Biperiodic Structure Research Articles

High-efficiency terahertz-wave generation based on extended interaction oscillator with strongly-coupled 2π mode operation

A slow-wave structure improvement for enhancing the 2π-mode electronic efficiency is embodied in the validation of an extended interaction oscillator (EIO), which has an electronic efficiency of 6.52% at 0.22 THz from particle-in-cell (PIC) calculations. A 2π-mode bi-periodic slow-wave structure (BPSWS) with staggered long and short slots is utilized for optimizing the circuit performance. The proposed BPSWS has the capability of combining the respective advantages for both π and 2π-mode in terms of coupling performance and output performance, thus supporting a strongly-coupled 2π-mode with higher coupling capability. Compared with the typical mono-periodic SWS (MPSWS), the adopted strongly-coupled 2π-mode effectively improves the characteristic impedance M2R/Q by 103% to 66.79 Ω, the coupling coefficient by 66% to 0.497, and the normalized wave-amplitude by 22%. Accordingly, 503 W of average output power can be derived for the BPSWS-EIO with a 25.7 kV and 0.3 A sheet beam injected. Cold-test experiments were conducted, confirming that the 0.22 THz structure exhibits commendable fabrication precision and consistency and thus demonstrates the expected frequency response.

Cation-permselective membranes enabled by synergistic ion channels of crown ethers and anionic sites

The specific interaction existing between crown ethers (CEs) and alkali metal ions serves a dual purpose in both facilitating the selective ion transport across polymeric membranes and exerting a significant influence on the microstructure by means of non-covalent interactions among the CEs. In this study, synergistic ion channels featuring a bi-periodic structure are constructed using both CEs and sulfonate (−SO3−) groups. It is observed that the membranes with reduced water uptake demonstrate enhanced ion permselectivity, attributable to the partial dehydration of ions during binding behavior. The bi-functional membranes exhibit excellent permselectivity for alkali metal ions, particularly K+, Na+ and Li+ ions, over Mg2+ ions. The permselectivity sequence of K+>Na+>Li+ and the notably superior K+/Mg2+ permselectivity, reaching up to 244.43, is attributed to the relatively stable CE-K+ complex within the channels, as supported by molecular dynamics simulations. Specifically, the fabricated membrane is successfully utilized in a 4-stage “ion-distillation” process, achieving an impressive separation factor for K+/Mg2+ over 40,000. The investigation of the synergy between CEs and anionic sites provides valuable insights for the development of cation-permselective membranes.

Study and simulation of cryogenic bi-periodic accelerating structure with TM02 mode

To further enhance the accelerating gradient of accelerators, we designed a cryogenic C-band standing wave bi-periodic accelerating structure for the Shanghai Soft X-ray Free Electron Laser Facility (SXFEL). According to the low-temperature environment, material characteristics and technological conditions, the design is completed and it is decided to design the accelerating structure into a bi-periodic magnetic coupling structure. It is a 17-cell structure consisting of 9 accelerating cavities and 8 coupling cavities. To guarantee the symmetry of the field, the structure is doubly-fed. Operating with the π/2 mode standing wave, it is much less sensitive than the standing-wave structure of π-mode. Additionally, the microwave mode is TM02 in coupling cavities that are larger and even less sensitive than the traditional bi-periodic structure. The shape of the coupling cavity can be redesigned to make it tunable.

Analysis of the Maximum Accelerating Field Limitations for a Biperiodic Structure of the SILA Project Injection Linear Accelerator

Analysis of the Maximum Accelerating Field Limitations for a Biperiodic Structure of the SILA Project Injection Linear Accelerator

A 0.35-THz Extended Interaction Oscillator Based on Overmoded and Bi-Periodic Structure

An improved topology of Extended interaction oscillators (EIO) is presented with enhanced efficiency at 0.35 THz. A bi-periodic ladder-type structure is used for optimizing the performance of the TM $_{{31}}- 2\pi $ mode operation, based on bi-periodic interaction gaps composed of staggered short and long slots. The bi-periodic interaction mechanism permits to operate the circuit with a standing-wave field between the $\pi $ and $2\pi $ modes, thus providing the potential to combine the advantages of both $\pi $ and $2\pi $ modes in terms of both coupling and output performance. The resulting transverse TM31 operating mechanism exhibits a good agreement with the bi-periodic structure in terms of coupling performance, with the short slot length positively correlated with the value of effective characteristic impedance ${M}^{\,{2}}{R}/{Q}$ . The circuit demonstrates attractive coupling and output characteristics by optimization of ${M}^{\,{2}}{R}/{Q}$ and ${Q}_{e}$ . A state-of-the-art value ${M}^{\,{2}}{R}/{Q}$ of 59.69 $\Omega $ and a moderate ${Q}_{e}$ of 2523.52 are achieved for a proposed eight-period ladder-type EIO. An RF power of 540 W is obtained with a 42.5 kV, 0.6 A sheet beam, with 2.1% electronic efficiency at 0.35 THz.

