Complete Band Gap Research Articles

Design of DNA Origami Diamond Photonic Crystals.

Self-assembled photonic crystals have proven to be a fascinating class of photonic materials for nonabsorbing structural colorizations over large areas and in diverse relevant applications, including tools for on-chip spectrometers and biosensors, platforms for reflective displays, and templates for energy devices. The most prevalent building blocks for the self-assembly of photonic crystals are spherical colloids and block copolymers (BCPs) because of the generic appeal of these materials, which can be crafted into large-area 3D lattices. However, because of the intrinsic limitations of these structures, these two building blocks are difficult to assemble into a direct rod-connected diamond lattice, which is considered to be a champion photonic crystal. Here, we present a DNA origami-route for a direct rod-connected diamond photonic crystal exhibiting a complete photonic bandgap (PBG) in the visible regime. Using a combination of electromagnetic, phononic, and mechanical numerical analyses, we identify (i) the structural constraints of the 50 megadalton-scale giant DNA origami building blocks that could self-assemble into a direct rod-connected diamond lattice with high accuracy, and (ii) the elastic moduli that are essentials for maintaining lattice integrity in a buffer solution. A solution molding process could enable the transformation of the as-assembled DNA origami lattice into a porous silicon- or germanium-coated composite crystal with enhanced refractive index contrast, in that a champion relative bandwidth for the photonic bandgap (i.e., 0.29) could become possible even for a relatively low volume fraction (i.e., 16 vol %).

Elastic metamaterial shaft with a stack-like resonator for low-frequency vibration isolation

This paper presents an elastic metamaterial shaft with a new class of stack-like resonators consisting of bonded periodically annular rubber and lead rings that support the formation of ultra-low-frequency vibration band gaps because of reduced stiffness resulting from the discretized rubber rings. By using finite element method, the band structures and the transmission power spectra of the proposed metamaterial shaft are investigated. Subsequently, the mechanism of the band gaps is illustrated by analyzing the displacement fields of extracted mode shapes at the edge of band gaps. Lastly, finite element method is used to explore the effects of geometrical parameters on the band gaps. The related results confirm the very-low-frequency vibration mitigation performance of the proposed meta-shaft below 120 Hz and indicate there is a complete bandgap in which flexural, longitudinal and torsional vibration can be simultaneously attenuated. Moreover, multiple flexural band gaps are observed in the concerned region of frequencies in our design, and the mechanism behind this characteristic is analyzed by eigenmodes. The new structure presented here can thus be used to reduce vibrations of shaft-like structures at low frequencies in the practical environment.

Seismic phononic crystals by elastodynamic Navier equation.

The phenomenon, known as a complete band gap in photonic crystals consisting of periodically arranged manmade nanostructures, caused a huge sensation in photonics. Inspired by the physical methodology, we extend it to large-scale wave propagation for seismic waves. In particular, we exploit the elastodynamic Navier equation in the medium for seismic phononic crystals to induce complete band gaps of body (P) and shear (S) waves. We also show a technique that uses weak formulation to analyze band structures. Estimation of evanescent modes by complex-valued wave vectors yields propagation length, then we redesign bulky phononic crystals to be as thin as possible. We also investigate how material properties affect the relation between propagation length and effective particle velocity. This study will contribute to seismic-resistant techniques in seismology.

Observation and Active Control of a Collective Polariton Mode and Polaritonic Band Gap in Few-Layer WS2 Strongly Coupled with Plasmonic Lattices.

Two-dimensional semiconductors host excitons with very large oscillator strengths and binding energies due to significantly reduced carrier screening. Two-dimensional semiconductors integrated with optical cavities are emerging as a promising platform for studying strong light-matter interactions as a route to explore a variety of exotic many-body effects. Here, in few-layered WS2 coupled with plasmonic nanoparticle lattices, we observe the formation of a collective polaritonic mode near the exciton energy and the formation of a complete polariton band gap with energy scale comparable to the exciton-plasmon coupling strength. A coupled oscillator model reveals that the collective mode arises from the cooperative coupling of the excitons to the plasmonic lattice diffraction orders via exciton-exciton interactions, leading to ultrastrong coupling. The emergence of the collective mode is accompanied by a superlinear increase of the polariton mode splitting as a function of the square root of the exciton oscillator strength. The presence of these many body effects, which are enhanced in systems which lack bulk polarization, not only allows the formation of a collective mode with periodically varying field profiles, but also further enhances the exciton-plasmon coupling. By integrating the hybrid WS2-plasmonic lattice device with a field-effect transistor, we demonstrate active tuning of the collective mode and the polariton band gap. We also report electrically tunable waveguiding in the polariton band gap region through a line defect, which can be turned off with gate bias that can extinguish the collective mode and the polariton band gap. These systems provide new opportunities for obtaining a deeper and systematic understanding of many body cooperative phenomena in two-dimensional materials coupled with periodic photonic systems and for designing more complex and actively controllable polaritonic devices including switchable polariton lasers, waveguides, and optical logical elements.

