Biperiodic Structure Research Articles

Sound diffusers based on sonic crystals.

A sound diffuser is proposed based on sonic crystals, structures formed by a periodic distribution of cylindrical scatterers in a host medium, which is usually air. The diffuser is a so-called biperiodic structure, as formed by two arrays of sonic crystals with slightly different periodicities. Large diffusivity at low frequencies is achieved when the typical scale of the blocks is much larger than the periodicity of the crystals, determined by its lattice constant. An interpretation of the low frequency behavior of the diffuser is given in the homogenization limit in terms of multiple reflections and interference between the fields scattered by the different blocks. It is also shown that sonic crystal based diffusers enhance time spreading in comparison with other conventional diffusers.

Post-selection free, integrated optical source of non-degenerate, polarization entangled photon pairs

We present an integrated source of polarization entangled photon pairs in the telecom regime, which is based on type II-phasematched parametric down-conversion (PDC) in a Ti-indiffused waveguide in periodically poled lithium niobate. The domain grating - consisting of an interlaced bi-periodic structure - is engineered to provide simultaneous phase-matching of two PDC processes, and enables the direct generation of non-degenerate, polarization entangled photon pairs with a brightness of B = 7 × 10(3) pairs/(s×mW×GHz). The spatial separation of the photon pairs is accomplished by a fiber-optical multiplexer facilitating a high compactness of the overall source. Visibilities exceeding 95 % and a violation of the Bell inequality with S = 2.57±0.06 could be demonstrated.

Low-Threshold Surface Plasmon Lasing using the Band Edge Mode in a Bi-Periodic Groove Array

We study surface plasmon lasing based on periodic and bi-periodic groove arrays etched on a silver substrate. It is interesting to find that the bi-periodic structure can open a clear band gap of surface plasmon polaritons near the first Brillouin zone boundary, and thus it is promising to utilize the band edge modes of surface plasmon polaritons. A low threshold for the surface plasmon lasing effect is demonstrated numerically, owing to the low group velocity of the band edge mode, which provides a feasible way to design surface plasmon lasers.

Homogenization of Maxwell's Equations in Lossy Biperiodic Metamaterials

A novel homogenization technique is proposed for computing the quasi-static effective parameters of the lossy bi-periodic artificial structure materials. This technique is based on the Floquet's Theorem which allows reducing the studied domain to the elementary cell with pseudo-periodic conditions on the lateral sides. The studied domain is extended by adding a vacuum layer in order to impose correctly the Silver-Müler absorbing boundary condition. This homogenization technique is a numerical method using the Finite Element Method and based on the evaluation of the macroscopic fields by averaging the local fields on the elementary cell. The effective constitutive parameters are obtained from the macroscopic fields and inductions. The numerical validation of this approach is presented in 2D and 3D by computing the effective conductivities for square cylinders and cubes suspended in a host isotropic medium. The obtained results are compared to our previous approach based on Unfolding Method and Finite Element Method (UFEM). On the one hand this technique can be applied to homogenize any bi-periodic metamaterial with elementary cells having inclusions of arbitrary geometry and on the other hand it takes into account the effect of the inclusions shape on the effective parameters.

On uniqueness in electromagnetic scattering from biperiodic structures

Consider time-harmonic electromagnetic wave scattering from a biperiodic dielectric structure mounted on a perfectly conducting plate in three dimensions. Given that uniqueness of solution holds, existence of solution follows from a well-known Fredholm framework for the variational formulation of the problem in a suitable Sobolev space. In this paper, we derive a Rellich identity for a solution to this variational problem under suitable smoothness conditions on the material parameter. Under additional non-trapping assumptions on the material parameter, this identity allows us to establish uniqueness of solution for all positive wave numbers.

Factorization Method for Electromagnetic Inverse Scattering from Biperiodic Structures

We investigate the Factorization method as an analytical as well as a numerical tool for solving inverse electromagnetic wave scattering problems from penetrable biperiodic structures in three dimensions. This method constructs a simple criterion whether a given point in space lies inside or outside the penetrable biperiodic structure, yielding a fast imaging algorithm. The required data consists of tangential components of Rayleigh sequences corresponding to (measured) scattered electromagnetic fields. In our setting, the incident electromagnetic fields causing these scattered waves are plane incident electromagnetic waves. We propose, on the one hand, a rigorous analysis for the Factorization method in this electromagnetic plane wave setting, building upon existing results for the method in the context of inverse electromagnetic scattering from bounded objects and of scalar periodic inverse scattering problems. On the other hand, we provide, to the best of our knowledge, the first three-dimensional nume...

Averaging of the magnetic properties of fibrous ferromagnetic composites

Within the framework of the model of regular structures, we average the magnetic properties of fibrous ferromagnetic composites with biperiodic structure. For the general case of packing of the fibers in any cross section, the problem is reduced to finding certain functionals determined from the solutions of a regular integral equation of the corresponding boundary-value problem of magnetostatics for the structure. For a special case of packing of the fibers with circular cross section, the solution is constructed in the form of a series in elliptic functions. As a result, we obtain approximate formulas for the macroparameters of the composites with perfect cells.