An adaptive edge finite element DtN method for Maxwell’s equations in biperiodic structures

Abstract We consider the diffraction of an electromagnetic plane wave by a biperiodic structure. This paper is concerned with a numerical solution of the diffraction grating problem for three-dimensional Maxwell’s equations. Based on the Dirichlet-to-Neumann (DtN) operator, an equivalent boundary value problem is formulated in a bounded domain by using a transparent boundary condition. An a posteriori error estimate-based adaptive edge finite element method is developed for the variational problem with the truncated DtN operator. The estimate takes account of both the finite element approximation error and the truncation error of the DtN operator, where the former is used for local mesh refinements and the latter is shown to decay exponentially with respect to the truncation parameter. Numerical experiments are presented to demonstrate the competitive behaviour of the proposed method.

Conditional robustness of propagating bound states in the continuum in structures with two-dimensional periodicity

For a periodic structure sandwiched between two homogeneous media, a bound state in the continuum (BIC) is a guided Bloch mode with a frequency in the radiation continuum. Optical BICs have found many applications, mainly because they give rise to resonances with ultra-high quality factors. If the periodic structure has a relevant symmetry, a BIC may have a symmetry mismatch with incoming and outgoing propagating waves of the same frequency and compatible wavevectors, and is considered as protected by symmetry. Propagating BICs with nonzero Bloch wavevectors have been found on many highly symmetric periodic structures. They are not protected by symmetry in the usual sense (i.e., there is no symmetry mismatch), but some of them seem to depend on symmetry for their existence and robustness. In this paper, we show that the low-frequency propagating BICs (with only one radiation channel) on biperiodic structures with an inversion symmetry in the plane of periodicity and a reflection symmetry in the perpendicular direction are robust to symmetry-preserving structural perturbations. In other words, a propagating BIC continues its existence with a slightly different frequency and a slightly different Bloch wavevector, when the biperiodic structure is perturbed slightly preserving the inversion and reflection symmetries. Our study enhances theoretical understanding for BICs on periodic structures and provides useful guidelines for their applications.

Edge finite element method for periodic structures using random meshes

ABSTRACT This paper introduces a new method to impose the periodic boundary conditions on the arbitrary mesh when we use the edge finite element method. By using the Floquet theorem, we reduce the analysis of an infinite bi-periodic structure to an elementary cell with pseudo-periodic conditions on the lateral sides. In this method, we establish a relationship between the electric field circulation along an edge on a face and the circulation of the associated edges on the opposite face. After that, we introduce periodic relations in the finite element system. To show the possibilities of the proposed method, we present two numerical studies and the obtained numerical results are compared to those produced by the existing methods.

Optimization of the S-band side-coupled cavities for proton acceleration

The proton beam with energy around 100 MeV has seen wide applications in modern scientific research and in various fields. However, proton sources in China fall short for meeting experimental needs owing to the vast size and expensive traditional proton accelerators. The Institute of Nuclear Science and Technology of Sichuan University proposed to build a 3 GHz side-coupled cavity linac (SCL) for re-accelerating a 26 MeV proton beam extracted from a CS-30 cyclotron to 120 MeV. We carried out investigations into several vital factors of S-band SCL for proton acceleration, such as optimization of SCL cavity geometry, end cell tuning, and bridge coupler design. Results demonstrated that the effective shunt impedance per unit length ranged from 22.5 to 59.8 MΩ/m throughout the acceleration process, and the acceleration gradient changed from 11.5 to 15.7 MV/m when the maximum surface electric field was equivalent to Kilpatrick electric field. We obtained equivalent circuit parameters of the biperiodic structures and applied them to the end cell tuning; results of the theoretical analysis agreed well with the 3D simulation. We designed and optimized a bridge coupler based on the previously obtained biperiodic structure parameters, and the field distribution un-uniformness was < 1.5% for a two-tank module. The radio frequency power distribution system of the linac was obtained based on the preliminary beam dynamics design.