Higher-order topological states in a three-dimensional acoustic metamaterial

Topologically gapless edge states, characterized by topological invariants and Berry’s phases of bulk energy bands, provide amazing techniques to robustly control the reflectionless propagation of electrons, photons and phonons. Recently, a new family of topological phases, dictated by the bulk polarization, has been observed, leading to the discovery of the higher-order topological insulators. The higher-order topological states located on the “boundaries of boundaries” can be used to limit and control the transmission of optical waves, acoustic waves and elastic waves. So far, the higher-order topological states have been demonstrated in two-dimensional mechanical, electromagnetic, optical, acoustic and elastic systems. However, the study of higher-order topological states in three-dimensional acoustic systems, which can increase the possibility of topological metamaterial design, is rarely reported. In this letter, we propose a three-dimensional acoustic metamaterial supporting topologically protected second-order hinge states along with topologically protected first-order surface states within the same bandgap. Only the nearest neighbor couplings are considered in this metamaterial, and the coupling strengths can be adjusted by changing the diameters of the connection pipes. The intra-cell coupling strength t 1 is proportional to the diameters of the intra-cell connection pipes d 1, and the inter-cell coupling strength t 2 is proportional to the diameters of the inter-cell connecting pipes d 2. The band structure of the unit cell of three-dimensional acoustic metamaterial with the same intra-cell and inter-cell coupling strengths can form a two-fold nodal line along the K-H direction of its Brillouin zone. When intra-cell and inter-cell coupling strengths are different, the two-fold nodal line is lifted to form a complete bandgap, yielding two different kinds of acoustic metamaterials, that are, trivial and topological non-trivial metamaterials. The numerical results of band structures and eigenfrequencies indicate that: When the intra-cell coupling strength t 1 is less than the inter-cell coupling strength t 2, the acoustic metamaterial has 3 second-order hinge bands, 12 first-order surface bands and 18 second-order hinge eigenfrequencies, 72 first-order surface eigenfrequencies in the complete bandgap range respectively; when the inter-cell coupling strength t 2 is less than the intra-cell coupling strength t 1, there is neither any energy bands nor any eigenfrequencies in the complete bandgap range. The second-order hinge states and first-order surface states have great immunity against defects, favorably evidencing the strong robustness of the topological states. The numerical results of the transmission spectra furtherly verify the above phenomena. When t 1 2, the transmission spectrum of the second-order hinge reaches its peak at 4670 Hz. For the first-order surface transmission spectrum, a high peak, located in the bandgap, is observed around 4555 Hz. When t 1 >t 2, the surface and hinge transmission spectra are very low within the complete bandgap, the acoustic energy is concentrated only at the excitation cylinder, showing that the acoustic wave will not propagate in any part of the acoustic metamaterial in the complete bandgap range and the acoustic metamaterial is trivial. The realization of the higher-order topological states in three-dimensional acoustic metamaterial breaks through the limitation of that in two-dimensional system, realizes the topologically transform of acoustic energy among bulk, surface and hinge states and has the potential application prospect in acoustic energy recovery and high-precision acoustic sensor.

Hyperuniform disordered waveguides and devices for near infrared silicon photonics

We introduce a hyperuniform-disordered platform for the realization of near-infrared photonic devices on a silicon-on-insulator platform, demonstrating the functionality of these structures in a flexible silicon photonics integrated circuit platform unconstrained by crystalline symmetries. The designs proposed advantageously leverage the large, complete, and isotropic photonic band gaps provided by hyperuniform disordered structures. An integrated design for a compact, sub-volt, sub-fJ/bit, hyperuniform-clad, electrically controlled resonant optical modulator suitable for fabrication in the silicon photonics ecosystem is presented along with simulation results. We also report results for passive device elements, including waveguides and resonators, which are seamlessly integrated with conventional silicon-on-insulator strip waveguides and vertical couplers. We show that the hyperuniform-disordered platform enables improved compactness, enhanced energy efficiency, and better temperature stability compared to the silicon photonics devices based on rib and strip waveguides.

Hybrid Acoustic Topological Insulator in Three Dimensions.

