Peculiarities of mode spectrum in two-dimensional Bragg structures

Two-dimensional (2D) Bragg structures have been suggested to realize 2D distributed feedback. The 2D Bragg structures can be obtained by providing 2D periodic perturbations of the waveguide surface. Such a structure can be used in a wide variety of applications including high-power microwave electronics and integrated optics. It has been suggested that such structures can be used as passive components such as narrow band mirrors, filters and multiplexers. In this work we present the results of the studies of the properties of such structures at microwave frequencies. It is important to note however that the results are applicable throughout the electromagnetic spectrum.

Making use of field expansion and the equivalent boundary, an analytical model is set up to describe the multi-mode intercoupling in two-dimensional coaxial Bragg structures with either one or both of the conductors corrugated with helical ripples. The coupled-mode equations and the explicit formulae of the coupling coefficients for all possible mode combinations are derived, and the general mode coupling rules are discussed. Based on the analytical model, the dependence of the coupling coefficients on structural parameters of the two-dimensional coaxial Bragg structures with overmoded operation is investigated by numerical calculation. The results show that the additional conductor provides more flexibility for adjustment of coupling coefficients compared with other types of two-dimensional Bragg structures with a single conductor. Taking advantage of this feature, a two-dimensional coaxial Bragg structure can provide strong reflection with high mode purity under overmoded operation by suppressing the parasitic coupling using an optimized combination of corrugated outer and inner conductors. In this way, the structure has potential applications in the design of high-Q improved Bragg resonators for high-power microwave oscillators operating in the millimeter wave or terahertz range.

On vibrations of thin plates with one-dimensional periodic structure

A coaxial backward wave oscillator with a two-dimensional Bragg structure mounted at the exit from the interaction space is studied theoretically and experimentally. Azimuthal wave fluxes arising in this structure permit one to synchronize radiation of different fractions of a tubular relativistic electron beam with a large diameter. A narrowband radiation of the 8-mm range with a megawatt level of power has been obtained in the experimental prototype of the backward wave oscillator. The prototype was implemented on the basis of the Saturn accelerator (300 keV/200 A/1 μs), as the perimeter of the system constituted more than 15 wavelengths.

Wave propagations exhibit direction and frequency selectivity in two-dimensional (2D) periodic structures, which provides possibilities to regulate wave dispersion and bandgap properties. Most of current researches focus on regulations of 1D waves, and there are few works about active regulations of 2D waves, especially in the structures with strong nonlinearities that have remarkable influences on dispersions. In this work, two types of 2D periodic nonlinear lattice structures with piezoelectric springs, which include a monatomic and a diatomic structure, are designed to implement controllable dispersion and propagation direction of 2D waves. Considering the strong nonlinearities caused by the cubic spring, dynamic models of the wave propagations in the two kinds of periodic structures are established, and an improved incremental harmonic balance (IHB) method is developed to implement efficient and accurate calculations of the 2D wave propagation. Influences of active and structural parameters on dispersion and bandgap properties are comprehensively studied, and the regulation ability of the piezoelectric springs is demonstrated where the proportional voltage constant is the active control parameter with particle displacements as the feedback. Results also show that a piezoelectric modulated bandgap and a critical wave vector region are created by positive and negative proportional constants, respectively, which indicate that the structures can be used to filter a wide range of low-frequency long-wavelength noises and waves at particular directions. The properties predicted by the improved IHB method are verified by numerical experiments.

The static and dynamic properties of coupled one-dimensional (1D) and two-dimensional (2D) periodic Ni80Fe20 structures fabricated using deep ultraviolet lithography were systematically studied using broadband ferromagnetic resonance spectroscopy, magneto-optical Kerr effects measurements, and magnetic force microscopy. We have probed the influence of dipolar coupling on the spin configurations and magnetization reversal mechanisms in three different types of magnonic crystals, namely, a 1D chain of coupled ellipsoids arranged in two basic configurations (elements coupled along the major or minor axis) and a 2D noncollinear array of rectangular elements. We observed that the “collective” modes present in the spin wave spectrums for the array are significantly dependent on the geometrical parameters of the magnetic elements, as well as on their arrangement. For instance, the eigenmodes corresponding to the linear chain of ellipsoidal elements are considerably shifted when compared to a continuous film due to the varying demagnetizing field. However, for 2D periodic magnetic structures in which the elements are arranged in a “C” cell configuration with each unit cell comprising of three rectangular elements, we observed the presence of two distinct eigenmodes that vary with the magnitude and orientation of the applied field.

