Bragg Gap Research Articles

Topology optimization of acoustic mirror-symmetric waveguides for interface states in Bragg and non-Bragg gaps

Topology optimization of acoustic mirror-symmetric waveguides for interface states in Bragg and non-Bragg gaps

Phase manipulation in reflective phase gradient photonic crystals.

Phase gradient photonic crystals (PGPCs) are proposed as promising candidates for phase manipulation and can enable arbitrary electromagnetic functions, such as deflection and focusing. In stark contrast to the proposed metasurfaces, the phase variation in PGPCs arises from simple edge-configuration rather than structure resonance. Moreover, the reflection magnitude maintains a constant of 1 for the reflective case in the Bragg gap, which affords significant convenience in design. Both theoretical and experimental results demonstrate that the deflector based on reflective PGPCs possesses strong angular stability and is applicable across a broadband frequency range. Our work provides a promising avenue for the implementation of phase manipulation on novel optical platforms, facilitating the development of innovative optical devices with distinctive features in the future.

Higher order gaps in the renormalized band structure of doubly aligned hBN/bilayer graphene moiré superlattice

This paper presents our findings on the recursive band gap engineering of chiral fermions in bilayer graphene doubly aligned with hBN. Using two interfering moiré potentials, we generate a supermoiré pattern that renormalizes the electronic bands of the pristine bilayer graphene, resulting in higher order fractal gaps even at very low energies. These Bragg gaps can be mapped using a unique linear combination of periodic areas within the system. To validate our findings, we use electronic transport measurements to identify the position of these gaps as a function of the carrier density. We establish their agreement with the predicted carrier densities and corresponding quantum numbers obtained using the continuum model. Our study provides strong evidence of the quantization of the momentum-space area of quasi-Brillouin zones in a minimally incommensurate lattice. It fills important gaps in the understanding of band structure engineering of Dirac fermions with a doubly periodic superlattice spinor potential.

Sound trapping and waveguiding in locally resonant viscoelastic phononic crystals

We describe the trapping and absorption of audible sound in centimeter-scale claddings of two-dimensional, locally resonant phononic crystals. In a square lattice of local resonators consisting of steel cores and cellulose shells, embedded in a viscous foam, dual acoustic-range band gaps extending from about 200 to 2850 text { Hz} are achieved. The spectral range consists of a low-frequency, local resonance gap, separated from a higher frequency Bragg resonance gap, by narrow bands of slow-sound modes. We demonstrate that thin claddings of such phononic crystal, of only three unit cells in thickness, can effectively prevent sound transmission, by a combination of reflection and absorption, over much of the audible spectrum. Moreover, frequency-selective sound transmission can be enabled by engineering waveguide channels that transmit sound through the local resonance gap, the Bragg gap, or both. This offers a path to sound-sculpting claddings that can surround a noise-generating source. The viscoelastic foam in our cladding is treated using a fractional Voigt model, capable of describing experimentally observed responses.

Quasi-static band gaps in metamaterial pipes with negative stiffness resonators

A novel configuration of periodically supported pipes with negative stiffness resonators (NSRs) at midspans is investigated in this paper. By leveraging the expanded bandwidth and enhanced damping effects offered by the NSRs, as well as the quasi-static (QS) band gaps of periodically supported pipes, this configuration enables the realization of ultrawide QS band gaps. The Floquet-Bloch theorem and Finite Element Method (FEM) are employed to determine the dispersion relationship of the infinite periodic pipe, elucidating the wave propagation characteristics. The band formation mechanism is revealed by conducting a comparative analysis with other systems in which unit cells only comprise periodic supports or NSRs. By analyzing the dispersion relationships, the effects of critical parameters on the transition and interplay between Bragg and local resonance (LR) band gaps are investigated. The results reveal that, with increasing absolute values of the negative stiffness ratio or mass ratio at a constant resonant frequency, the LR band gap created by NSRs eventually transforms into a wide QS band gap. The study further extends to metamaterial pipes of finite length, where FEM simulations are carried out using ANSYS to confirm the physical band-gap properties observed in the periodic systems. The advantage of the wave attenuation bandwidth introduced by NSRs is demonstrated by comparing the results with those obtained by traditional types of resonators. With the same added mass, the system with NSRs exhibits a substantially wider LR band gap than the traditional resonators. Finally, owing to the damping magnification mechanism of NS elements, when a reasonable amount of damping is introduced, the proposed system shows superiority in achieving ultrawide QS band gaps through band-gap merging over pipe systems with suspended resonators.

