Arbitrary Periodic Structures Research Articles

Low-Overhead RF Impedance Measurement Using Periodic Structures

Due to the need for higher reliability and performance from RF circuits, multi-port reflectometers are increasingly used as low-overhead impedance monitors. In this work, using periodic structures as multi-ports is proposed. Periodic structures impose a new constraint on the multi-port theory and simplify it significantly. This simplification leads to closed form solution for calibration and measurement procedures. The closed-form solution also shows that any arbitrary periodic structure will always have a unique solution for both procedures. Therefore, the proposed technique does not rely on frequency-dependent behavior of devices, such as directivity and phase shift to measure impedance. This fact leads to increased bandwidth and simplified design procedure. In addition, proposed multi-port structures can be calibrated by using fewer known loads than existing multi-port techniques. This fact, coupled with the closed-form solution, reduces computation overhead and test time. The theory and its robustness against non-idealities, such as part-to-part variation, are verified with Monte-Carlo simulations. A practical embodiment of the technique is demonstrated with EM simulations and hardware experiments. In this embodiment, the multi-port structure is embedded into an LC matching network. Hardware experiments show that the embedded multi-port structure can measure test loads with high accuracy from 1.5 GHz to 3.5 GHz, without degrading matching network performance.

Multimodal antireflective coatings for perfecting anomalous reflection from arbitrary periodic structures

Metasurfaces possess vast wave-manipulation capabilities, including reflection and refraction of a plane wave into non-standard directions. This requires meticulously-designed sub-wavelength meta-atoms in each period of the metasurface which guarantee unitary coupling to the desired Floquet-Bloch mode or, equivalently, suppression of the coupling to other modes. Herein, we propose an entirely different scheme to achieve such suppression, alleviating the need to devise and realize such dense scrupulously-engineered polarizable particles. Extending the concept of anti-reflective coatings to enable simultaneous manipulation of multiple modes, we show theoretically and experimentally that a simple superstrate consisting of only several uniform dielectric layers can be modularly applied to \textit{aribtrary} periodic structures to yield perfect anomalous reflection. This multimodal anti-reflective coating (MARC), designed based on an analytical model, presents a conceptually and practically simpler paradigm for wave-control across a wide range of physical branches, from electromagnetics and acoustics to seismics and beyond.

Relativistic positrons dynamics in the electrostatic field of perfect periodic positively charged structures

In this paper, the channeling effect is considered, which consists in the ability of charged particles to penetrate relatively large distances into the interior of the crystal, in which particles move in the interplanar space and are affected by an electrostatic field created by ions of the crystal lattice. Interest in this effect arises due to the fact that channeling is accompanied by directed electromagnetic radiation. This was facilitated, on the one hand, by the versatility and complexity of the problem from a theoretical point of view and, on the other hand, by the practical possibility of using such radiation, the parameters of which can vary in a wide range by changing the parameters of the crystal structure in many fields of science and technology. In the work, the electrostatic field inside an arbitrary periodic structure is considered and a mathematical model is constructed that describes the main characteristics of the field in the ellipsoidal approximation: the scalar potential of the electric field and its intensity. The paper also provides all the necessary mathematical relationships.

Deaf band based engineered Dirac cone in a periodic acoustic metamaterial: A numerical and experimental study

A Dirac-cone-like dispersion at the center of the Brillouin zone where the wave number $\stackrel{P\vec}{k}=0$ [L. Brillouin, Wave Propagation in Periodic Structures (Dover, New York, 1953)], is rare and only happens due to accidental degeneracy. At certain frequencies, the Dirac cone breaks the time-reversal symmetry of acoustic waves, which has not yet been fully explored. In this paper, even the simplest geometric microarchitecture of phononic crystals (PnCs) in a periodic structure can be modulated to obtain the accidental triple degeneracies that make a Dirac-like cone at the \ensuremath{\Gamma} point ($\stackrel{P\vec}{k}=0$). While doing so, it was observed that the frequency of a nondispersive band obtained from any arbitrary periodic structure made of similar PnCs remains unaltered. Then, a deaf band based predictive modulation of the PnCs is realized, and multiple occurrences of the Dirac-like points are demonstrated. The claims are validated using a numerical and experimental study of a baseline periodic structure having a square array of cylindrical polyvinylchloride inclusions in an air matrix. Phenomena such as orthogonal wave transport, negative refraction, and wave vortex are verified to exist at the deaf band based engineered Dirac cone.

A microsphere assembly method with laser microwelding for fabrication of three-dimensional periodic structures

The orderly build-up of monosized microspheres with sizes of hundreds of micrometres enabled us to develop three-dimensional (3D) photonic crystal devices for terahertz electromagnetic waves. We designed and manufactured an original 3D particle assembly system capable of fabricating arbitrary periodic structures from these spherical particles. This method employs a pick-and-place assembling approach with robotic manipulation and interparticle laser microwelding in order to incorporate a contrivance for highly accurate arraying: an operation that compensates the size deviation of raw monosized particles. Pre-examination of particles of various materials revealed that interparticle laser welding must be achieved with local melting by suppressing heat diffusion from the welding area. By optimizing the assembly conditions, we succeeded in fabricating an accurate periodic structure with a diamond lattice from 400 µm polyethylene composite particles. This structure demonstrated a photonic bandgap in the terahertz frequency range.

