Sheath Helix Research Articles

Model Dispersion Analysis of Circular Waveguide in Normal and Reverse Boundary Condition

The dispersion characteristics of the circular step index fiber with helical windings between the core-cladding region is investigated. Sheath helix is wounded between the core and cladding using two directions, namely in the clock wise and anticlockwise direction. Substituting the field components into the modified boundary conditions due to the addition of the helical windings the modal characteristics are derived for both fibers. Representations of the helical windings are done by using normal boundary conditions and reverse boundary conditions. The Eigen equation is obtained in the form of Bessel functions and modified Bessel functions for both the waveguides. The dispersion curves are plotted for two specific pitch angles ψ=0° and ψ=90 for each fiber and the results are compared. The direction of wrapping the helical material results in a change in the dispersion properties with regards to the way the modes propagate in both fibers. These changes are seen by the presents and absence of (1) band gap,(2) splitting of modes and (3) adjacent modes depending on the direction and pitch angle of the helical windings. Results obtained in this work suggest that direction and pitch angle of the helical winding are parameters that are able to control the behavior of the modes.

Scattering due to uniaxial anisotropic chiral medium-coated PEC cylinder with conducting helix loading

ABSTRACT A perfect electrically conducting (PEC) cylinder (having a circular cross-section) encapsulated with uniaxial anisotropic chiral medium was studied emphasizing the features of scattering. A conducting sheath helix structure having a varying orientation with respect to the optical axis (or pitch angle) was assumed to be at the outermost surface. This allows alterations in scattering patterns. The echo width of the structure was evaluated under the assumption of parallel polarized oblique incidence of waves. The effect on scattering was evaluated under varying chirality and permittivity of the coating medium along with the variations in the helix pitch angle. The obtained results are compared with those achieved by replacing the chiral coating with a simple anisotropic kind of medium (without chirality).

Calculation of Pierce’s Parameters <inline-formula> <tex-math notation="LaTeX">${C}$ </tex-math> </inline-formula> and <inline-formula> <tex-math notation="LaTeX">${Q}$ </tex-math> </inline-formula> by Differentiation of the TWT “Hot” Dispersion Relation

A new method of calculating the values of Pierce’s parameters ${C}$ and ${Q}$ , which appear in the fourth-order polynomial TWT characteristic equation for the phase constants, is derived and illustrated. The use of this method avoids the need to compute the power flow by integration of the Poynting flux in the absence of the beam, which can be difficult to do analytically. By introducing the coupling coefficient ${K}_{c}$ and the depression coefficient $\Gamma$ in place of ${C}$ and ${Q}$ , it becomes possible to analyze the TWT characteristic equation in the limit of zero density of the e-beam when parameter ${C}$ is equal to zero. It is shown that ${K}_{c}$ and $\Gamma$ can generally be determined by differentiation of the dispersion relation in the presence of the beam with respect to the transverse constant $\gamma$ , evaluated in the limit that the beam current vanishes. ${K}_{c}$ (and therefore impedance ${K}$ ) is shown to be determined by the first derivative and $\Gamma$ (and therefore ${Q}$ ) is shown to be determined by the combination of the first and second derivatives with respect to $\gamma$ . This method is applied to two TWTs based on two different types of slow-wave structure, a “comb” and a “sheath helix.”

Complex-structured liquid crystal clad elliptical guides – the cases of with and without conducting sheath helix loadings

Electromagnetic (EM) wave propagation through three-layer liquid crystal clad elliptical optical guides was investigated under the situations when those were loaded with and without conducting sheath helix structures. Due to exceptional features of liquid crystals, such as durable electro-optic behaviour as well as optical anisotropy, the presence of these greatly affects wave propagation, thereby controlling the confinement of power in guides. The present work was aimed to investigate the comparison between three-layer elliptical optical guide having radially anisotropic liquid crystal as its outer clad, and loaded with and without conducting sheath helix structure at the core-inner (dielectric) clad interface. The results reveal prudent use of the former kind (of guide) over the latter one owing to its having on-demand control over the propagation of power, and also, enhanced confinement in the outermost section for the guide. These features allow such sheath helix-loaded guides to be useful in optical sensing applications.