A novel back-side light trapping structure for thin silicon solar cells

Decreasing silicon consumption is one of the most important ways of reducing the cost of solar cells. High-quality light trapping provides the possibility of making thinner silicon solar cells without sacrificing optical efficiency. In this work we introduce an advanced bi-periodic back-side structure with promising light trapping properties. The structure combines high coupling efficiency of light to oblique travelling modes with the ability of keeping the light within the solar cell for multiple reflections between the front and the rear side. We have done numerical simulations of light trapping for normal incidence in our structure, and we show that our structure with real materials holds the potential to exceed the light trapping of an ideal Lambertian surface. We also investigate the behaviour of our light trapping structure as a function of incidence angle and state of polarization, and compare it to the Lambertian behaviour.

The linear sampling method for the inverse electromagnetic scattering by a partially coated bi-periodic structure

In this paper, we consider the inverse problem of recovering a doubly periodic Lipschitz structure through the measurement of the scattered field above the structure produced by point sources lying above the structure. The medium above the structure is assumed to be homogenous and lossless with a positive dielectric coefficient. Below the structure is a perfect conductor partially coated with a dielectric. A periodic version of the linear sampling method is developed to reconstruct the doubly periodic structure using the near field data. In this case, the far field equation defined on the unit ball of R^3 is replaced by the near field equation which is a linear integral equation of the first kind defined on a plane above the periodic surface.

A technique for measuring and tuning the accelerating sections

A technique has been developed for measuring and tuning one of the accelerating sections based on a biperiodic structure with on-axis coupling cells for a 1.5-GeV double-sided racetrack microtron before and after the section is brazed. The technology and results of tuning of the microwave power input coupler for the accelerating section are described.

Structural characterization of kerogen in 3.4 Ga Archaean cherts from the Pilbara Craton, Western Australia

Hydrogen-lean kerogen (atomic H/C < 0.46) isolated from the 3.4 Ga Strelley Pool Chert in the North Pole area, Pilbara Craton, Western Australia, were studied by vibrational spectroscopy (Fourier transform infrared (FTIR) spectroscopy and Raman spectroscopy), nuclear magnetic resonance spectroscopy (solid state 13C NMR spectroscopy), catalytic hydropyrolysis followed by gas chromatography mass spectrometry (HyPy–GC–MS), and isotope ratio mass spectrometry (IRMS). The kerogen occurs in sedimentary rocks as clasts and clots deposited together with other detrital materials that are finely disseminated throughout a chert matrix. The bulk kerogen δ 13C values range from −28.3 to −35.8‰. Solid-state 13C NMR spectroscopy and FTIR spectroscopy reveals that the kerogen is highly aromatic ( f a varying from 0.90 to 0.92) and contains only minor aliphatic carbon or carbon-oxygenated (C–O) functionalities. The Raman carbon first-order spectra for the isolated kerogens are typical of spectra obtained from disordered sp 2 carbons with low 2-D ordering (biperiodic structure). The implications of the Raman results show low 2-D ordering throughout the carbonaceous network indicate the incorrect usage of the term graphite in the literature to describe the kerogen or carbonaceous material in the Warrawoona cherts. Hydropyrolysates contain aromatic compounds consisting of 1-ring to 7-ring polycyclic aromatic hydrocarbons which were covalently bound into the kerogen as well as alkanes (linear, branched and cyclic) which were most probably trapped in the microporous network of the kerogen. These PAHs have mainly C1- and C2-alkylation while C 3+-substitued aromatics are low in abundance and do not show a high degree of branched alkylation. For the first time we have shown a correlation between elemental analysis (H/C atomic ratios), Raman spectroscopic parameters ( I D1/ I G, I D1/( I D1 + I G), and L a), and the degree of alkylation of bound polyaromatic molecular constituents generated from HyPy for Archaean kerogens. Similarities in molecular profiles exist between HyPy products of Strelley Pool Chert kerogens and an oil-window-mature Mesoproterozoic kerogen from Roper Group (ca. 1.45 Ga), which is biogenic in origin, suggesting that the Strelley Pool Chert kerogens may also be derived from diagenesis and thermal processing of biogenic organic matter. A combination of Raman spectroscopy, for identifying the least metamorphosed kerogens, used together with HyPy for liberating trapped and bound molecular components of these kerogens, offers a powerful strategy for assessing the origins of Earth's oldest preserved organic matter.

Maxwell's equations in periodic chiral structures

AbstractConsider a time–harmonic electromagnetic plane wave incident on a biperiodic structure in ℝ3. The periodic structure separates two homogeneous regions. The medium inside the structure is chiral and heterogeneous. In general, wave propagation in the chiral medium is governed by Maxwell's equations together with the Drude– Born–Fedorov (constitutive) equations. In this paper, the diffraction problem is formulated in a bounded domain by introducing a pair of transparent boundary conditions. It is then shown that for all but possibly a discrete set of parameters, there is a unique quasi–periodic weak solution to the diffraction problem. Our proof is based on the Hodge decomposition, a compact imbedding result, and the Lax–Milgram Lemma. In addition, an energy conservation for the weak solution is also shown.

