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A review is given on the merits of magnetotransport spectroscopy for investigations of the subband structure of dual one-dimensional electron systems (1DES). In particular, spatially coincident and tunnel-coupled vertically stacked dual 1DES are discussed which were prepared by nanolithography with subband spacings of more than 10 meV. Mode coupling between degenerate one-dimensional (1D) subbands depends on the symmetry of the confining potential and the coupling strength. In dual 1DES with different 1D confining potentials each subband structure can be identified by magnetotransport spectroscopy on behalf of the distinct magnetic field dispersions. Exemplarily, mode spectra in longitudinal and transversal applied magnetic fields are discussed for spatially coincident 1DES with an asymmetric vertical component in the 1D confinement. Nearly identical confinement, instead, can be prepared for example in vertically stacked tunnel-coupled 1DES. Here, longitudinal magnetic fields have strong influence on tunnel-coupled modes.

In this paper, we theoretically investigate the propagation characteristics of Lamb wave in a two-dimensional (2D) asymmetric phononic crystal (PC) plate composed of cylinder stubs of different radius deposited on both sides of a thin homogeneous plate. The dispersion relations, transmission spectra and displacement fields of the eigenmodes are calculated by using the finite element method (FEM). Two complete bandgaps (BGs) can be found in low-frequency range and the transmission spectra coincide with the band structures. We investigate the evolution of dispersion relations with the decrease of the upper stub radius. The physical mechanism of the upper stub radius effect is also studied with the displacement fields of the unit cell. Numerical results show that the symmetry of the stub radius can remarkably influence the band structures and the asymmetric double-sided plate exhibits a new bandgap (BG) in lower frequency range due to the coupling between the lower stub’s resonant mode and the plate’s Lamb mode becomes weak and the adjacent bands separate. Moreover, we further investigate the effect of the stub height on the dispersion relations and find that the BGs shift to lower frequency regions with the increase of the stub height. In addition, the BGs’ sensitivity to the upper stub radius and the stub height is discussed. The low-frequency BGs in the proposed PC plate can potentially be used to control and insulate vibration in low frequency range.

We propose a new design to achieve optical waveguide switch. We construct a photonic crystal waveguide with one yttrium iron garnet (YIG) rod array on the two sides of the waveguide. Through the mode analysis, we find in special frequency range a few YIG rods under magnetic field can form the magnetic reflectance wall that blocks the light flow. Removing the magnetic field will delete the reflection wall and let the blocked light to be switched on.

To investigate statistical problem of moderate to low-frequency sound scattering on the two-dimensional (2D) random inhomogeneities of a shallow sea with horizontal boundaries (bottom and surface) and loss local-mode approach has been utilized. An explicit-form solution by quadrature for modal amplitudes as a function of distance is represented. In adiabatic approximation asymptotical estimations have been performed, which demonstrate how medium weak fluctuations influence the local eigenvalues and statistical characteristics of a field. It is shown that general effects previously established while studying the random layered problem keep the force. Spatial scales of statistical influence and laws of dependences are determined. Also it follows from the analysis of the explicit-form solution for modal amplitudes that in this shallow-sea model with horizontal boundaries and in the absence of regular variations of sound speed the coupling of modes is insignificant. General statistical effects are described well within the framework of adiabatic approximation.

In this work, the dynamics of a pulse train propagating through a bimodal optical fiber whose core refractive index varies periodically along its main axis are studied numerically. The mathematical model is based on a coupled system of nonlinear Schrödinger-like equations. First- and second-order dispersions are taken into account, as well as the number of solitons propagating through the fiber. The physical conditions for self-compression of coupled cnoidal waves are obtained and discussed.

A number of previous papers have used the coupled-mode method to assess three-dimensional scattering by cylindrically symmetric anomalies (seamounts, hills) or anomalies which are invariant in a horizontal direction (wedges, ridges). This paper makes an extension to combinations of these two anomaly types. The upper and lower depth boundaries of the anomalies may be flat or irregular, and the sound source may be anywhere in the medium. After a discretization of the anomalies of the two types with laterally homogeneous rings and strips, respectively, an adaptation of the coupled-mode method yields the solution of the pertinent Helmholtz equation. The adaptation involves a combination of Fourier-series summations to handle the ring anomalies and adaptive wavenumber integrations to handle the strip structure. For each anomaly, recursively computed reflection matrices relate the expansion coefficients for incoming and outgoing normal modes. Iterative solution of a linear equation system for the amplitudes of the scattered cylindrical waves from the ring anomalies, involving formulas for transformation between plane and cylindrical waves, yields an expansion of the field. Related expansions allow isolation of partial waves, multiply scattered among the anomalies. The paper includes examples from underwater acoustics and atmospheric acoustics.