Existence Of Complete Band Gap Research Articles

Numerical Analysis and Parametric Study of Phononic Band Gap Structures

Phononic band gap crystals (PnCs) are periodic composite materials and well known for their novel property that can prohibit the propagation of mechanical waves in certain range of frequency. This paper develops the finite element method to calculate band structures of bi-material phononic crystals. Through finite element analysis, complete band gap for longitudinal and transverse waves are obtained by characterizing the dispersion relation in phononic crystals. Phononic crystals with different inclusion shapes in a square and hexagonal unit cell are investigated to study the influence of unit cell topology on band gap size. For a specific pattern, the existence of complete band gap in relation to the density and Lamé constant modulus of composites is studied and critical density ratio and Lamé constant ratio of inclusions versus base material for opening complete band gap are given. The results provide theoretical guidance for designing phononic crystals in practical applications.

Periodic co-continuous acoustic metamaterials with overlapping locally resonant and Bragg band gaps

This Letter reports a group of triply periodic co-continuous acoustic metamaterials exhibiting simultaneous wave filtering capability and enhanced mechanical properties. We numerically demonstrate the existence of complete band gaps in these acoustic metamaterials, which is attributed to the coupling effects of local resonances and Bragg scattering. Intrinsically, the coupling effects are governed by the topological arrangements of the co-continuous structures and mechanical properties of constituent phases. We further show that the frequency tunability of the complete band gaps can be achieved by tailoring the geometrical arrangements and volume fraction distribution of the co-continuous acoustic metamaterials. This work provides a clue to the design of mechanically robust acoustic metamaterials to absorb acoustic and elastic waves under harsh environments.

Existence of complete band gaps in 2D steel-water phononic crystal with square lattice

This paper theoretically and experimentally studies the existence of complete band gaps in two-dimensional (2D) phononic crystal consisting of parallel steel rods in water with square lattice. The band structure of phononic crystal is calculated by a plane wave expansion (PWE) method. Based on the well-known ultrasonic immersion transmission technique, the overlapping transmission spectra of acoustic waves, a complete band gap, is experimentally measured along the two high-symmetry directions of the first irreducible Brillouin zone. There is a very good agreement between the experimental result and the range of frequencies of the complete band gap.

Photonic band structure of three-dimensional colloidal crystals with field-induced lattice structure transformation

By utilizing the electrorheological effect, three-dimensional colloidal crystals can be produced, whose lattice structure can be changed from the body-centered-tetragonal lattice to other lattices under the application of electric fields. This paper calculates photonic band structures of such crystals with lattice structure transformation, and demonstrates the existence of complete band gaps for some intermediate lattices. Thus, it becomes possible to use the electrorheological effect to achieve photonic crystals with desired photonic gap properties resulting from tunable structures.

Evidence of complete band gap and resonances in a plate with periodic stubbed surface

In this paper, we numerically and experimentally demonstrate the existence of complete band gaps and resonances in a plate with a periodic stubbed surface. Numerical results show that a complete band gap forms as the stub height reaches about three times the plate thickness. In the experiment, we used a pulsed laser to generate broadband elastic waves and used optical devices as well as point piezoelectric transducers to detect wave signals. The results show that the numerical predictions are in very good agreement with those measured experimentally. Remarkable resonances on the top surface of the stubs are found and discussed.

Photonic band gap properties of 6-fold hybrid triangular photonic crystals formed by holographic lithography

A new kind of two-dimensional (2D) photonic crystals conforming to the 6-fold hybrid triangular configuration formed by holographic lithography is proposed. The relations between their photonic band gap (PBG) properties and their specific holographic designs for both the inverse and the normal structures are systematically investigated. Computations have shown that a series of complete band gaps of large sizes exist over a wide range of system parameters for inverse structures; especially, when the dielectric constant ε = 13.6, the optimized relative PBG can reach 24.1%, among the highest in all 2D structures. Furthermore, complete PBGs can also be obtained in normal structures of this kind even with a much lower dielectric constant contrast such as 5.3 : 1. The evolutions of band gap maps of these structures and their dependence on the structure parameters are demonstrated. The transverse electric and magnetic light propagations are simulated to prove the existence of complete band gaps in normal structures of low dielectric constant and their potential use as waveguides.

Complete band gaps and deaf bands of triangular and honeycomb water-steel phononic crystals

Phononic crystals with triangular and honeycomb lattices are investigated experimentally and theoretically. They are composed of arrays of steel cylinders immersed in water. The measured transmission spectra reveal the existence of complete band gaps but also of deaf bands. Band gaps and deaf bands are identified by comparing band structure computations, obtained by a periodic-boundary finite element method, with transmission simulations, obtained using the finite difference time domain method. The appearance of flat bands and the polarization of the associated eigenmodes is also discussed. Triangular and honeycomb phononic crystals with equal cylinder diameter and smallest spacing are compared. As previously obtained with air-solid phononic crystals, it is found that the first complete band gap opens for the honeycomb lattice but not for the triangular lattice, thanks to symmetry reduction.