Topological insulators (TIs), featured by a symmetry-protected gapless surface Dirac cone(s) in their complete energy band gaps, have been extended from condensed-matter physics to classical bosonic systems in the last decade. However, acoustic TIs in three dimensions remain elusive because of a lack of a spin or polarization degree of freedom for longitudinal airborne sound. Here, we experimentally demonstrate a feasible way to hybridize an acoustic TI in three dimensions based on band inversion through a three-dimensional (3D) hybrid Dirac point (HDP). Such a 3D HDP, with linear dispersion in the layer plane while quadratic out of the layer, is distinct from a general point with linear dispersion in all directions. Interestingly, a single nearly gapless conical-like dispersion for acoustic surface states can be achieved at both zigzag and armchair interfaces, supporting robust sound transport. Our findings can serve as a tabletop platform for exploring unique acoustic applications based on the two-dimensional topological interfaces.

Phoamtonic designs yield sizeable 3D photonic band gaps

We show that it is possible to construct foam-based heterostructures with complete photonic band gaps. Three-dimensional foams are promising candidates for the self-organization of large photonic networks with combinations of physical characteristics that may be useful for applications. The largest band gap found is based on 3D Weaire-Phelan foam, a structure that was originally introduced as a solution to the Kelvin problem of finding the 3D tessellation composed of equal-volume cells that has the least surface area. The photonic band gap has a maximal size of 16.9% (at a volume fraction of 21.6% for a dielectric contrast [Formula: see text]) and a high degree of isotropy, properties that are advantageous in designing photonic waveguides and circuits. We also present results for 2 other foam-based heterostructures based on Kelvin and C15 foams that have somewhat smaller but still significant band gaps.

Quantitative Analysis of Photon Density of States for One-Dimensional Photonic Crystals in a Rectangular Waveguide

Light propagation in one-dimensional (1D) photonic crystals (PCs) enclosed in a rectangular waveguide is investigated in order to achieve a complete photonic band gap (PBG) while avoiding the difficulty in fabricating 3D PCs. This work complements our two previous articles (Phys. Rev. E) that quantitatively analyzed omnidirectional light propagation in 1D and 2D PCs, respectively, both showing that a complete PBG cannot exist if an evanescent wave propagation is involved. Here, we present a quantitative analysis of the transmission functions, the band structures, and the photon density of states (PDOS) for both the transverse electric (TE) and transverse magnetic (TM) polarization modes of the periodic multilayer heterostructure confined in a rectangular waveguide. The PDOS of the quasi-1D photonic crystal for both the TE and TM modes are obtained, respectively. It is demonstrated that a “complete PBG” can be obtained for some frequency ranges and categorized into three types: (1) below the cutoff frequency of the fundamental TE mode, (2) within the PBG of the fundamental TE mode but below the cutoff frequency of the next higher order mode, and (3) within an overlap of the PBGs of either TE modes, TM modes, or both. These results are of general importance and relevance to the dipole radiation or spontaneous emission by an atom in quasi-1D periodic structures and may have applications in future photonic quantum technologies.

Highly degenerate photonic flat bands arising from complete graph configurations

Inspired by complete graph theory, we demonstrate that a metallic claw "meta-atom" structure can carry a high number of nearly degenerate resonant modes. A photonic meta-crystal composing of a lattice of such meta-atoms exhibits a large number of flat bands that are squeezed into a narrow frequency window, and these flat bands can be designed to locate in a wide complete 3D bandgap. The degeneracy dimension (Nf) of the flat bands is determined by the number of branches (Nb) of the metallic claw with Nf=Nb-3, which is geometrically related to the complete graph theory. Different from those flat bands emerging from special lattice arrangements (e.g., Kagome lattice), the isolated flat bands here are insensitive to lattice perturbations. The proposed mechanism offers a new platform for realizing various dispersion-less phenomena and a new paradigm to realize high density of states and spectra compressing.

Thermal tuning of negative effective mass density in a two-dimensional acoustic metamaterial with hexagonal lattice

The unique characteristics like periodic and locally resonant behaviors of acoustic metamaterials result in an anomalous response to the wave propagation and exhibit complete elastic wave bandgaps. However, these unusual properties arise from the geometry of the artificially designed metastructure and can be significantly affected under the exposure of the thermal environment. In this paper, we present a thermally tunable two-dimensional acoustic metamaterial with a hexagonal lattice. The numerical results demonstrated that by adjusting the externally applied temperature to the structure and imposing several different load conditions like thermal deformation and thermal stress, a tunable effective mass density of the metamaterial could be obtained. The proposed concept further extends the ongoing research in the field of tunable acoustic metamaterials.