Superluminal k-Gap Solitons in Nonlinear Photonic Time Crystals.

We propose superluminal solitons residing in the momentum gap (k gap) of nonlinear photonic time crystals. These gap solitons are structured as plane waves in space while being periodically self-reconstructing wave packets in time. The solitons emerge from modes with infinite group velocity causing superluminal evolution, which is the opposite of the stationary nature of the analogous Bragg gap soliton residing at the edge of an energy gap (or a spatial gap) with zero group velocity. We explore the faster-than-light pulsed propagation of these k-gap solitons in view of Einstein's causality by introducing a truncated input seed as a precursor of a signal velocity forerunner, and find that the superluminal propagation of k-gap solitons does not break causality.

Transmission properties in Fibonacci quasi-periodic photonic crystal containing negative-zero-positive index metamaterials

The transmission properties in Fibonacci quasi-periodic photonic crystals containing negative-zero-positive index metamaterials (NZPIM) are investigated systematically. Because of linear dispersion, an asymmetric band gap appears near the optical Dirac point (DP) only at an oblique incidence. Zero- gaps and Bragg gaps exist when the refractive indexes of NZPIM are negative and positive, respectively. We also obtain gaps induced by total reflection on both sides of the DP gap. The corresponding Goos-Hänchen (GH) shifts and phase variations are also demonstrated in detail. It is shown that the characteristics of the band gaps, GH shifts, and phase variations depend crucially on the incident angle, number of periods, and layer thickness.

Electric control of a phononic crystal constituted of Piezoelectric layers using Schottky diode

A one-dimensional piezoelectric phononic crystal (PPC) consisting of a periodic pattern made of two perfectly bonded materials: one active (piezoelectric), the other passive (elastic) and exhibiting a strong acoustic impedance contrast is studied. We are interested in the tunability of piezoelectric inclusions in order to control the propagation of ultrasonic waves in the MHz range from a nonlinear electrical component connected to the terminals of the piezoelectric elements. After modeling the dynamic resistance of the Schottky diode, based on the piezoelectricity equations, a one-dimensional analytical model is proposed to take into account the resistive impedance effect of this diode connected to the electrodes of the active plate. Thus, we have shown that the application of various electrical boundary conditions (EBCs) on the electrodes (open-circuit, short-circuit, connecting an electrical load) allows to change the effective properties of the piezoelectric plate in particular and those of the PPC in general. The dispersion of the waves is then electrically tuned and, depending on the applied EBCs, we have demonstrated numerically the possibility of opening Bragg or hybridization gaps in the PPC band structure.

Polarization-dependent zero-plasma-permittivity, zero-permittivity, and zero-permeability gaps in a 1D photonic crystal composed of lossy double-negative and magnetic cold plasma materials

