Planar Helices Research Articles

A New Method to Obtain PH-Helical Curves in E^(n+1)

Helical curves are constructed by the property that their unit tangents make a constant angle with a chosen constant direction. There are relations between polynomial planar curves, helices and Pythagorean-hodograph or shortly PH-curves. The aim of this paper is to obtain a method which generate PH-curves and PH-helical curves from a planar curve in Euclidean Space E^(n+1). Furthermore, some examples are given in E^4 and E^5 to explain the method neatly.

Paramagnetic filaments in a fast precessing field: Planar versus helical conformations

We examine analytically equilibrium conformations of elastic chains of paramagnetic beads in the presence of a precessing magnetic field. Conformations of these filaments are determined by minimizing their total energy, given in the harmonic approximation by the sum of the bending energy, quadratic in its curvature, and the magnetic dipolar interaction energy, quadratic in the projection of the vector tangent to the filament onto the precession axis. In particular, we analyze two families of open filaments with their ends aligned along the precession axis and described by segments of planar curves and helices. These configurations are characterized in terms of two parameters encoding their features such as their length, separation between their ends, as well as their bending and magnetic moduli, the latter being proportional to the magnitude and precession angle of the magnetic field. Based on energetic arguments, we present the set of parameter values for which each of these families of curves is probable to occur.

Broadband and high-efficiency circular polarizer based on planar-helix chiral metamaterials

We reveal a broadband and high-efficiency circular polarizer based on chiral metamaterials composed of an array of planar helices, which can effectively reject the incident left-hand circularly polarized (LCP) wave, while allowing the right-hand circularly polarized (RCP) wave to pass through it. The physical mechanism of the proposed circular polarizer is explained with the aid of the current distributions under the excitations of LCP and RCP waves. Microwave experiments are performed to verify this idea, and measured results are in good agreement with the numerical ones. Experimental results show that a fractional bandwidth of 75.6% for the transmittance of the LCP wave lower than 0.2 can be obtained. Moreover, the proposed circular polarizer exhibits a high transmittance of over 0.9 for the RCP incident wave and a high circular polarization selection efficiency of over 0.95. The proposed circular polarizer will be potentially very useful for satellite and optical communications.

Mid-infrared circular polarization switching in helical metamaterials

Circular polarization switching in helical metamaterial structures in the mid-infrared regime is numerically demonstrated. The low loss and broad transmission of right- and left-circularly polarized waves is found within the circular polarization switching bands. The switching behavior is maintained until the helix pitch or helix height reaches a quarter of the operating wavelength in the conventional and connected 4-layer planar helices, while the electromagnetic couplings among the four quarter helical parts conserve the ‘helical-like’ properties for the free-stand 4-layer planar helices, when the helix height is up to one eighth of the operating wavelength. These different helical orientations can be favorable in circular polarization switching and optical and light applications. Since the transmission switching bands are greater than 25% bandwidth, these switching designs could operate in the broadband spectral domain.

Connected Pair of Planar Helices With Straight-Edge Connections for Application in TWTs

A novel planar slow wave structure (SWS) consisting of a connected pair of planar helices with straight-edge connections (PH-SEC) has been proposed in this paper. It is shown with the help of dispersion and coupling impedance characteristics that this structure offers a larger electron-beam tunnel and lower risk of backward-wave oscillation compared with a single PH-SEC. Fabrication using printed-circuit techniques is reported and measured $S$ -parameters over 1–7 GHz are presented to demonstrate the ease of feed-design and wideband characteristics for the new SWS. Using particle-in-cell simulations, hot-test parameters such as the output power, gain, and efficiency are also obtained and reported. It is shown that the connected pair of PH-SECs has a higher gain growth rate than that for the single PH-SEC. The proposed SWS is also compared at frequencies around 60 GHz with a recently reported structure which is derived from meander-line SWS; the comparison shows that the connected pair of PH-SECs offers a significantly higher coupling impedance. With a good potential for fabrication using microfabrication techniques, the connected pair of PH-SECs can be an attractive candidate for application in mm-wave traveling wave tubes.

Shapes of a Suspended Curly Hair

We investigate how natural curvature affects the configuration of a thin elastic rod suspended under its own weight, as when a single strand of hair hangs under gravity. We combine precision desktop experiments, numerics, and theoretical analysis to explore the equilibrium shapes set by the coupled effects of elasticity, natural curvature, nonlinear geometry, and gravity. A phase diagram is constructed in terms of the control parameters of the system, namely the dimensionless curvature and weight, where we identify three distinct regions: planar curls, localized helices, and global helices. We analyze the stability of planar configurations, and describe the localization of helical patterns for long rods, near their free end. The observed shapes and their associated phase boundaries are then rationalized based on the underlying physical ingredients.

Analysis of Coupled Planar Helices with Straight-Edge Connections for Application in Millimeter-Wave TWTs

Two different types of coupled planar helix structures with straight-edge connections (PH-SECs), namely, an unconnected pair and a coaxial pair of planar helices, are proposed and analyzed in the context of application in millimeter-wave traveling-wave tubes. It is shown that the nature of the propagating modes, dispersion characteristics, field distribution, and coupling impedance for the proposed structures can be obtained as special cases of a generic structure that consists of four parallel infinite unidirectionally conducting screens. For both the coupled planar helix structures, the results based on simple analytical approximations of the generic structure match well with the simulation results. As an application of these structures, simulation results are presented to show that the unconnected pair of planar helices has a reduced interaction with backward waves compared with that for a corresponding single planar helix. The proposed PH-SECs offer easier fabrication using printed-circuit or microfabrication techniques compared with their circular counterparts.

A left-handed composite medium based on waveguiding structures with a bianisotropic filling

A new composite medium based on waveguiding structures loaded with bianisotropic gratings of planar double split rings (PDSRs) and planar helices is considered. The microwave transmission spectra of this medium are studied experimentally. The effective parameters of the medium are determined theoretically, and its passbands are investigated. The characteristics of the medium are compared to those of infinite homogeneous bianisotropic media. A relationship between the spectral transmission characteristics and the type of resonance excitation is established. The transparency bands and overforbidden bands of the composite medium are revealed. The combinations of the medium’s effective parameters that correspond to these bands are determined. It is shown that the transparency bands where the medium is characterized simultaneously by negative permittivity and negative permeability can be identified.

The Dynamics of Scroll Waves in Excitable Media

An overview is given of the attempts to understand the behavior of scroll waves in three-dimensional excitable media using analytical methods, and these results are compared with recent numerical and experimental results. The behavior of untwisted planar scroll rings, twisted rings and helices, and knotted scroll wave filaments is discussed.

On Dynamics of Soliton Excitations in Coupled Chains

Effects of interchain coupling on soliton dynamics are studied analytically based on the model describing, e . g ., ferromagnet chains with planar anisotropy or DNA double helices. In the framework of the perturbation theory the interaction of solitons belonging to different chains is investigated, a coupling constant being a small parameter. In particular, the interaction energy of the solitons is calculated, and it is demonstrated analytically that two slow solitons can form a bound state. Some radiative effects accompanying the soliton bound-state dynamics are considered by means of the perturbation theory based on the inverse scattering technique. It is also demonstrated that the slightly excited bound state of the solitons emits the longitudinal vibrations in the framework of a more general model used in the DNA theory.

Coupled Planar Helices

Properties of a system of coupled planar helices are investigated. A set of transmission line equations are derived for the coupled system. From these transmission line equations, a dispersion relation is obtained. The computed results for the planar helix couplers indicate that its performance is comparable with that of its circular helix counterpart and hence it can be used to couple in and out of a planar helix slow wake structure.