Dispersion Characteristics of Arbitrary Periodic Structures with Rectangular Grooves

The dispersion characteristics of a circular cylindrical waveguide with periodic surface corrugations consisting of rectangular grooves with smoothing are examined using the Space Harmonic Method (SHM). The whole structure is divided into two regions, one describing the propagation volume and one inside the grooves. In the first region, the Floquet theorem is applicable and the field distribution is expressed as a summation of spatial Bloch components, whereas in the second one an appropriate Fourier expansion of standing waves is used. Applying the boundary conditions an infinite system of equations is obtained, which is solved numerically by truncation. Several cases are considered, including the limiting cases of a sinusoidal and a rectangular corrugation profile, to check the accuracy of the method proposed as well as its dependence on the corrugation profile. Numerical results are presented only for transverse magnetic modes, although the formalism can be easily extended to include all kinds of waves that can in principle propagate in such a structure.

Generalization of the coupled dipole method to periodic structures

We present a generalization of the coupled dipole method to the scattering of light by arbitrary periodic structures. This new formulation of the coupled dipole method relies on the same direct-space discretization scheme that is widely used to study the scattering of light by finite objects. Therefore, all the knowledge acquired previously for finite systems can be transposed to the study of periodic structures.

Homogenized thermoelastic model for a beam of a periodic structure

In this paper, the transition from a 3-D thermoelasticity problem to a 1-D beam model is made on the basis of a two-scale asymptotic method. A non-homogeneous beam of arbitrary periodic structure is considered.

On the effective medium theory of subwavelength periodic structures

Abstract The effective medium theory of one-dimensional and two-dimensional periodic structures are investigated. A method based on a Fourier decomposition of the wave propagating along the direction perpendicular to the periodic structures allows one to determine the zeroth-, first- and second-order effective indices. For one-dimensional problems, we derive closed-form expressions of the effective indices for both TE and TM polarization. Our result can be applied to arbitrary periodic structure with symmetric or non-symmetric lamellar or continuously varying index profiles. The theoretical predictions are carefully validated using rigorous coupled-wave analysis. For the two-dimensional case, only symmetric structures are discussed and the computation of the zeroth-, first-, and second-order effective indices requires the inversion of an infinite matrix which can be truncated and simply solved numerically. The EMT prediction is qualitatively validated using rigorous computation for small period-to-wavelen...

Multiple multipole program computation of periodic structures

The three-dimensional multiple multipole program (MMP) code based on the generalized multipole technique is outlined for readers who are not familiar with its concepts. This code was originally designed for computational electromagnetics. Rayleigh expansions and periodic boundary conditions are two new features that make MMP computations of arbitrary periodic structures efficient and that at the same time allow us to take advantage of the benefits of other MMP features, including surface impedance boundary conditions and a variety of available basis functions for modeling the electromagnetic field. The application of three-dimensional MMP to a simple grating of highly conducting wires with rectangular cross sections illustrates the high accuracy and the fast convergence of the method as well as the use of surface impedance boundary conditions. A more complicated biperiodic array of helical antennas demonstrates the application of thin-wire expansions in conjunction with regular MMP expansions. This model can be considered a simulation of a thin, anisotropic chiral slab with interesting characteristics.

Analysis of general double periodic structure diffraction phenomena based on the ambiguity function

We present a general configuration made up of two arbitrary periodic structures and a thin lens under partially coherent illumination. The separation of these elements along the optic axis can be adjusted to meet some special requirements (system conditions) to form a meaningful pattern on the observation screen. An elegant analytic expression is deduced to describe the intensity distribution based on the ambiguity function approach. Two extremes of illumination are considered. The Talbot self-imaging effect, the moire effect of double-grating superposition, the classical Lau effect, the generalized Lau effect, incoherent grating–lens imaging, and misfocus diffraction convolution are discussed.

Surface acoustic waves in periodic structures

A noniterative technique is described for obtaining surface-wave solutions in periodic layered media by expanding the field quantities in an orthonormal series of Laguerre functions perpendicular to the surface and in a Fourier series in the propagation direction. The principle is illustrated with uniform layered media, thin and thick metallic gratings, and grooved arrays. The technique is general and applicable to arbitrary periodic structures.

A finite element study of harmonic wave propagation in periodic structures

The vibration behaviour of periodic structures may be described by a characteristic “propagation constant”. The natural frequencies of the finite periodic structure are related to the variation of the purely imaginary part of this propagation constant, known as the phase constant. A method is presented for using the finite element technique to evaluate the phase constant of an arbitrary periodic structure. The method is applied to two types of periodic construction. The first is a periodically supported infinite beam. The second is a skin rib structure, with dimensions typical of a tailplane. Two models of the tailplane are considered, a beam model and a plate model.