Bragg Gap Research Articles

Multiple stopbands and wavefield asymmetry of surface water waves in non-Bragg structures

In this paper, we use laboratory wave tank experiments to study the effect of asymmetry and defects on the bandgaps of surface water waves and use the finite element numerical method to validate our results. We demonstrate here that breaking the mirror symmetry around the midplane of a periodic structure introduces multiple bandgaps in the spectrum caused by the involvement of high-order transverse modes. The results show that the presence of a defect in the structure leads to the formation of a strong defect mode in the Bragg gap, which is localized around the defect element and a weak mode in the induced non-Bragg gap. The results show that the bandgap excited by symmetry breaking is much narrower due to the weak mode coupling. In addition, at the non-Bragg resonance frequency in the defect state, the transverse water surface wavefield distribution around the defect is asymmetric about the midplane of the channel. The multiple transmission modes in the spectrum of the structure can be applied in the design of Bragg reflection-based wave attenuation structures that can help protect shorelines and coastal infrastructure. The asymmetry of the surface wavefield in the non-Bragg gap can be applied in the development of energy harvesting technologies. Due to the generality of wave phenomena in periodic structures, the findings of this research provide a basis for more research in physical acoustics and optics and may lead to the development of cutting-edge appliances, such as bandpass filters.

Transverse mode competition in defect states of a waveguide with corrugated walls

We investigate the defect states arising in the Bragg and non-Bragg gaps by inserting a straight duct into a waveguide with periodically corrugated walls. In periodic waveguides, the Bragg gap is created by the interference of the same transverse modes whereas the different mode coupling leads to the non-Bragg one. Due to the involved high-order modes, there are two defect states observed in the non-Bragg gap while only one in the Bragg gap, indicating that transverse modes play a significant role in the creation of defect states. Furthermore, the frequency of each defect state highly relies on the defect geometries and their band widths can be optimized by the number of waveguide segments. The proposed transverse mode competition analysis reveals the mechanism of frequency shifting and provides an opportunity for guided wave control engineering, which would definitely benefit their applications in various functional devices, such as filters, sensors, and amplifiers.

Electrically controlled lateral shift of the reflected optical beams from a nanocomposite structurally chiral medium

In this paper, we theoretically investigate the influence of an external electric field on the lateral shifts of the reflected right-handed circularly polarized beam from a nanocomposite slab at the edge wavelengths of the photonic bandgaps of the structure. The nanocomposite slab is a non-dissipative dielectric chiral material with the randomly dispersed silver nanoparticles inside it. We show that the increase of the applied electric field results in the decrease of the positive lateral shift at the lower edge of the Bragg gap, while the negative lateral shift at the upper edge of the Bragg gap increases by increasing the applied field. Moreover, we show that the impact of the applied voltage is more noticeable at larger incident angles for both the lower and upper edge wavelengths of the Bragg gap. Also, it is shown that the tilt angle of the chiral structure and the slab thickness have considerable effects on the controlling behavior of the externally applied voltage. Finally, we investigate the effect of the filling fraction of nanoparticles and show that the inclusion of the nanoparticles can change the influence of the applied voltage on the lateral shift of the reflected beams.

Dispersion engineering of two-dimensional photonic crystals composed of graphene-covered tellurium rods

We investigate theoretically the frequency spectrum of two-dimensional photonic crystals using the well-known Dirichlet-to-Neumann (D-to-N) map method. The PhCs with square and triangular arrangements are built by graphene-covered tellurium rods which are surrounded by ion gel. The resulting frequency spectrum represents two forbidden frequency band, termed Bragg and graphene photonic band gaps. It is demonstrated that these forbidden band gaps can be controlled actively by altering the graphene chemical potential through applying external voltage. A tuning range of 4.81 THz and 5.31 THz was achieved for Bragg photonic band gap in square and triangular lattices, respectively, and a wide tuning range of 13.85 THz and 14.69 THz was achieved for graphene photonic band gap, when the chemical potential varies from μc = 0 to μc = 1.2 eV. These achievements may have future applications in some optical devices such as filters, sensors, nano-composites and energy storage devices in THz spectrum.

