside. These interfaces are related to each other via the time-reversal operator and it is this subtlety that allows us to ignite the third outgoing lead. The geometrical construction of our structured medium allows for the three-way splitter to be adiabatically converted into a wave steerer around sharp bends. Due to the tunability of the energies directionality by geometry, our results have far-reaching implications for applications such as beam-splitters, switches and filters across wave physics.
“…Numerical studies that demonstrate the robustness of these topological states versus conventional designs for Newtonian systems are found in [50,[53][54][55]. Theoretical studies that demonstrate the existence of these modes under disorder are found in [56,57].…”
Section: D Dispersion Curves and Edge Statesmentioning
We create hybrid topological-photonic localisation of light by introducing concepts from the field of topological matter to that of photonic crystal fiber arrays. S-polarized obliquely propagating electromagnetic waves are guided by hexagonal, and square, lattice topological systems along an array of infinitely conducting fibers. The theory utilises perfectly periodic arrays that, in frequency space, have gapped Dirac cones producing band gaps demarcated by pronounced valleys locally imbued with a nonzero local topological quantity. These broken symmetry-induced stop-bands allow for localised guidance of electromagnetic edge-waves along the crystal fiber axis. Finite element simulations, complemented by asymptotic techniques, demonstrate the effectiveness of the proposed designs for localising energy in finite arrays in a robust manner.
“…On the other hand, “topological acoustics” has attracted considerable attention over the past two years due to the fascinating quantum‐like effects in acoustic systems, which originates from studies of condensed‐matter states . Earlier pioneering approaches in the quest for constructing acoustic topological states in 2D systems relied on circulating fluid flows to mimic the quantum Hall effect, coupled resonator ring waveguides to mimic Floquet topological insulators, phononic “graphene” with double Dirac cones to mimic the quantum spin Hall effect and C 3v point symmetry phononic crystals composed of triangular rods, square lattices containing square inclusions to design a new class of valley‐Hall topological insulators (VHTI) . Furthermore, recently extensions into 3D were launched demonstrating the existence of Weyl points and Fermi arcs in topological acoustics …”
Realizing directional acoustic signal transmittance and reception robust against surrounding noise and competing signals is crucial in many areas such as communication, navigation, and detection for medical and industrial purposes. The fundamentally wide-angled radiation pattern of most current acoustic sensors and transducers displays a major limitation of the performance when it comes to precise targeting and probing of sound particular of interest in human speaking and hearing. Here, it is shown how topological acoustic valley transport can be designed to enable a unique beamforming mechanism that renders a superdirective needle-like sound radiation and reception pattern. The strategy rests on out-coupling valley-polarized edge states, whose beam is experimentally detected in the far-field with 10° width and a sound-intensity enhancement factor ≈10. Furthermore, anti-interference communication is proposed where sound is received from desired directions, but background noise from other directions is successfully suppressed. This type of topological acoustic antenna offers new ways to control sound with improved performance and functionalities that are highly desirable for versatile applications.
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