Scattering response of featured uniaxial anisotropic chiral medium-coated twisted PEC cylinder

Scattering of electromagnetic waves from a perfectly electrical conducting (PEC) cylinder of circular cross-section, coated with uniaxial non-magnetic chiral anisotropic medium, was discussed. A conducting sheath helix structure with adjustable pitch angle exists over the outer surface of coated cylinder, which is interfaced with the free-space. Under the uniform parallel polarized plane wave with fixed oblique incidence angle, the echo widths were determined emphasizing the other relevant scattering-related parameters (e.g. scattering/extinction efficiency etc.), taking into account different pitch angle values (of the sheath helix) and the kinds of coating mediums. The results revealed that the coating of negative uniaxial chiral medium causes enhancement in scattering efficiency (of the scatterer). Also, the scattering efficiency was found to be the same as the extinction efficiency, thereby yielding vanishing absorption of the medium. The obtained results were also compared with the situation of vanishing chirality of coating medium over the PEC cylinder; the echo width and scattering efficiency both decrease in this case.

Effects of admittance and gyrotropy on the scattering due to chiro-ferrite medium coated microstructured PMC cylinder

The paper deals with scattering of electromagnetic (EM) waves by perfectly magnetic conducting (PMC) cylinder coated with chiro-ferrite medium under the assumption of oblique angle of incidence wave with perpendicular polarization (transverse electric; TE). An on-demand (in respect of orientation) kind of conducting sheath helix structure is assumed to exist at the outer surface of cylinder. The effects of sheath helix orientation, along with the material parameters, such as chirality admittance and gyrotropy, on the echo width as well as the magnitude and phase of the electric and magnetic fields are investigated. Control on the anisotropic property remains greatly useful in obtaining the required optical response from the scatterer — the feature which would find fabulous sensing related applications.

Plasma effects on the growth rate of a helix magnetron-type conducting cylinder

The linear theory of magnetron amplifier in the presence of the partially plasma loaded sheath helix is presented. The hollow electron beam and plasma column are exposed to the axial magnetic field. The dispersion relation is obtained by using the appropriate boundary conditions. The effects of electron beam, plasma column parameters and sheath helix are studied numerically on the gain. The numerical results show that the presence of the plasma column considerably increases the gain. It is shown that the bandwidth increases by increasing the plasma density. One of the interesting results are that the maximum gain occurs at the special value of the plasma and beam radius. The maximum of gain occurs when the helix approaches the vane. The results show that the gain and bandwidth at lower harmonics are greater than at higher harmonics. The gain and bandwidth in the presence of the plasma column are larger than when applying the dielectric rod.

Field analysis for a configuration of sheath helix in the presence of a metallic rod

The field analysis for a configuration of sheath helix in the presence of a coaxial metallic rod and strongly magnetized plasma under two conditions, i.e. , is presented. The electromagnetic field components in the configuration are obtained. The effects of a coaxial metallic rod in a plasma-loaded sheath helix traveling wave tube by means of a theoretical approach, in which infinite magnetic field has been adopted to represent the plasma response, is investigated. We presume that for the finite beam term, the mode structures remain unmodified and only the eigenfrequencies are modified. Therefore, the growth rate of slow electromagnetic waves and so their dispersion relation is calculated. Effects of frequency and plasma frequency on the growth rate are investigated. The obtained results are graphically presented.