Enhancement of magneto-optical properties in magnetic photonic crystal slab waveguide based on yttrium iron garnet

In this work, a polarization-independent waveguide based on magnetic photonic crystal (MPC) with a triangular lattice of air holes in Yttrium Iron Garnet (YIG) slab grown on alumina (Al2O3) substrate is proposed, where both TE-like and TM-like periodic band gaps overlap. YIG is well known for its attracting magneto-optical (MO) properties and used to produce a coupling between the TE and TM modes. Thus, a nonreciprocal effect can be obtained by applying an external magnetic field parallel to the direction of propagation. At 1550 nm, the complete photonic band gap is simulated and optimized using the three dimensional plane-wave expansion method. The aim of this study is to enhance Faraday rotation (FR) while maintaining a low modal birefringence. A numerical analysis in function of magnetic gyration (g) has been reported, using the BeamProp software. The results reveal a proportional relation between FR, Δn and g, such for g = 0.5, a large FR of 26.11×104 °/cm with Δn = 7×10−6. The results show a real improvement of this MPC structure based on YIG with larger FR, lower modal birefringence and minimal losses. The notable enhancement in the MO behaviour could improve the performance of optical isolators, and makes it suitable for nonreciprocal devices.

Optimal design of lattice structures for controllable extremal band gaps

This paper presents very large complete band gaps at low audible frequency ranges tailored by gradient-based design optimizations of periodic two- and three-dimensional lattices. From the given various lattice topologies, we proceed to create and enlarge band gap properties through controlling neutral axis configuration and cross-section thickness of beam structures, while retaining the periodicity and size of the unit cell. Beam neutral axis configuration and cross-section thickness are parameterized by higher order B-spline basis functions within the isogeometric analysis framework, and controlled by an optimization algorithm using adjoint sensitivity. Our optimal curved designs show much more enhanced wave attenuation properties at audible low frequency region than previously reported straight or simple undulated geometries. Results of harmonic response analyses of beam structures consisting of a number of unit cells demonstrate the validity of the optimal designs. A plane wave propagation in infinite periodic lattice is analyzed within a unit cell using the Bloch periodic boundary condition.

PERIODIC BARRIERS WITH CRUCIFORM TRENCHES FOR SEISMIC SURFACE WAVES

Seismic surface waves with large amplitudes, long distances of propagation and low frequencies can cause great damage to structures. To isolate the seismic Rayleigh surface waves, periodic barriers with cruciform trenches distributed in a homogeneous semi-infinite soil substrate in a square lattice are designed and investigated. By using finite element method, numerical simulations were carried out on the band structures and the frequency responses of the surface wave barriers. The effects of the structure parameters on the complete band gaps were discussed. As an application example, the time-history responses to the Oroville seismic waves were analyzed. The results show that the periodic barriers with cruciform trenches present effective attenuation zones for lower frequencies, and exhibit good performance on the isolation of Oroville seismic surface waves.

Forming Low-Frequency Complete Vibration Bandgaps in a thin Nonmetallic Elastic Metamaterial Plate

Low-frequency vibration-bandgaps in elastic metamaterials open new possibilities to minimize low-frequency vibration and noise. Unfortunately, fabricating a complete vibration bandgap for low frequencies still represents a challenging engineering task. In this paper, a new type of a low-frequency complete vibration bandgap in a thin non-metal elastic metamaterial plate is introduced and investigated numerically. The proposed elastic metamaterial plate consists of decoupling-resonators, which are deposited on a 2D, locally resonant phononic-crystal plate, made of an array of rubber fillers, which are embedded in a nonmetallic plate. The dispersion relationship, the power-transmission spectrum, and the displacement fields for the eigenmode are calculated using the finite element method. It is shown that coupling between the local resonance mode of the decoupling-resonators and the Lamb-wave mode of the epoxy plate, consistent with the modal superposition principle, is responsible for the formation of vibration bandgaps. Moreover, the equivalent spring-mass system for the coupling-resonators can be decoupled by introducing a rubber filler. In addition, both longitudinal and the transverse elastic wave bandgaps can be tuned to the same low-frequency range. As a result, a novel kind of low-frequency complete vibration bandgap, which can damp a low-frequency elastic wave, is produced. Furthermore, the effects of the decoupling-resonators on the vibration bandgap are investigated. It is now possible that an elastic metamaterial plate can be dampen with complete low-frequency vibration bandgaps, which can potentially be used for commercial noise and vibration reduction.

Concentric Split Aluminum with Silicon-Aluminum Nitride Annular Rings Resonators.

