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Despite extensive exploration of acoustic vortices carrying orbital angular momentum (OAM), the generation of acoustic vortices with OAM orientations beyond the conventional longitudinal direction remains largely unexplored. Spatiotemporal (ST) vortices, featuring spiral phase twisting in the ST domain and carrying transverse OAM, have recently attracted considerable interest in optics and acoustics. Here, we report the generation of three-dimensional (3D) ST acoustic vortices with arbitrarily oriented OAM, thereby opening up a new dimension in acoustic OAM control. By utilizing a two-dimensional (2D) acoustic phased array, we introduce two approaches to manipulate the orientation of OAM: through the direct rotation of vortices in 3D space and the intersection of vortices carrying distinct types of OAM. These methods enable unprecedented control over the orientation of acoustic OAM, providing a new degree of freedom in the manipulation of acoustic waves. The arbitrarily oriented OAM holds promise for enhancing acoustic communication by broadening capacity and enabling more complex particle manipulation techniques. Our work establishes a foundation for future explorations into the complex dynamics of novel structured acoustic fields in the ST domain.

Bound states in the continuum (BICs) in photonic crystals represent the unique solutions of wave equations possessing an infinite quality-factor. We design a type of bilayer photonic crystal and study the influence of symmetry and coupling between TE and TM polarizations on BICs. The BIC modes possess $C_{3v}$ symmetry in the x-y plane while the mirror-flip symmetry in the z-direction is broken, and they provide selective coupling into different layers by varying frequency. The enhanced TE-TM coupling due to broken mirror-flip symmetry in the z-direction gives rise to high-Q factor BIC states with unique spatial characteristics. We show the emergence of such BIC states even in the presence of coupling between the TE- and TM-like modes, which is different from the existing single polarization BIC models. We propose to study BICs in multilayer systems, and the results may be helpful in designing photonic settings to observe and manipulate BICs with various symmetries and polarizations for practical applications., Comment: 15 pages, 6 figures

The explorations of the quantum-inspired symmetries in optical and photonic systems have witnessed immense research interests both fundamentally and technologically in a wide range of subjects of physics and engineering. One of the principal emerging fields in this context is non-Hermitian physics based on parity-time symmetry, originally proposed in the studies pertaining to quantum mechanics and quantum field theory, recently ramified into diverse set of areas, particularly in optics and photonics. The intriguing physical effects enabled by non-Hermitian physics and PT symmetry have enhanced significant applications prospects and engineering of novel materials. In addition, it has observed increasing research interests in many emerging directions beyond optics and photonics. This Review paper attempts to bring together the state of the art developments in the field of complex non-Hermitian physics based on PT symmetry in various physical settings along with elucidating key concepts and background and a detailed perspective on new emerging directions. It can be anticipated that this trendy field of interest can be indispensable in providing new perspectives in maneuvering the flow of light in the diverse physical platforms in optics, photonics, condensed matter, opto-electronics and beyond, and offer distinctive applications prospects in novel functional materials., Comment: 88 Pages, 18 Figures

Two-dimensional (2D) coupled resonant optical waveguide (CROW), exhibiting topological edge states, provides an efficient platform for designing integrated topological photonic devices. In this paper, we propose an experimentally feasible design of 2D honeycomb CROW photonic structure. The characteristic optical system possesses two-fold and three-fold Dirac points at different positions in the Brillouin zone. The effective gauge fields implemented by the intrinsic pseudo-spin-orbit interaction open up topologically nontrivial bandgaps through the Dirac points. Spatial lattice geometries allow destructive wave interference, leading to a dispersionless, nearly-flat energy band in the vicinity of the three-fold Dirac point in the telecommunication frequency regime. This nontrivial nearly-flat band yields topologically protected edge states. The pertinent physical effects brought about due to non-Hermitian gain/loss medium into the honeycomb CROW device are discussed. The generalized gain-loss lattice with parity-time symmetry decouples the gain and the loss at opposite zigzag edges, leading to purely gain or loss edge channels. Meanwhile, the gain and loss effects on the armchair boundary cancel each other, giving rise to dissipationless edge states in non-Hermitian optical systems. These characteristics underpin the fundamental importance as well as the potential applications in various optical devices such as polarizers, optical couplers, beam splitters and slow light delay lines., Comment: 16 pages, 4 figures

The topological properties in topological superconductors are usually characterized by the bulk Chern numbers, edge-state spectra, and Majorana zero modes. Whether they are equivalent or inequivalent is not well understood. Here, we investigate this issue with focus on a checkerboard-lattice model combining the Chern insulator and chiral $p$-wave superconductivity. Multiple topologically superconducting phases with Chern numbers up to $\mathcal{N}=4$ are produced. We explicitly demonstrate the mismatch between the Chern numbers, edge states and Majorana zero modes in this two-dimensional topological-superconductor model. The intrinsic reason is that some edge states in the superconducting phases inherited from the Chern-insulator phase are not protected by the particle-hole symmetry. We further check the mismatches in vortex states. Our results therefore clarify these different but complementary topological features and suggest that further considerations are required to characterize various topological superconductors., Comment: 14 pages, 5 figures