Scattering of waves by chiral medium-coated dielectric elliptical/circular cylinders with PEC sheath helix loading

The paper reports scattering of plane waves by elliptical/circular homogenous, isotropic, and non-magnetic dielectric cylinders coated with chiral medium and surrounded by a perfectly electrical conducting sheath helix structure. The effect of pitch angle on the echo width under the assumption of parallel polarization is discussed, and the results are compared taking into account dielectric cylinders of different dimensions. The introduction of negative refraction in chiral mediums, and its effects on both the elliptical- and circular-shaped scattering objects are evaluated. The results indicate significant impact of the used chiral medium coating as well as the embedded sheath helix structure to alter the bi-scattering echo width of the object.

Scattering due to twisted PEC cylinder coated with chiral/chiroferrite mediums

Scattering of electromagnetic waves by perfectly electrical conducting (PEC) cylinder, coated with chiroferrite medium, is investigated under the oblique angle of incident. The coated PEC cylinder is wrapped with perfectly conducting sheath helix structure. For this structural configuration, the bi- and the mono-scattering echo widths are computed numerically while assuming the incident wave with parallel polarization. The roles of pitch angle (of sheath helix structure) and the material parameters on the echo width are analyzed. The obtained results for scattering echo widths are compared with those achieved when the PEC cylinder is coated with simply chiral material. It is found that the chiro-ferrite coating causes larger scattering of waves than the situation when the PEC cylinder is coated with simply chiral medium. Furthermore, a parallel orientation of the helix structure results in larger echo width.

Current density distribution along conducting sheath helix encapsulated silver metal cylinder coated with dielectric material under L-nihility and upon oblique incidence

This communication is aimed at investigating the electromagnetic (EM) characteristics of silver metal cylinder coated with homogeneous dielectric material, which is loaded with tightly wound perfectly electrical conducting sheath helix (outside of the dielectric layer) structure of different angles of orientation. Considering the L-nihility kind of behavior of silver metal at a particular frequency, the current density distributions are discussed corresponding to the parallel polarization (transverse magnetic) of the incident EM wave. The investigations are made taking into account the different values of oblique incidence, and also, the orientation angle of sheath helix structure. It is found that the current density, and hence the scattering of radiation, greatly depends on these parameters, and its magnitude increases with the increase in helix pitch as well as the angle of incidence.

On the power distributions in elliptical and circular helically designed chiral nihility core optical fibers

The structural designs of nonmagnetic chiral nihility-based optical fibers of elliptical and circular cross-sections, embedded with conducting sheath helix structure at the core–cladding interface, are investigated. Emphasis is given to the power confinement patterns while considering the hybrid EH01, EH11, and EH21 modes in the fiber and their comparative features. Variations in fiber dimensions are considered, and the corresponding effects on the power confinements under different orientations of sheath helix structure are reported. It has been found that the chiral nihility-based fiber structure results in the enhancement of the confined power, particularly in the case of an elliptic fiber. Apart from these, keeping in mind the possible lossy nature of chiral nihility mediums, the dispersive characteristic of material is also considered for both kinds of cross-sectional geometry, and the results are compared with situations when the mediums are lossless. The results essentially indicate less confinement of power in the case of lossy mediums.

On the Fast-Waves in Dispersive Core-Twisted Clad Waveguides

The propagation of fast-waves through twisted clad waveguide is reported, taking into account the group velocity of wave through the guide. Twists are considered in the form of conducting sheath helix structure loaded at the core–clad interface of the guide. The dispersion behavior is evaluated through developing the eigenvalue relation for guiding structure under suitable boundary conditions. Results indicate that the group velocity can be tailored, and it gets enhanced by taking into account dispersive double-negative medium in the core section. Apart from this, the condition close to mode degeneracy is also achieved. It is suggested that the guiding structure under consideration would find potential applications in dual-mode filtering purpose.