Terahertz Thermal Sensing by Using a Defect-Containing Periodically Corrugated Gold Waveguide

A terahertz (THz) thermal sensor has been developed by using a periodically corrugated gold waveguide. A defect was positioned in the middle of this waveguide. The periodicities of waveguides can result in Bragg and non-Bragg gaps with identical and different transverse mode resonances, respectively. Due to the local resonance of the energy concentration in the inserted tube, a non-Bragg defect state (NBDS) was observed to arise in the non-Bragg gap. It exhibited an extremely narrow transmission peak. The numerical results showed that by using the here proposed waveguide structure, a NBDS would appear at a resonance frequency of 0.695 THz. In addition, a redshift of this frequency was observed to occur with an increase in the ambient temperature. It was also found that the maximum sensitivity can reach 11.5 MHz/K for an optimized defect radius of 0.9 times the mean value of the waveguide inner tube radius, and for a defect length of 0.2 (or 0.8) times the corrugation period. In the present simulations, a temperature modification of the Drude model was also used. By using this model, the thermal sensing could be realized with an impressive sensitivity. This THz thermal sensor is thereby very promising for applications based on high-precision temperature measurements and control.

Tunable lateral shift of the reflected optical beams from a nanocomposite structurally chiral medium

The lateral shifts of the reflected and transmitted circularly polarized beams from a slab of nanocomposite structurally chiral medium are investigated at the edges of the photonic bandgaps of the structure using the transfer matrix method. The nanocomposite structurally chiral medium consists of the structurally chiral material with the silver nanoparticles randomly dispersed inside it. Due to the presence of metallic nanoparticles, this structure also contains an omnidirectional bandgap in addition to the conventional Bragg gap. By obtaining the co-polarized and cross-polarized reflection and transmission spectra of the structure, we show that only the reflected co-polarized right-handed circularly polarized beam has a considerable lateral shift at the edges of the Bragg gap. Moreover, we have shown that the circularly polarized beams do not have a significant lateral shift at the edges of the nanoparticles created bandgap. We also reveal that the reflected beam experiences a positive lateral shift at the lower edge of the Bragg gap and a negative lateral shift at the upper one. Then we examine the influences of the different parameters, such as the filling fraction of nanoparticles, incidence angle, tilt angle, and slab thickness on the lateral shift of the reflected co-polarized right-handed circularly polarized beam.

Waves over Curved Bottom: The Method of Composite Conformal Mapping

A compact and efficient numerical method is described for studying plane flows of an ideal fluid with a smooth free boundary over a curved and nonuniformly moving bottom. Exact equations of motion in terms of the so-called conformal variables are used. In addition to the previously known applications for shear flows with constant (including zero) vorticity, here a generalization is made to the case of potential flows in uniformly rotating coordinate systems, where centrifugal and Coriolis forces are added to the gravity force. A brief review is given of previous results obtained by this method in a number of physically interesting problems such as modeling of tsunami waves caused by the movement of nonuniform bottom, the dynamics of Bragg (gap) solitons over a spatially periodic bottom profile, the Fermi-Pasta-Ulam (FPU) recurrence phenomenon for waves in a finite pool, the formation of anomalous waves in an opposing nonuniform current, and the propagation of a solitary wave in a shear current and its runup on a depth difference. In addition, a number of new numerical results are presented concerning the nonlinear dynamics of a free boundary in closed rotating containers partially filled with a fluid -- centrifuges of complex shape. In this case, the equations of motion differ in some essential details from those of $x$-periodic systems.