On the Diffraction by Biperiodic Anisotropic Structures

This article studies the scattering of electromagnetic waves by a nonmagnetic biperiodic structure. The structure consists of anisotropic optical materials and separates two regions with constant dielectric coefficients. The time harmonic Maxwell equations are transformed to an equivalent strongly elliptic variational problem for the magnetic field in a bounded biperiodic cell with nonlocal boundary conditions. This guarantees the existence of quasiperiodic magnetic fields in H 1 and electric fields in H (curl) solving Maxwell's equations. The uniqueness is proved for all frequencies excluding possibly a discrete set. The analytic dependence of these solutions on frequency and incident angles is studied.

Maxwell's Equations in a Perturbed Periodic Structure

The paper is concerned with electromagnetic wave propagation in a perturbed periodic structure. Consider a time-harmonic electromagnetic plane wave incident on a biperiodic (grating) structure. A single inhomogeneous object is placed inside the biperiodic structure. The scattering problem is to study the electromagnetic field distributions. The problem arises in the study of near-field optics and has recently found many applications in physics and biology. In this paper, an integral representation approach is presented to solve the problem. Using the approach, well-posedness of the model problem is established. In addition, it is shown that the perturbation due to the object is exponentially decaying along the periodic directions of the structure, provided that no surface waves occur.

An Injection and Acceleration System of a Pulsed Race-Track Microtron

A pulsed race-track microtron (RTM) with a maximum beam energy of 70 MeV [1] is described. This device was developed at the Research Institute of Nuclear Physics of Moscow State University (Russia) in cooperation with World Physics Technologies Inc. (USA). For this project, several new elements, including bending magnets (based on rare-earth permanent magnets) [2], a system for injection of the bunched electron beam through a compact α-magnet (also based on permanent magnets [3]), and a rectangular cavity biperiodic structure (RCBS) [4, 5], were developed. Unlike axially symmetric accelerating structures, the RCBS has small transverse dimensions and, as a result, does not present an obstacle for the electron beam traveling in the first orbit. Moreover, the RCBS possesses a quadrupole focusing with the value and sign of the focal power depending on the relationship between the size of the drift aperture and the dimensions of the microtron cavity and on the phase of the microwave field. These properties substantially simplify the RTM design and tuning. Tests, the tuning procedure, and measured characteristics of the injection and acceleration systems of the race-track microtron are described.

On the scattering by a biperiodic structure

On the scattering by a biperiodic structure

Analysis of the diffraction from periodic chiral structures

Consider a time-harmonic electromagnetic plane wave incident on a biperiodic structure in R 3. The periodic structure separates two homogeneous regions. The medium inside the structure is chiral and heterogeneous. In general, wave propagation in the chiral medium is governed by Maxwell's equations together with the Drude-Born-Fedorov (constitutive) equations. In this Note, it is shown that for all but possibly a discrete set of parameters, there is a unique quasiperiodic weak solution to the diffraction problem. Our proof is based on a Hodge decomposition, a compact imbedding result, as well as the Lax-Milgram Lemma.

Variational Approximation of Maxwell's Equations in Biperiodic Structures

Consider a plane wave incident on a biperiodic diffractive structure. The diffraction problem may be modeled by Maxwell's equations with transparent boundary conditions and solved by a finite element method. In this paper, a variational approximation is studied. The well-posedness of the continuous and discretized problems is established in the following sense. In the continuous case, it is shown that the model problem attains a unique ${\cal H}^1$ solution for all but possibly a discrete set of frequencies. In the discrete case, error estimates for the variational (finite element) approximation of the model problem with or without truncation of the nonlocal boundary operators are obtained.

Exact solution of a boundary-value problem for a rectangular checkerboard field

A class of two-phase composite materials with a biperiodic structure is investigated by the methods of complex analysis. Two interface conditions -continuity of normal component of a desired vector w and tangential component of ρw at the contact boundary as well as the double-periodicity condition - are involved in rigorous form. The exact analytic solution of the corresponding generalized Riemann boundary-value problem is obtained. The explicit values of the effective parameters, namely effective resistivity and dissipation of energy of an elementary cell and resistivities along the symmetry axes are calculated in closed analytic form. The coincidence of our formulae with the well-known effective resistivity (conductivity) formula of Keller (1964), Dykhne (1970) and Mendelson (1975) and the dissipation formula of Dykhne (1970) is shown in the case of square checkerboard field. The Keller (1963) identity is generalized for the heterogeneous structure studied.

Disk-and-washer structure with biperiodic support

The disk-and-washer (DAW) linac structure with particular biperiodic washer-support geometries was studied. RF measurements on the DAW model cavities with 2-T and 4-T support configurations were carried out, and the results were compared with SUPERFISH and MAFIA calculation results. The results show that the biperiodic structure can overcome the mode overlapping problem. The support power losses caused by the electric field in addition to the magnetic field are studied. For a β = 1.0, 1300 MHz accelerating structure, the calculated shunt impedance of 71 MΩ/m is expected with a biperiodic 2-L structure which is a variant from the biperiodic 4-T configuration.