Precise control of elastic waves in modes and coherences is of great use in reinforcing nowadays elastic energy harvesting/storage, nondestructive testing, wave-mater interaction, high sensitivity sensing and information processing, etc. All these implementations are expected to have elastic transmission with lower transmission losses and higher degree of freedom in transmission path. Inspired by topological states of quantum matters, especially quantum spin Hall effects (QSHEs) providing passive solutions of unique disorder-immune surface states protected by underlying nontrivial topological invariants of the bulk, thus solving severe performance trade-offs in experimentally realizable topologically ordered states. Here, we demonstrate experimentally the first elastic analogue of QSHE, by a concise phononic crystal plate with only perforated holes. Strong elastic spin-orbit coupling is realized accompanied by the first topologically-protected phononic circuits with both robustness and negligible propagation loss overcoming many circuit- and system-level performance limits induced by scattering. This elegant approach in a monolithic substrate opens up the possibility of realizing topological materials for phonons in both static and time-dependent regimes, can be immediately applied to multifarious chip-scale devices with both topological protection and massive integration, such as on-chip elastic wave-guiding, elastic splitter, elastic resonator with high quality factor, and even (pseudo-)spin filter.

Discovery of novel topological orders of condensed matters is of a significant interest in both fundamental and applied physics due to the associated quantum conductance behaviors and unique symmetry-protected backscattering-immune propagation against defects, which inspired similar fantastic effects in classical waves system, leading to the revolution of the manipulation of wave propagation. To date, however, only few theoretical models were proposed to realize acoustic topological states. Here, we theoretically and experimentally demonstrate a two dimensional acoustic topological insulators with acoustic analogue of quantum spin Hall Effect. Due to the band inversion mechanism near the double Dirac cones, acoustic one-way pseudospin dependent propagating edge states, corresponding to spin-plus and spin-minus, can be observed at the interface between two graphene-like acoustic crystals. We have also experimentally verified the associated topological immunity of such one-way edge states against the different lattice defects and disorders, which can always lead to inherent propagation loss and noise. We show that this unique acoustic topological phenomenon can offer a new promising application platform for the design of novel acoustic devices, such as one-way sound isolators, acoustic mode switchers, splitters, filters etc., Comment: 13 pages, 3 figures

Symmetry-protected photonic topological insulator exhibiting robust pseudo-spin-dependent transportation, analogous to quantum spin Hall (QSH) phases and topological insulators, are of great importance in fundamental physics. Such transportation robustness is protected by time-reversal symmetry. Since electrons (fermion) and photons (boson) obey different statistics rules and associate with different time-reversal operators (i.e., Tf and Tb, respectively), whether photonic counterpart of Kramers degeneracy is topologically protected by bosonic Tb remains unidentified. Here, we construct the degenerate gapless edge states of two photonic pseudo-spins (left/right circular polarizations) in the band gap of a two-dimensional photonic crystal with strong magneto-electric coupling. We further demonstrated that the topological edge states are in fact protected by Tf rather than commonly believed Tb and their pseudo-spin dependent transportation is robust against Tf invariant impurities, discovering for the first time the topological nature of photons. Our results will pave a way towards novel photonic topological insulators and revolutionize our understandings in topological physics of fundamental particles., Comment: 20 pages, 4 figures

We propose an optical counterpart of the quantum spin Hall (QSH) effect in a two-dimensional photonic crystal composed of a gyrotropic medium exhibiting both gyroelectric and gyromagnetic properties simultaneously. Such QSH effect shows unidirectional polarization-dependent transportation of photonic topological edged states, which is robust against certain disorders and impurities. More importantly, we find that such unique property is not protected by conventional time-reversal symmetry of photons obeying the Bosonic statistics but rather by the same symmetry, as electron's time-reversal symmetry. Based on the tight-binding approximation approach, we construct an effective Hamiltonian for this photonic structure, which is shown to have a similar form to that of an electronic QSH system. Furthermore, the invariant of such model is calculated in order to unify its topological non-trivial character. Our finding provides a viable way to exploit the optical topological property, and also can be leveraged to develop a photonic platform to mimic the spin properties of electrons., Comment: 20 pages, 5 figures

Larval zebrafish exhibit a variety of complex undulatory swimming patterns. This repertoire is controlled by the 300 neurons projecting from brain into spinal cord. Understanding how descending control signals shape the output of spinal circuits, however, is nontrivial. We have therefore developed a segmental oscillator model (using NEURON) to investigate this system. We found that adjusting the strength of NMDA and glycinergic synapses enabled the generation of oscillation (tail-beat) frequencies over the range exhibited in different larval swim patterns. In addition, we developed a kinematic model to visualize the more complex axial bending patterns used during prey capture., Comment: 7 pages with five embedded figures. Presented at "Computational Neuroscience 2004" conference in Baltimore, Maryland. To be published in conference proceedings in Neurocomputing