Properties of omnidirectional gap and defect mode of one-dimensional graphene-dielectric periodic structures

We theoretically investigate the optical response of one-dimensional graphene based photonic crystal (1D-GPC) structures with and without defect layer in the low terahertz (THz) frequency region. The 1D-GPC is composed of alternated layers of isotropic dielectric material (SiO2) and graphene monolayer sheets. Using the transfer matrix method (TMM), the effects of several parameters such as the incidence angle, width, thickness, and refractive index of the defect layer and the chemical potential of graphene sheets on the device response will be explored in detail for both TE and TM polarizations. Our simulation results indicate that when a defect layer is introduced, the structure may support two kinds of defect modes. One kind is created in the Bragg gap and the other one is created in the graphene-induced photonic band gap (GIPBG). Our results reveal that a defect mode can appear within the GIPBG only for an optical thickness of the defect layer greater than that of the alternated dielectric layers of the 1D-GPC. While, the defect modes in the Bragg gap may be created by simply breaking of the periodicity of the dielectric lattice. In addition, the resonance frequency of defect mode in the GIPBG is found to be almost insensitive to the incident angle for both polarizations. Moreover, we show that an effective Brewster angle for our structure can be deduced from the variation of the amplitude of defect mode with the incident angle. Our analysis has shown an innovative idea for the realization of tunable broadband reflectors and narrowband filtering devices.

Tunable Tamm states at the interface of a 1D graphene-based photonic crystal and a nonlinear dielectric slab

We investigate the dispersion of the Tamm states at the interface of a 1D graphene-based photonic crystal and a nonlinear dielectric slab. We use the nonlinear transfer matrix method to obtain the dispersion of the Tamm states in both the graphene induced and Bragg gaps in the terahertz region. We explore the spectral tunability of the surface modes by adjusting parameters such as the thickness of the nonlinear slab, the intensity of the surface modes, and the chemical potential of graphene layers. We reveal that the penetration depth of the graphene induced bandgap modes in the uniform environment is several times greater than that of the conventional Bragg gap modes. Also, it is shown that we can improve the penetration depth of the surface modes by adjusting the thickness of the nonlinear slab, the intensity of the Tamm states, or the chemical potential of the graphene layers.

Multiband Hypersound Filtering in Two-Dimensional Colloidal Crystals: Adhesion, Resonances, and Periodicity.

The hypersonic phonon propagation in large-area two-dimensional colloidal crystals is probed by spontaneous micro Brillouin light scattering. The dispersion relation of thermally populated Lamb waves reveals multiband filtering due to three distinct types of acoustic band gaps. We find Bragg gaps accompanied by two types of hybridization gaps in both sub- and superwavelength regimes resulting from contact-based resonances and nanoparticle eigenmodes, respectively. The operating GHz frequencies can be tuned by particle size and depend on the adhesion at the contact interfaces. The experimental dispersion relations are well represented by a finite element method model enabling identification of observed modes. The presented approach also allows for contactless study of the contact stiffness of submicrometer particles, which reveals size effect deviating from macroscopic predictions.

Temperature-switchable mode selector in superconducting photonic crystals based on the Thue–Morse sequence

In this paper, a novel one-dimensional superconducting photonic crystal based on the quasi-periodic Thue–Morse (ThM) arrangement is theoretically investigated by the transfer matrix method, which can switch two transmission properties by controlling ambient temperature. Its transmission spectrum realizes omnidirectional photonic band gap (OBG) characteristics in low-temperature zones (about 10 K) and wide-angle broadband absorption characteristics in high-temperature zones (about 90 K) as the whole structure remains the same in the terahertz regime. The intrinsic reason for switchable functions can be ascribed to the superconducting negative permittivity that is dependent on both temperature and frequency under the superconducting state, which causes an OBG corresponding to the zero-averaged (volume) refractive index (zero- n ¯ ) and broadband absorption induced by high permittivity dissipation. From the numerical results, the OBG from the Bragg gap or absorption bandwidth can be notably tuned by manipulating the periodicity of the ThM sequence and dielectric or superconducting thicknesses. The effects of incident angle and polarization modes on the proposed structure are also considered. We report that the proposed structure has a preeminent zero- n ¯ OBG ranging from 0.1 to 1.7 THz at 10 K and stable broadband absorption for a wide angle (at most 70 deg) in TM mode at 90 K, which provides theoretical guidance for the design and application of the temperature-switchable mode selector.

