Related papers: Sub-wavelength resonances in two-dimensional multi…
We consider the 3D Schr\"odinger operator $H = H_0 + V$ where $H_0 = (-i\nabla - A)^2$, $A$ is a magnetic potential generating a constant magnetic field of strength $b>0$, and $V$ is a short-range electric potential which decays…
A method combining the Lagrange-mesh and the complex Kohn variational methods is developed for computing the $\mathcal{S}$ matrix of a 2$+$1 elastic scattering in the frame of three-body Coulomb systems. Resonance parameters can be obtained…
We establish a decoupling result for the $P$ and $S$ waves of linear, isotropic elasticity, in the setting of twice-differentiable Lam\'e parameters. Precisely, we show that the $P\leftrightarrow S$ components of the wave propagation…
Electromagnetic response of dielectric resonators with high refractive index is governed by optically induced electric and magnetic Mie resonances facilitating confinement of light with the amplitude enhancement. However, strong…
We study the low-energy two-body scattering in optical lattices with all higher-band effects included in an effective potential, using a renormalization group approach. As the potential depth reaches a certain value, a resonance of low…
We survey functional analytic methods for studying subwavelength resonator systems. In particular, rigorous discrete approximations of Helmholtz scattering problems are derived in an asymptotic subwavelength regime. This is achieved by…
We have studied microwave response of a high-mobility two-dimensional electron system (2DES) contacted by two side electrodes. Using kinetic inductance of the 2DES and inter-electrode capacitance, we have constructed a subwavelength 2D…
Light behaviours in disordered materials have been of research interest primarily at length scales beyond or comparable to the wavelength of light, because order and disorder are often believed to be almost indistinguishable in the…
This work presents a new design for broadband absorption of low-frequency acoustic waves using a thin coating made of subwavelength acoustic resonators arranged periodically on a reflective surface. We first study the associated scattering…
We investigate the propagation of surface acoustic waves (SAWs) in a layered half-space system comprising a continuous, sub-wavelength-thick layer weakly adhering to a substrate. Using finite element simulations, we demonstrate that this…
Interlayer coupling in two-dimensional (2D) layered nanomaterials can provide us novel strategies to evoke their superior properties, such as the exotic flat bands and unconventional superconductivity of twisted layers, the formation of…
This work provides a mathematical framework for elucidating physical mechanisms for confining waves at subwavelength scales in periodic systems of nonlinear resonators. A discrete approximation in terms of the linear capacitance operator is…
We propose a fundamentally new method for the design of metamaterial arrays, valid for any waves modeled by the Helmholtz equation, including scalar optics and acoustics. The design and analysis of these devices is based on eigenvalue and…
Recent experiments (Kudrolli, Pier and Gollub, 1998) on two-frequency parametrically excited surface waves exhibit an intriguing "superlattice" wave pattern near a codimension-two bifurcation point where both subharmonic and harmonic waves…
We observe and analyze d-wave resonant scattering of bosons in tightly confining harmonic waveguides. It is shown that the d-wave resonance emerges in the quasi-1D regime as an imprint of a 3D d-wave shape resonance. A scaling relation for…
We consider the double layer potential (Neumann-Poincar\'e) operator appearing in 3-dimensional elasticity. We show that the recent result about the polynomial compactness of this operator for the case of a homogeneous media follows without…
An incremental wave superimposed on a pre-deformed hyper-elastic material perceives an elastic media with the instantaneous modulus of the current material. This offers a new route with a broadband feature to control elastic waves by…
Elastic waves scattering off a periodic single and double array of thin cylindrical defects is considered for isotropic materials. An analytical expression for the scattering matrix is obtained by means of the Lippmann-Schwinger formalism…
With analytical (generalized Mie scattering) and numerical (integral-equation-based) considerations we show the existence of strong resonances in the scattering response of small spheres with lossless impedance boundary. With increasing…
The interaction between electromagnetic waves and objects is strongly affected by the shape and material composition of the latter. Artificially created materials, formed by a subwavelength structuring of their unit cells, namely…