This paper presents a novel approach of annular concentric split rings microelectromechanical resonators with tether configuration to reduce anchor loss and gives very high-quality factor (Q) 2.97 Million based on FEA (Finite Element Analysis) simulation. The operating frequencies of these resonators are 188.55 MHz to 188.62 MHz. When the proposed SR (square rectangle) hole shaped one dimensional phononic crystal (1D PnC), and two dimensional phononic crystal (2D PnC) structure consist of very wide and complete band gaps is applied to novel design rings MEMS resonators, the quality factor (Q) further improved to 19.7 Million and 1750 Million, respectively, by using the finite element method. It is also observed that band gaps become closer by reducing the value of filling fraction, and proposed SR PnC gives extensive peak attenuation. Moreover, harmonic response of ring resonator is verified by the perfect match layers (PML) technique surrounded by resonators with varying width 1.5λ, and 3λ effectively reduce the vibration displacement.

The Stability of a Nanoparticle Diamond Lattice Linked by DNA.

The functionalization of nanoparticles (NPs) with DNA has proven to be an effective strategy for self-assembly of NPs into superlattices with a broad range of lattice symmetries. By combining this strategy with the DNA origami approach, the possible lattice structures have been expanded to include the cubic diamond lattice. This symmetry is of particular interest, both due to the inherent synthesis challenges, as well as the potential valuable optical properties, including a complete band-gap. Using these lattices in functional devices requires a robust and stable lattice. Here, we use molecular simulations to investigate how NP size and DNA stiffness affect the structure, stability, and crystallite shape of NP superlattices with diamond symmetry. We use the Wulff construction method to predict the equilibrium crystallite shape of the cubic diamond lattice. We find that, due to reorientation of surface particles, it is possible to create bonds at the surface with dangling DNA links on the interior, thereby reducing surface energy. Consequently, the crystallite shape depends on the degree to which such surface reorientation is possible, which is sensitive to DNA stiffness. Further, we determine dependence of the lattice stability on NP size and DNA stiffness by evaluating relative Gibbs free energy. We find that the free energy is dominated by the entropic component. Increasing NP size or DNA stiffness increases free energy, and thus decreases the relative stability of lattices. On the other hand, increasing DNA stiffness results in a more precisely defined lattice structure. Thus, there is a trade off between structure and stability of the lattice. Our findings should assist experimental design for controlling lattice stability and crystallite shape.

Observation of Complete Photonic Bandgap in Low Refractive Index Contrast Inverse Rod-Connected Diamond Structured Chalcogenides

Three-dimensional complete photonic bandgap materials or photonic crystals block light propagation in all directions. The rod-connected diamond structure exhibits the largest photonic bandgap known to date and supports a complete bandgap for the lowest refractive index contrast ratio down to $n_{high}/n_{low} \sim 1.9$. We confirm this threshold by measuring a complete photonic bandgap in the infrared region in Sn--S--O $(n\sim1.9)$ and Ge--Sb--S--O $(n\sim2)$ inverse rod-connected diamond structures. The structures were fabricated using a low-temperature chemical vapor deposition process via a single-inversion technique. This provides a reliable fabrication technique of complete photonic bandgap materials and expands the library of backfilling materials, leading to a wide range of future photonic applications.

Three channel GHz-ranged demultiplexer in solid-solid phononic crystals

We present the design procedure for the elastic GHz-ranged demultiplexer based on a solid-solid phononic crystal platform. It consists of a T-shaped waveguide with three arms. The PnC platform consists of a square array of infinitely long rods of Tungsten embedded in PMMA background. In order to have a wide band gap, it is essential that constituent materials have large contrast in physical properties. These materials have large contrast in their physical properties and it gives us the possibility of having complete band gaps with low filling fractions. To calculate the band diagram and transmission field map, the finite element method (FEM) has been employed. The main waveguides are made by removing one row or one column of rods. For each arm, the radius of rods is modified to have three different defects. Therefore, the designed demultiplexer can separate three frequencies in the range of GHz. To the best of our knowledge, it is for the first time.

Tunable composite waveguide based on piezoelectric phononic crystal

The acoustic artificial structures with tunable parameters have attracted much research interest in these days. In this paper, we present a tunable composite waveguide based on the piezoelectric phononic crystal shunted by an inductor circuit. A pass band based on local resonance will emerge in the complete band gap through modulating the shunted inductor circuit. This local-resonant pass band can be used to realize a waveguide. Both the work frequency and the shape of this waveguide can be tuned simultaneously by modulating the inductance and the space distribution of the external inductor circuit. For the excellent tunable ability, the proposed tunable composite waveguide could be useful in elastic wave sensors and frequency filters.