Frequency Tunable Phononic Crystal Flat Lens for Subwavelength Imaging

In this paper, we present a thickness-contrast based flat lens for subwavelenth imaging in an aluminum plate. The lens is made of phononic crystal (PC) with a triangular lattice arrangement of through holes drilled over an aluminum plate. Subwave-length imaging is achieved by exploiting the concept of negative refraction of A0 plate mode for the optical dispersion branch of the PC. The wavenumbers are matched at a design frequency by creating a step change in the thickness of the PC-lens and host plate. The thickness-contrast results in refractive index of minus one at the interface of the lens and host plate. Negative refraction-based lens overcomes the diffraction limit and enables focusing of flexural waves in an area less than a square wavelength. We validate the flat lens design at a single design frequency through numerical simulations and experiments. Further, we numerically demonstrate the tunability of the lens design over a broadband frequency range by modifying the thickness-contrast between the lens and host plate. The proposed frequency tunable design is promising for many applications such as ultrasonic inspection, tetherless energy transfer, and energy harvesting, where the localization of wave energy in a small spot is desirable.

Dispersion of Electromagnetic Excitations in a Non-Ideal Microporous Lattice

We develop a numerical model for a defect-containing 2D lattice of microporous lattice with embedded ultracold atomic clusters (quantum dots). It is assumed that certain fractions of quantum dots and micropores are absent, which leads to transformation of polariton spectrum of the structure. The dispersion relations for polaritonic modes are derived as functions of defect concentrations and on this basis the band gap as well as the effective masses of lower and upper dispersion branch polaritons.

X-ray dynamical diffraction analogues of the integer and fractional Talbot effects

The X-ray integer and fractional Talbot effect is studied under two-wave dynamical diffraction conditions in a perfect crystal, for the symmetrical Laue case of diffraction. The fractional dynamical diffraction Talbot effect is studied for the first time. A theory of the dynamical diffraction integer and fractional Talbot effect is given, introducing the dynamical diffraction comb function. An expression for the dynamical diffraction polarization-sensitive Talbot distance is established. At the rational multiple depths of the Talbot depth the wavefield amplitude for each dispersion branch is a coherent sum of the initial distributions, shifted by rational multiples of the object period and having its own phases. The simulated dynamical diffraction Talbot carpet for the Ronchi grating is presented.

A rational framework for dynamic homogenization at finite wavelengths and frequencies

In this study, we establish an inclusive paradigm for the homogenization of scalar wave motion in periodic media (including the source term) at finite frequencies and wavenumbers spanning the first Brillouin zone. We take the eigenvalue problem for the unit cell of periodicity as a point of departure, and we consider the projection of germane Bloch wave function onto a suitable eigenfunction as descriptor of effective wave motion. For generality the finite wavenumber, finite frequency homogenization is pursued in R d via second-order asymptotic expansion about the apexes of ‘wavenumber quadrants’ comprising the first Brillouin zone, at frequencies near given (acoustic or optical) dispersion branch. We also consider the junctures of dispersion branches and ‘dense’ clusters thereof, where the asymptotic analysis reveals several distinct regimes driven by the parity and symmetries of the germane eigenfunction basis. In the case of junctures, one of these asymptotic regimes is shown to describe the so-called Dirac points that are relevant to the phenomenon of topological insulation. On the other hand, the effective model for nearby solution branches is found to invariably entail a Dirac-like system of equations that describes the interacting dispersion surfaces as ‘blunted cones’. For all cases considered, the effective description turns out to admit the same general framework, with differences largely being limited to (i) the eigenfunction basis, (ii) the reference cell of medium periodicity, and (iii) the wavenumber–frequency scaling law underpinning the asymptotic expansion. We illustrate the analytical developments by several examples, including Green's function near the edge of a band gap and clusters of nearby dispersion surfaces.

DISTRIBUTION OF THE RAYLEIGH WAVE ALONG THE BORDER OF THE HALF-SPACE, DESCRIBED BY THE SIMPLIFIED MODEL OF THE COSSERAT

We consider a simplified (reduced) dynamic model of a Cosserat medium, which occupies an intermediate position between the classical dynamic theory of elasticity and the proper Cosserat medium model, which has asymmetry in the stress tensor and the presence of moment stresses. In contrast to the latter, in the simplified model, three of the six elastic constants are zero and, as a result, there is no moment stress tensor. In the two-dimensional formulation for the model of a reduced medium, the problem of the propagation of an elastic surface wave along the half-space boundary was solved. The solution of the equations was described as the sum of the scalar and vector potentials, and only one component of the vector potential is nonzero. It is shown that such a wave, in contrast to the classical surface Rayleigh wave, has a dispersion. In the plane “phase velocity-frequency” for such waves there are two dispersion branches: the lower (acoustic) and upper (optical). With increasing frequency, the phase velocity of the wave related to the lower dispersion branch decreases. The phase velocity of the wave related to the upper dispersion branch increases with increasing frequency. The phase velocity of the surface wave in the entire frequency range exceeds the phase velocity of the bulk shear wave. The stresses and displacements arising in the zone of propagation of the surface wave are calculated.

Dispersion characteristics of surface magnetostatic wave with dissipation

It is shown that the dispersion characteristics of spin surface waves with dissipation unlike undamped waves have the wave number maximum value at which there is a reversal in the dispersion curve of wavenumber downward. This forms the upper branch of the dispersion curve with the inverse dispersion and high attenuation, which gives rise to ambiguous depending on the frequency of the wave vector. Lower primary dispersion branch corresponds to waves with a direct dispersion, attenuation is proportional to the small parameter of dissipation. However, near the wave number maximum value the attenuation coefficient of the waves sharply increases. Some angular and frequency limits of the of surface wave propagation are changed as well.

TIME-RESOLVED STUDY OF PHONON-POLARITONS IN LiTaO3 AT ROOM TEMPERATURE

We present a time-resolved study of phonon-polaritons in the ferroelectric LiTaO 3 at room temperature. The coherent generation and phase-sensitive detection of polaritons, using femtosecond Laser pulses, allow precise determination of polariton frequencies and dephasing times. The experimental data clearly show a resonance at 0.95 THz that has not been found in previous IR and Raman studies. The simultaneous coherent excitation of polaritons in the upper and the lower dispersion branch associated with this resonance leads to the observation of phonon-polariton beats, A quantum-mechanical model of the lowest A 1 lattice vibration in LiTaO 3 is developed, which provides a quantitative description of the low-frequency dielectric response, including the polariton dispersion and dephasing. Within this model, the transition at 0.95 THz can be identified as a classically forbidden tunneling resonance.