Nonlocal Metamaterials Research Articles

Evidence of zero group velocity at the lowest dispersion branch through local interactions

Zero group velocity (ZGV) modes can be utilized in many applications in both optics and acoustics. There exist numerous realizations of metamaterials with ZGVs at higher dispersion branches. However, to engineer the lowest dispersion branch to retain ZGVs, non-local metamaterials with couplings beyond the nearest neighbor are usually at play (i.e., roton-like dispersion). To date, there exists no realization of roton-like dispersion for the lowest branch without non-local couplings. Non-locality, while rich in dynamics, can render designs rather complex. Here, we provide the first experimental evidence of a ZGV point for the lowest dispersion branch within the first Brillouin zone with local interactions. We utilize nonlinear magnetic lattices as a platform to sculpt our dispersion. Our findings might enable the realization of exotic metamaterials with simple designs.

Nonlocal topological states in elastic wave metamaterials with active feedback control

Topological elastic wave metamaterials provide a new mechanism to tune wave energy and provide engineering applications which are difficult to realize by traditional structures. This work reports topological characteristics of nonlocal elastic wave metamaterials with active feedback control. The effects of nonlocal connection on band structures and dynamic behaviors of rectilinear lattices are studied. Then, the honeycomb lattice with nonlocal interactions is investigated, which realizes interface transmission and hybrid order topological states. The introduction of active feedback control systems can change the Young’s modulus of nonlocal metamaterials, which flexibly tune the topological characteristic of elastic waves. According to finite element simulation and experiment, the interface transmission and hybrid order can be generated by active feedback control, which agrees with theoretical predictions.

Gradient continuum model of nonlocal metamaterials with long-range interactions

Compared with classical metamaterials, nonlocal metamaterials have distributed long-range interactions. In this paper, a gradient continuum model is developed to properly predict the dispersive behaviour of a one-dimensional nonlocal metamaterial with long-range interactions. First, a discrete monoatomic model is reconstructed into a supercell model. Then, a Taylor expansion based on supercell model is applied to the continuous displacement field, resulting in a gradient continuum model. The dispersive relation of the gradient continuum model is obtained and compared with discrete supercell model to evaluate its suitability. The proposed gradient continuum model with the eighth-order truncation is found to be enough to capture the dispersion behaviours all over the first Brillouin zone. The results indicate that the proposed gradient continuum model can predict the dispersion behaviour of the one-dimensional nonlocal system very well. Furthermore, the gradient continuous model of two mass-in-mass system with long-range interactions are verified.

Type-II Dirac points and topological Fermi arcs in nonlocal metamaterials

Dirac semimetals are topological materials with degenerated Dirac points in their band structures. In particular, the Dirac points play a central role in the topologically protected phases. Recently, it was reported that the peculiar type-II Dirac points could be realized in photonics by means of photonic crystals (PCs). Nevertheless, the practical implementation is rather challenging. In this paper, we demonstrate that the nonlocal effect in the interior of a homogeneous photonic metamaterial (HPM) enables the existence of type-II Dirac points in the HPM's band structure. With theoretical formulations and numerical evaluations, we discuss the evolution of the HPM's band type and present the interesting transition between type-I and type-II Dirac degeneracy of the HPMs. Remarkably, a pair of the type-II Dirac points can be generated at two different frequencies, which is supported by the mode overlapping in the HPMs with weak nonlocality. The Fermi arc surface states connect the projections of the type-II Dirac points at the boundary between the vacuum and HPMs. The topological protection of the Fermi arc surface states is verified by the reflectionless transmission with sharp corners. Our paper provides a fundamental understanding of topological photonics by type-II Dirac points in HPMs.

Complete and detailed inverse design for any arbitrary dispersion relations via non-local metamaterials

Phononic crystals and vibro-elastic metamaterials are characterized by their dispersion relations—how frequency depends on wave number/vector. While there are many existing methods to solve the forward problem of obtaining the dispersion relation from any arbitrarily given design. The inverse problem of obtaining a design for any arbitrarily given dispersion bands have only had very limited success so far. Here, we report a new design scheme capable of leading to arbitrary dispersion relations by incorporating non-local interactions between unit cells. Considering discrete models of one-dimensional mass-spring chain, we investigate the effects of both local (i.e., springs between the nearest neighbors) and non-local (i.e., springs between the next nearest neighbors and other longer range springs) interactions. First, we derive the general governing equations of non-local phononic chains. Next, we examine all design constraints for a linear, periodic, passive, statically stable, non-gyroscopic, and free-standing system. Finally, we perform analytical calculations and numerical simulations to solve the inverse problems. The results illuminate a new path toward novel wave manipulation functionalities, such as sophisticated combinations of roton-like, maxon-like, undulation-point and other zero-group-velocity (ZGV) modes, as well as multi-wavelength and multi-speed propagations of the same mode at the same frequency.