G-band Rectangular Beam Extended Interaction Klystron Based on Bi-Periodic Structure

A rectangular beam G-band extended interaction klystron (EIK) based on planar bi-periodic slow wave structure (SWS) is proposed. Such structure has the advantages of uniform and strong electric field, as well as the large frequency spacing, which implies that EIK adopting such structure will have strong beam–wave interaction and will be easy to avoid the mode competition. Furthermore, the planar structure is compatible to the microfabrication technology, thus reducing the fabrication difficulty of THz vacuum electron devices with small sizes. Compared with the sheet beam and large beam current, the rectangular beam with small aspect ratio and the decreased current is easy to realize the beam focusing and high power in engineering. Under the voltage of 16.5 kV, current of 0.3 A, and beam size of 0.30 mm × 0.13 mm, particle in cell simulations show a considerable output power of 390 W, with gain of 38.9 dB, efficiency of 7.9%, and relatively wide bandwidth of 800 MHz. The high-frequency structure has been fabricated by computer numerical control method, and the measurement results are close to the simulations. The proposed planar bi-periodic SWS shows certain superiorities in the performance improvement of millimeter-wave and terahertz EIK.

Analysis of time-domain Maxwell's equations in biperiodic structures

This paper is devoted to the mathematical analysis of the diffraction of an electromagnetic plane wave by a biperiodic structure. The wave propagation is governed by the time-domain Maxwell equations in three dimensions. The method of a compressed coordinate transformation is proposed to reduce equivalently the diffraction problem into an initial-boundary value problem formulated in a bounded domain over a finite time interval. The reduced problem is shown to have a unique weak solution by using the constructive Galerkin method. The stability and a priori estimates with explicit time dependence are established for the weak solution.

Time domain scattering for elastic waves in a biperiodic structure

This paper concerns the mathematical analysis of the scattering of anelastic plane wave by a biperiodic structure. The wave propagation isgoverned by the time-domain Navier equation in three dimensions. The method ofa compressed coordinate transformation is developed to reduce equivalently thescattering problem into an initial-boundary value problem formulated in abounded domain over a finite time interval. The reduced problem is shown to havea unique weak solution by using the constructive Galerkin method. The stabilityand a priori estimates with explicit time dependence are established for theweak solution.

Specific features of magnetic domain structure in epitaxial magneto-optical ferrite-garnet films

We describe the experimental studies of both domain and crystal defect structure of magneto-optical bismuth-substituted ferrite-garnet films (FGF) with high Faraday effect. Indentation and scratching (sclerometric) tests of either magnetically uniaxial or easy plane anisotropy (“planar”) films were carried out in parallel with traditional chemical etching. We demonstrate the effect of strong local changes of magnetic anisotropy on the domain structure due to local mechanical stresses. New types of biperiodic domain structure imposed by external stresses were found to exist.

One-dimensional dielectric bi-periodic photonic structures based on ternary photonic crystals

We investigate the transmittivity spectra, fields, and energy distribution of the electromagnetic eigenwaves propagating in a one-dimensional (1D) dielectric photonic crystal [(TiO2/SiO2)NAl2O3]M with two periods formed by unit cells TiO2/SiO2 and (TiO2/SiO2)NAl2O3. Spectra of TE- and TM-modes depend on the geometric parameters of the structure and undergo modifications with the change in the period numbers, layer thicknesses, and incidence angle. Special attention is paid to the applicability of the hybrid effective medium approximation comprising the long-wave approximation and two-dimensional (2 × 2) transfer matrix method. We demonstrate spectral peculiarities of the bi-periodic structure and also show the differences between the band gap spectra of the bi-periodic and ternary 1D dielectric photonic crystals. The presented photonic crystal structure can find its applications in optoelectronics and nanophotonics areas as omnidirectional reflectors, optical ultra-narrow bandpass filters, and antireflection coatings.

A Heuristic Approach to the Determination of the Effective Thermal Conductivity Coefficients of Biperiodic Composite Media

A heuristic approach to determining the effective thermal conductivity coefficients of unidirectionally reinforced biperiodic composite media is suggested allowing one to substantially refine the calculated values of the effective coefficients of transverse thermal conductivity of the indicated compositions by using the simplest partitioning of a periodicity cell into thin layers (subelements) with subsequent application of the simplest formulas of averaging by simple and inverse mixture rules. A comparison of the calculated values of these coefficients with familiar experimental data is made. The good agreement of the prediction with experiment allows an assumption that the method developed can be used for practical calculations of the thermophysical characteristics of fibrous media with biperiodic structure. At the present time the accuracy of more complex structural models of the thermal conductivity of unidirectionally reinforced composites lacks a strict experimental justification.