Theoretically, we have employed a transfer matrix to examine the tunable band structure and transmission properties of a one-dimensional photonic crystal that consists of periodic layers of a lossy double-negative index and magnetic cold plasma materials. Our study shows that the existence of unconventional photonic bandgaps (PBGs) is due to the material dispersion properties of double-negative and magnetic cold plasma layers and fundamentally differs from Bragg gaps, which arise due to an interference mechanism. The two new gaps, called zero-permittivity ( ε = 0 ) and zero-permeability ( μ = 0 ), near the frequency at which the permittivity and permeability of double-negative material change signs, have been found for non-zero incidence angles corresponding to p and s polarizations, respectively. These gaps can be easily tuned as well as enlarged by the application of an external magnetic field in both right-hand and left-hand polarization configurations. At a fixed magnetic field, ε = 0 and μ = 0 gaps corresponding to p and s polarizations, respectively, can be further enhanced by increasing the angle of incidence to higher values. Additionally, we have found a tunable zero-plasma-permittivity ( ε P = 0 ) gap close to the frequency at which the magnetic-field-dependent electric permittivity of a cold plasma layer changes sign at a non-zero incident angle corresponding to p polarization only. Finally, we present a way by which the zero-effective-phase gap, ε = 0 gap, and ε P = 0 gap can be joined together to produce an enlarged PBG at a non-zero incidence angle corresponding to p polarization only in the presence of an external magnetic field of value B L = 0.473 T . The proposed study may be used for designing of polarization triggered tunable optical devices in microwave engineering applications.

Q-Factor Enhancement of Coupling Bragg and Local Resonance Band Gaps in Single-Phase Phononic Crystals for TPOS MEMS Resonator.

This paper presents a type of single-phase double “I” hole phononic crystal (DIH-PnC) structure, which is formed by vertically intersecting double “I” holes. By using the finite element method, the complex energy band curve, special point mode shapes, and different delay lines were calculated. Numerical results showed that DIH-PnC yielded ultra-wide band gaps with strong attenuation. The formation mechanism is attributed to the Bragg-coupled local resonance mechanism. The effects of the pore width in DIH-PnC on the band gaps were further explored numerically. Significantly, as the pore width variable, the position of the local resonance natural frequency could be modulated, and this enabled the coupling between the local resonance and the Bragg mechanism. Subsequently, we introduced this DIH-PnC into the thin-film piezoelectric-on-silicon (TPOS) resonator. The results illustrated that the anchor loss quality factor () of the DIH-PnC resonator was 20,425.1% higher than that of the conventional resonator and 3762.3% higher than the of the cross-like holey PnC resonator. In addition, the effect of periodic array numbers on was researched. When the reached 1.12 × 106, the number of the period array in DIH-PnC only needed to be 1/6 compared with cross-like holey PnC. Adopting the PnC based on the coupling Bragg and local resonance band gaps had a good effect on improving the of the resonator.

Invariant embedding approach to secondary electron emission from metals

Based on an invariant embedding principle for the backscattering function, we calculate the electron emission yield for metal surfaces at very low electron impact energies. Solving the embedding equation within a quasi-isotropic approximation and using the effective mass model for the solid experimental data are fairly well reproduced provided (i) incoherent scattering on ion cores is allowed to contribute to the scattering cascades inside the solid and (ii) the transmission through the surface potential takes into account Bragg gaps due to coherent scattering on crystal planes parallel to the surface as well as randomization of the electron’s lateral momentum due to elastic scattering on surface defects. Our results suggest that in order to get secondary electrons out of metals, the large energy loss due to inelastic electron–electron scattering has to be compensated for by incoherent elastic electron–ion core scattering, irrespective of the crystallinity of the sample.

Multimode propagation in phononic crystals with overlapping Bragg and hybridization effects

Unusual dispersion properties are observed in a phononic crystal of nylon rods in water when the lattice constant is adjusted so that Bragg and hybridization gaps overlap in frequency. On the basis of experimental and numerical analyses of time-dependent transmission and spatial field maps, the presence of two coexisting propagation modes of similar amplitude is demonstrated near the resonance frequency. This phenomenon is attributed to the coupling of the rod resonances arranged in a triangular lattice, with phase shifts driven by the Bragg condition.