Efficient and accurate method for 2D periodic structures based on the physical features of the transient heat conduction

Acoustic waves localized at the surface of two-dimensional (2D) periodic elastic structures, or 2D phononic crystals, are studied theoretically by taking account of the elastic anisotropy of constituent materials. The surface considered is perpendicular to the axis of a periodic array of cylinders embedded in a background material. The dispersion relations of the surface modes are calculated for circular cylinders of AlAs which form a square lattice in a GaAs matrix. The folding and anisotropy of the surface wave branches, as well as the existence of pseudosurface waves, are found. The stop band distributions of the surface, pseudosurface, and bulk waves are plotted in a form relevant for comparison with ultrasound imaging experiments.

ON THE VIBRATION OF ONE-DIMENSIONAL PERIODIC STRUCTURES

Different analytic methods (perturbation theory in the Born approximation and under Bragg reflection, as well as coupled-wave theory and its modifications) are used to derive and discuss approximate analytic expressions for electromagnetic wave fields in bounded one-dimensional periodic dielectric structures and the corresponding reflection coefficients. The range of validity of each of the analytic solutions is established and it is shown that the modified coupled-wave method, which is valid simultaneously for large and small modulation periods and appreciable modulation depths, has the widest range of validity. The method is used to calculate the reflection coefficients of such structures as functions of the incident-wave frequency, taking into account the finite size of the structures, the properties of the ambient media, absorption, and small nonlinearity and aperiodicity.

In this paper, we present a theory on the formation of exceptional points (EPs) of resonance states in two-dimensional periodic structures. Exceptional points are spectral degeneracies that may occur in non-Hermitian systems for some values of the system parameters. At an EP, two or more eigenfunctions coalesce and their eigenvalues coincide. Due to the local behavior of the eigenvalues and eigenfunction at and near the EPs, they have found important applications in sensing, lasing, unidirectional operations, etc. In this work, we employ the Dirichlet-to-Neumann (DtN) maps and mode matching methods to study EPs of resonance states on two different periodic structures; namely, a slab with a periodic array of circular holes and a slab with two-segment piece-wise constant periodic permittivity. The study reveals that a family of EPs exist continuously as the periodic structures tend to a uniform slab. Furthermore, the EP path continues to exist below the light line and eventually ends at a point that can be accurately determined.

This study reports on the employment of the interference lithography (IL) technique, using photoresist based on the chalcogenide glass (ChG) films, for fabrication of one-dimensional (gratings) and two-dimensional (arrays) periodic plasmonic structures on the surface of glass plates. The IL technique was optimized for patterning of the Au and Al layers and formation of gratings and arrays with a spatial frequency of 2000 mm−1. Optical properties of obtained structures were studied using measurements of spectral and angular dependence of transmission and reflection of polarized light. It was shown that the spectral and angular position of the surface plasmon polariton and local surface plasmon resonance, which are observed in these samples, can be adjusted over a wide range by selecting the geometric parameters of structures and technological modes of their manufacturing.

Numerous materials in micro- or nanoscale hierarchical structures with surface gradients serve as the enablers in directional liquid transportation. However, concurrent high-speed and long-range liquid transport is yet to be fully realized so far. Here, an overall-improved approach is achieved in both water transport distance and velocity aspects using a 2D periodic Janus gradient structure, which is inspired by the Janus-wettable desert beetle back, tapered asymmetric cacti spine, and periodic Nepenthes alata microcavity. This 2D channel can efficiently regulate the kinetics of liquid transport within its confined structure, in which the terminal potential well and periodic Janus topological structure enable sustaining water propelling through a long distance. In addition, the rapidly formed aqueous film facilitates a high initial momentum and fast transport of liquid droplets along the channel, achieving an averaged velocity of over 400mm s-1 and a maximum normalized transport distance of 23.4 for a 3µL droplet, as well as an ultralow liquid volume loss of 6.02% upon high-flux water transport. This scalable, controllable, and easy-fabricable 2D water transport system provides an insightful pathway in realizing high-performance water manipulation and possibly facilitates substantial innovative applications in multidisciplinary fields.

On the Modal Density and Energy Flow Characteristics of Periodic Structures

A meshless collocation method for band structure simulation of nanoscale phononic crystals based on nonlocal elasticity theory