Flexural band gaps and response attenuation of periodic piping systems enhanced with localized and distributed resonators

Novel metamaterial concepts can be used to economically reduce flexural vibrations in coupled pipe-rack systems. Here, we model pipe on flexible supports as periodic systems and formulate dispersion relations using Floquet-Bloch theory which is verified by a finite element model. Owing to the flexibility of the coupled system, a narrow pass band is created in low frequency regime, in contrast to the case of pipe without any rack. Two types of vibration reduction mechanisms are investigated for pipe with different supports, i.e. simple and elastic support. In order to tune the band gap behaviour, lateral localized resonators are attached at the centre of each unit cell; conversely, the lateral distributed resonators are realized with a secondary pipe existing in the system. The results reveal that both Bragg and resonance type band gaps coexist in piping systems due to the presence of spatial periodicity and local resonance. Although, the response attenuation of a coupled pipe-rack system with distributed resonators is found to be little lower than the case with the localized one, the relatively low stiffness and damping values lead to cheaper solutions. Therefore, the proposed concept of distributed resonators represents a promising application in piping, power and process industries.

Design of output-graded narrow polychromatic filter by using photonic quasicrystals

The properties of one-dimensional photonic quasicrystals built according to one-dimensional-generalized Fibonacci (GF)/Generalized Thue-Morse (GTM) were investigated in order to design an output polychromatic filter. This main aperiodic multilayered structure was made up of alternate two dielectrics materials Silica and Bi4Ge3O12(BGO)with higher and lower refractive indices respectively. The Transfer Matrix Method (TMM) was adopted to calculate the photometric response. The transmittance spectrum exhibited a stacking of similar Bragg gaps (BGs) for specific arrangement (m = n) of GF and GTM. We noted that the positions and the number and size of BGs were sensitive to the constituent of the Photonic quasicrystal (PQC) system and lattice parameter of quasiperiodic sequence. Therefore, these configurations of multilayered stacks can be useful as a graded polychromatic filter.

Non‐Bragg Bands in Acoustic Quasi‐Periodic Fibonacci Waveguides

In this Letter, an algebraic topology analysis on the bandgaps in phononic Fibonacci waveguides consisting of wide and narrow stainless steel pipes is presented. It has been found that the non‐Bragg forbidden gaps can also exist in quasi‐periodic waveguide structures based on the constructed relations between the quasi‐periodic and periodic waveguides. The so‐called non‐Bragg gaps are caused by the resonances between different transverse modes while the same modes with matching longitudinal wavenumbers always result in the traditional Bragg gaps. In the experiments in this study, the observed non‐Bragg gap appears earlier than the Bragg one in the previous generations of Fibonacci sequences, and the sound attenuation is much more intense, because the lower generations with shorter lengths can only provide enough interaction effects in the transverse dimension. The algebraic topology methods and the observations of non‐Bragg gaps in quasi‐periodic waveguides can not only enrich the knowledge on wave structure interactions but also benefit various applications in wave control engineering.

Manipulation of Bragg and graphene photonic band gaps in one-dimensional photonic crystal containing graphene

Using the Kronig-Penney method, we have investigated the photonic band gap properties of one-dimensional photonic crystal composed of dielectric and multilayer dielectric-graphene layers in terahertz frequency region for both electric and magnetic polarizations. The computational results represent two kinds of photonic band gaps (i.e. Bragg and graphene), and the effect of incident angle and chemical potential of graphene nanolayers are investigated on these photonic band gaps. The obtained results show that the width of both band gaps are more influenced by changing the chemical potential of graphene, but the incident angle has little effect. The proposed PC structure can be used for designing tunable optical devices in the terahertz frequency range.

Tunable flexural wave band gaps in a prestressed elastic beam with periodic smart resonators

This paper theoretically studies the propagation of flexural waves in an actively controllable locally resonant (LR) beam. It is shown that the band gaps can be simultaneously tuned by the axial force and the active electrical control actions. In some special cases, a super-wide pseudo-gap resulted from the combination of the resonance and Bragg gaps can be observed. The condition of inducing such pseudo-gap is further obtained with a closed-form expression with respect to the electrical control parameter and the axial force, which can be explored to actively control the broadband pseudo-gap by tuning these two parameters.