Tunable band structures design for elastic wave transmission in tension metamaterial chain

This paper reports a novel band structure manipulation mechanism stemmed from taut strings to shift the Bragg and local resonance band gaps simultaneously. We first developed a metamaterial chain encompassing periodic tighten strings, which are essentially elastic foundations with tunable effective stiffnesses controlled by the tensions of the grounded strings. Subsequently, band edge functions were analyzed against the tension applied, thereby revealing an ultra-wide band gap with a tunable pass band. Nonlinear dispersion characteristics of the proposed system were further corrected by multiple-scale perturbation, and the band gap boundaries are reduced slightly with larger incoming amplitudes. Transmission spectra of the finite specimen indicated reasonable agreement with theoretical analysis. With respect to the band-pass property, a very narrow band filter was achieved with a precise frequency selection. It was shown that, by actively tuning string tensions, broader attenuation bands appear; tightening strings in different locations could be used to control different frequency branches. The space-time distribution of the transmitted wave also confirmed that the pass band would narrow to the specified band by the tension design. This work enables broadband wave blocking and meticulous wave filtering through proper string tensions.

Omnidirectional cylindrical graphene-based Bragg fiber in terahertz

The optical properties of a graphene-based cylindrical photonic crystal are theoretically investigated based on the generalized cylindrical transfer matrix method to include the out-of-plane propagation of the cylindrical waves. It is found that Maxwell's equations have solutions for both E- and H-polarized waves only at the azimuthal mode number m = 1 . We study the reflectance spectrum of the structure to obtain its photonic bandgaps. We show that the reflection spectrum, in addition to the usual Bragg gaps, contains an omnidirectional bandgap at low terahertz frequencies for both E and H-polarized cylindrical waves. The robustness of this bandgap under random variations of geometrical parameters is investigated. This few-period structure is an ideal candidate for guiding waves at the low terahertz region because of its weak absorption and transmission losses. In contrast to the usual Bragg gap, the results show that in both polarizations, the width of graphene-produces bandgap reaches its maximum value when the refractive indices of the two cylindrical shells have their lowest possible values. The width of this unusual omnidirectional bandgap increases by decreasing the thicknesses of the cylindrical shells and increasing the chemical potential of the graphene monolayers.

Interface States in the Acoustic Quasiperiodic System Based on Non‐Bragg Resonances

Bragg resonances have been observed in traditional quasiperiodic waveguides for years. To enhance Bragg resonances and form Bragg gaps with high attenuation, a large number of units have been included. Here, a Fibonacci quasiperiodic acoustic waveguide based on an intense resonance mechanism is proposed to realize non‐Bragg resonances. In a waveguide with fewer units, non‐Bragg resonances can still be excited and create the related non‐Bragg gaps with high attenuation beyond the Bragg ones. Furthermore, an interface state arising in non‐Bragg gaps is experimentally observed by fabricating the mirror‐symmetry structure of Fibonacci quasi‐periodic waveguides. The field distribution of interface states exhibits a significant feature of sound energy, which is localized at a quarter wavelength from the interface of the mirror structures on both sides. Unlike the interface state in Bragg gaps (the localized sound energy distributes along the longitudinal direction), the interface state in non‐Bragg gaps displays localization along the longitudinal and radial directions, and the field distribution is like a dipole, which can be used to optimize traditional quasiperiodic waveguide structures and pave the way for various functional devices, which include multimode filters, sensors, couplers, and so on.

Defect modes in non-Bragg resonant structures for guided surface water waves

We report our experimental observation of a single and stable defect mode arising in the non-Bragg bandgap of surface water waves by introducing a defect element into a water channel with periodically corrugated sidewalls. By investigating the existence of the non-Bragg defect mode and its frequency shifting, we find that unlike the Bragg defect mode which arises within an extended region around the Bragg gap in the spectrum, the non-Bragg type defect mode exists within a much smaller region. It is further proved by the experiments that the frequency shifting property of the defect mode in the non-Bragg gap is comparable to that of the Bragg type. The results show that the location of the defect mode in the bandgap is dependent on the length of the defect element. The ability to tune the defect modes for surface water waves would guide existing and next-generation wave energy control and coastal protection technologies.