Design and analysis of photonic crystal biperiodic waveguide structure based optofluidic-gas sensor

We present a photonic crystal (PhC) biperiodic waveguide (BPW) structure for both gas and fluid sensing based on modulation of refractive index (RI) of supercavities. The proposed structure has been designed by creating a BPW in silicon (Si) substrate with triangular array of air holes. This BPW structure consists of an array of supercavities and only the resonant wavelength is allowed to pass through the waveguide while the rest of the wavelengths are reflected by the structure. The principle of sensing is based on the shift of the resonance wavelength of supercavities when infiltrated by any liquid or gas. The transmission spectra of sensor have been analyzed numerically by finite difference time domain (FDTD) method. The proposed design can be utilized as a gas sensor or fluid sensor by selectively filling the holes of supercavities. For gas sensing application, the sensitivity of the sensor has been found to be 610nm per refractive index unit (RIU) with minimum detection limit of 0.0001RIU. Sensitivity of 300nm/RIU with wider RI detection range of 1.0–1.5 is obtained when the structure is used as a fluid sensor.

Problems of Beam Focusing by Electromagnetic Field in Linear Electron Accelerator with Standing Wave, Based on Biperiodic Structure

In the presented paper problems of particles dynamics in linear electron accelerators with standing wave are discussed. The focus of the study is a possibility of use of focusing properties of electromagnetic accelerating field for passing an electronic beam through aperture of biperiodic slow-wave structure (BSS), which will lead to a significant reduction of an accelerator's sizes. The calculation methodology is proposed and results of the study of particle dynamics in accelerators with standing wave based on BSS are presented, which prove a possibility of beam passing without using external focusing elements. The proposed methodology can be used for a calculation and design of linear electron accelerator (LEA).

Effect of Cavity in Bi-periodic Photonic Crystal Switch

In this paper designing of Narrow Band Pass filter which is based on the Bi-periodic structure and its performance is analyzed considering the knowledge of cavity as resonator with the optiFDTDTM software.

Three-dimensional nanotub submicrometer diffraction gratings for solar cells.

Diffraction gratings are a promising approach for reducing reflection and achieving light-trapping in solar cells. Using square lattices as a base structure, we investigate a novel bi-periodic nanotub three-dimensional grating structure and compare it with established textured structures for thin-film and wafer applications. For wafer application, simulations show that optimal AR coated nanotubs demonstrated solar weighted reflectance (SWR) of 2% compared to AR coated square pyramids with values 1.9%. Nanotubs also show SWR below 8% for polar angles to 60°. Simulated short-circuit current thin-film cells with nanotubs using smaller dimensions show higher yields (3-6 mA/cm2 average) compared to square pyramids. For periods greater than 700 nm at aspect ratios of 0.7 and greater, nanotubs have reduced current attributed to the increased planar surface area of the nanotub base, and evident in increased SWR. A simple nanoimprint lithography process was employed in experiments to define a square array of circular holes, utilizing a polydimethylsiloxane (PDMS) stamp applied onto a sol-gel imprint resist. The underlying silicon was then wet etched to produce the nanotub textures of 200 nm height and 513 nm period. AR coated nanotub wafers were produced via plasma enhanced chemical vapor deposition (PECVD), with an experimental and theoretical SWR of 6.4% and 5.4%, respectively.

Guided Mode Resonance Sensor With Enhanced Surface Sensitivity Using Coupled Cross-Stacked Gratings

Cross-stacked gratings are introduced for refractive index sensing based on guided mode resonance (GMR) effect. Reflection from and transmission through cross-stacked gratings is computed after converting the diffraction problem into an equivalent transmission line formulation. This formulation, which lends itself for the analysis of a biperiodic dielectric structure, can be used to calculate diffraction characteristics of the cross-stacked gratings with a high degree of accuracy. With the help of this analysis, it is shown that the cross-stacked gratings possess two mutually coupled GMRs. The method of analysis is then applied to various cross-stacked gratings to estimate their performance when used as a biosensor. It will be shown that, in comparison with conventional single grating GMR sensor with equal available area, a roughly two-fold surface sensitivity, equal bulk sensitivity, and extremely narrow resonance linewidth can be obtained by using cross-stacked gratings. Consequently, this structure improves detection ability of the GMR biosensor particularly for small analyte detection.