Enhanced attenuation due to lattice resonances in a two-dimensional plasma photonic crystal

We describe the experimental generation of a deep attenuation band in a finite size (7 × 7) two-dimensional photonic crystal constructed from an array of gaseous plasma columns. The attenuation band, centered at approximately 6 GHz, is due to the lattice resonance between the localized surface plasmon modes at the edge of the plasma columns and the internal Bragg fields of the photonic crystal. The attenuation band has a nearly 40 dB floor with Q ≈ 1. Enhancements are seen in the extinction of normal incidence transverse electric waves when the localized surface plasmon modes of the plasma columns are shifted into the vicinity of the photonic crystal Bragg resonances. Simulations and experiments are in reasonable agreement and confirm the appearance of a Fano-like profile with deep and broad extinction bands. The broadening of the spectra as surface plasmon modes come into coincidence with Bragg gaps suggests that the Bragg fields couple strongly into the radiating dipoles to drive enhanced damping of the photonic crystal resonance.

Analysis of photonic band gaps in metamaterial-based one-dimensional ternary photonic crystals

In the present work, we propose a one-dimensional ternary photonic crystals composed of alternatively stacked dispersive metamaterial layers including double-negative (electric permittivity e 0), and mu-negative material (μ 0) within some frequency ranges. Various types of photonic band gaps including Bragg gaps, zero-permittivity gap, zero-permeability gap, and a special band gap are, respectively, presented and discussed against the periodic number, thickness of dielectric layer, and incident angle. In the case of normal incidence, the band width, position, and transmittance for the Bragg and special band gaps are related to the thickness of each layer and periodic number. Under the oblique incidence (incident angle 0° < θ < 90°) condition, both the zero-permittivity band gap for TM wave and zero-permeability band gap for TE wave are achieved, which are significantly broadened and blue-shifted with respect to the increase in incident angle. As such, the incident angle-dependent Bragg band gaps and special band gap are also exhibited by selecting TE- and TM-polarized waves, respectively.

Creating the Coupled Band Gaps in Piezoelectric Composite Plates by Interconnected Electric Impedance.

In this paper, we investigate the coupled band gaps created by the locking phenomenon between the electric and flexural waves in piezoelectric composite plates. To do that, the distributed piezoelectric materials should be interconnected via a ‘global’ electric network rather than the respective ‘local’ impedance. Once the uncoupled electric wave has the same wavelength and opposite group velocity as the uncoupled flexural wave, the desired coupled band gap emerges. The Wave Finite Element Method (WFEM) is used to investigate the evolution of the coupled band gap with respect to propagation direction and electric parameters. Further, the bandwidth and directionality of the coupled band gap are compared with the LR and Bragg gaps. An indicator termed ratio of single wave (RSW) is proposed to determine the effective band gap for a given deformation (electric, flexural, etc.). The features of the coupled band gap are validated by a forced response analysis. We show that the coupled band gap, despite directional, can be much wider than the LR gap with the same overall inductance. This might lead to an alternative to adaptively create band gaps.

Zero-frequency Bragg gap by spin-harnessed metamaterial

The Bragg gap that stops wave propagation may not be formed from zero or a very low frequency unless the periodicity of a periodic system is unrealistically large. Accordingly, the Bragg gap has been considered to be inappropriate for low frequency applications despite its broad bandwidth. Here, we report a new mechanism that allows formation of the Bragg gap starting from a nearly zero frequency. The mechanism is based on the finding that if additional spin motion is coupled with the longitudinal motion of a mass of a diatomic mechanical periodic system, the Bragg gap starting from a nearly zero frequency can be formed. The theoretical analysis shows that the effective mass and stiffness at the band gap frequencies are all positive, confirming that the formed stop band is a Bragg gap. The periodic system is realized by a spin-harnessed metamaterial which incorporates unique linkage mechanisms. The numerical and experimental validation confirmed the formation of the low-frequency Bragg gap. The zero-frequency Bragg gap is expected to open a new way to control hard-to-shield low-frequency vibration and noise.