Interface states of dipole-like distributions in a quasi-periodic acoustic waveguide

Interface states of dipole-like distributions are experimentally observed in an acoustic waveguide with designed quasi-periodically corrugated walls. Due to the orthogonality breaking of guided transverse modes induced by the wall corrugations, a type of non-Bragg nature forbidden bands can be generated based on the interactions between different transverse modes. An interface state arises from the non-Bragg gap when we connect the two corrugated ducts to form a mirror structure. It is worth noting that the interface state in non-Bragg gaps exhibits two maximum sound pressures with totally opposite phases near the structure interface, while that in traditional Bragg gaps always has only one maximum. Our experimental measurements and numerical analysis reveal that the observed interface state with different mode characteristics is caused by the interaction of different transverse modes, which has the localization effect and high Q factor.

Slanted-eye featured forbidden bands in a water channel with undulated sidewalls

Resonances induced by structure periodicity can always lead to frequency gaps, which are forbidden bands of propagating waves. Besides the traditional Bragg gaps, non-Bragg gaps have been found in periodic waveguides for years, which have been proved to be caused by the different transverse mode interference. Here, we demonstrate another observable slanted-eye feature of non-Bragg gaps by introducing the sidewall corrugations into a water channel. Based on the multiple scale expansion and group theory, we have derived the dispersion relations for water surface waves propagating in a channel with periodically corrugated sidewalls and introduced the resonance selection rule to identify the characteristics of forbidden bands. It has been experimentally found that the creation and enhancement of Bragg and non-Bragg gaps highly depend on the phase difference between the two sidewall corrugations. Furthermore, the non-Bragg nature forbidden bands are quite different from those of Bragg ones when the duty ratio of corrugations varies from 0 to 1. The non-Bragg gaps have unexpectedly formed a slanted-eye structure rather than the Bragg’s normal eye in spectra, though the both forbidden bands experience a process of producing, enhancement, decaying, and disappearing. The slanted-eye feature confirms the different nature of non-Bragg gaps over Bragg ones and could benefit applications in wave control engineering.

Optical properties of molybdenum disulfide based photonic crystal

In this paper, the transmission properties of a one-dimensional photonic crystal containing molybdenum disulfide ( $$MoS_2$$ ) monolayers are studied theoretically using the transfer matrix method. The considered photonic crystal structure contains $$MoS_2$$ monolayers, which are embedded between dielectric layers. It is found that the presence of $$MoS_2$$ causes to creation of a new photonic band gap which is almost omnidirectional and also polarization insensitive. Besides, the spatial distribution of the tangential component of the electric field for a TE-polarized plane wave has been shown for some wavelengths. It is found that the behaviour of the waves from the $$MoS_2$$ induced band gap is different from that of Bragg gaps. Finally, the Gaussian beam propagation inside and outside of the photonic crystal have been simulated using the finite element method for critical wavelengths and different incident angles which verify the behavior of field profiles.

Nonlinear acoustic metamaterial for efficient frequency down-conversion.

Frequency conversion is one of the most important nonlinear wave phenomena that has been widely used in the field of electromagnetic waves for changing signal frequencies. Recently, studies on frequency conversion have been actively performed in the field of acoustics owing to its importance in nonlinear ultrasonic nondestructive evaluation and directional speakers. However, acoustic frequency conversion presents relatively poor efficiency owing to the small amplitudes of the converted frequencies and undesired intermodulation. Herein, we propose an acoustic metamaterial to achieve an efficient frequency down-conversion of acoustic waves. Based on background theory, we discovered that the amplitudes of the converted frequencies are inversely proportional to the cube of the speed of sound. Accordingly, we amplify the converted frequency components by reducing the effective speed of sound by coiling up space while suppressing undesired intermodulation by the Bragg gap. Numerical simulation and analytical results show that efficient frequency down-conversion is possible using the corresponding metamaterial. Additionally, dissipation due to viscosity and boundary layer effects is considered. We expect our study results to facilitate research regarding acoustic frequency conversion.