Splitting of waves in rotor-in-rotor nonlocal metamaterials by internal rotor coupling

Mechanical metamaterials can be used to control wave propagation because they are flexibly adjustable. In this paper, a one-dimensional rotor-in-rotor metamaterial with internal rotor coupling is proposed. This metamaterial introduces a new connection between lattices into a rotor-in-rotor system to produce a nonlocal metamaterial. Meanwhile, a zero-frequency bandgap with negative mass can be obtained. The vibration reduction efficiency of bandgaps is analysed based on the recursive method and numerically verified. Furthermore, wave splitting is found in the rotor-in-rotor metamaterial due to strong equivalent nonlocal interactions. Its dispersion relation shows a “dual wavevector” phenomenon: there are frequency ranges where a positive slope and a negative slope coexist. Numerical simulations using finite cell analysis are performed to validate the wave splitting by calculating the phase velocity and group velocity. The finding of wave splitting in the dual wavevector region is expected to provide new insights to control wave propagation.

Splitting of Waves in Rotor-in-Rotor Nonlocal Metamaterials by Internal Rotor Coupling

Splitting of Waves in Rotor-in-Rotor Nonlocal Metamaterials by Internal Rotor Coupling

On the Topological Structure of Nonlocal Continuum Field Theories

An alternative to conventional spacetime is proposed and rigorously formulated for nonlocal continuum field theories through the deployment of a fiber bundle-based superspace extension method. We develop, in increasing complexity, the concept of nonlocality starting from general considerations, going through spatial dispersion, and ending up with a broad formulation that unveils the link between general topology and nonlocality in generic material media. It is shown that nonlocality naturally leads to a Banach (vector) bundle structure serving as an enlarged space (superspace) inside which physical processes, such as the electromagnetic ones, take place. The added structures, essentially fibered spaces, model the topological microdomains of physics-based nonlocality and provide a fine-grained geometrical picture of field–matter interactions in nonlocal metamaterials. We utilize standard techniques in the theory of smooth manifolds to construct the Banach bundle structure by paying careful attention to the relevant physics. The electromagnetic response tensor is then reformulated as a superspace bundle homomorphism and the various tools needed to proceed from the local topology of microdomains to global domains are developed. For concreteness and simplicity, our presentations of both the fundamental theory and the examples given to illustrate the mathematics all emphasize the case of electromagnetic field theory, but the superspace formalism developed here is quite general and can be easily extended to other types of nonlocal continuum field theories. An application to fundamental theory is given, which consists of utilizing the proposed superspace theory of nonlocal metamaterials in order to explain why nonlocal electromagnetic materials often require additional boundary conditions or extra input from microscopic theory relative to local electromagnetism, where in the latter case such extra input is not needed. Real-life case studies quantitatively illustrating the microdomain structure in nonlocal semiconductors are provided. Moreover, in a series of connected appendices, we outline a new broad view of the emerging field of nonlocal electromagnetism in material domains, which, together with the main superspace formalism introduced in the main text, may be considered a new unified general introduction to the physics and methods of nonlocal metamaterials.

Degenerate-band-edge engineering inspired by nonlocal transformation optics

We address the engineering of degenerate-band-edge effects in nonlocal metamaterials. Our approach, inspired by nonlocal-transformation-optics concepts, is based on the approximation of analytically-derived nonlocal constitutive “blueprints”. We illustrate the synthesis procedure, and present and validate a possible implementation based on multilayered metamaterials featuring anisotropic constituents. We also elucidate the physical mechanisms underlying our approach and proposed configuration, and highlight the substantial differences with respect to other examples available in the topical literature.

Light emission in nonlocal plasmonic metamaterials.

We present analytical and computational studies of light emission in nonlocal metamaterials formed by arrays of aligned plasmonic nanowires. We demonstrate that the emission lifetime in these composites is a complex function of geometrical and material parameters of the system that cannot be reduced to the "trivial" hyperbolic or elliptical dispersion topology of a homogenised metamaterial. In particular, our studies suggest that the Purcell factor can often be maximized when the composite operates in the elliptic regime, with strong radiation coupling to an additional TM-polarized mode supported by the nonlocal composite, in contrast to the accepted "hyperbolicity related" enhancement.