On the conducting sheath double-helix loaded liquid crystal optical fibers

This work presents analysis of wave propagation in a rather new type of three-layer optical fiber wherein the outermost region being composed of radially anisotropic liquid crystal, and conducting sheath helix loadings exist at the core–inner clad as well as the inner clad–outer liquid crystal clad interfaces. The fiber structure offers two-way control on wave propagation through it. Focus is, however, made on the wave confinements in fiber due to the helix structures, as characterized by the respective pitch angles. Specific values of helix pitch angles at the two layer interfaces are taken into account, and the confinement patterns are analyzed. The dominant property of sheath helix structure over confinement patterns is quite an obvious fact. Clearly, the helix pitch angle greatly controls over the power confinement characteristics, which can be altered upon suitable adjustments of helical windings. Treatments have been made to illustrate the power patterns in all possible scenarios for critical pitch variations in each layer interface.

Theory of Magnetron Amplifier in a Helix-Loaded Waveguide With the Inner Dielectric Material

The theory of the propagation of the magnetized hollow relativistic electron beam with a dielectric rod at its axis through the sheath helix that inserted into the magnetron-type conductor is presented. The dispersion relation is obtained with the aid of the proper boundary conditions. The effects of an electron beam, inner dielectric, helix, and magnetron-type conductor parameters on the growth rate are studied numerically. The numerical results show that the presence of the cavity considerably increases the growth rate. In the fast wave mode, we have the maximum value of the growth rate when the dielectric rod and the electron beam are close to each other. The maximum growth rates for the fast and slow wave modes occur to the special value of the helix radius. The results show that the growth rate increases with the decreasing of the axial momentum spread. Comparison of the two modes shows that the growth rate of the slow wave mode is higher than that of the fast wave mode, but the bandwidth of the fast wave mode is wider than that of the slow wave mode.

Scattering from silver metal cylinder due to L-nihility coated with conducting sheath helix embedded dielectric medium

In this article, scattering from silver metal cylinder due to L-nihility, coated with dielectric material that encapsulates perfectly electric conducting sheath helix structure, is presented. The orientation of helix can be altered, and the cases of both the parallel (TM) and the perpendicular (TE) polarizations of electromagnetic (EM) waves are analyzed. Co- and cross-polarized fields for different values of pitch angle are formulated under oblique angle of incidence. The bi-static echo width of the scatterer is investigated as a function of at the L-nihility frequency which lies within the optical frequency range. The results are compared with those obtained for perfect electric conductor (PEC) at different values of the angle of incidence. It is observed that the considered guiding structure behaves identically with the simple PEC cylinder under the situation when the helix structure is oriented parallel to the axial direction of the guide. However, for the other forms of the helix orientation, the structure behaves differently – thereby confirming the validity of the analytical approach for the aforementioned complex structured guide presented in the article.

A Study of the Effects of Helix Misalignment on the Cold Parameters of a Sheath Helix Slow-Wave Structure

The cold parameters including the dispersion properties and the average interaction impedance of a sheath eccentric helix slow-wave structure in a circular waveguide are investigated. With the applications of orthogonal properties of the helix modes and Graf's addition theorem for modified Bessel functions, the closed-form characteristic equations concerning the helix modes are derived rigorously. The obtained characteristic equations show that the misaligned structure admits only the field solutions existing in the form of the superposition of hybrid modes. Numerical calculations show that the normalized phase velocity and the average interaction impedance of the helix dominant mode decrease as the misalignment of the inner helix increases and that more hybrid modes must be considered for satisfactory convergence with the increase in the misalignment. The effects of different misalignments on the cold parameters of the eccentric structure are investigated and the results are discussed.

Conducting tape helix loaded radially anisotropic liquid crystal clad optical fiber

The paper reports investigation of a rather new type of optical fiber composed of three layers with the outermost region being radially anisotropic liquid crystal material, and the inner two regions as linear, homogeneous, and isotropic dielectrics. As such, the anisotropy remains in the outermost section of fiber. The core–clad interface of the inner dielectric regions is assumed to be loaded with conducting tape helix structure. It has been found that the width of the tape as well as the helix pitch angle are the effective parameters to govern the dispersion characteristics. Taking into account the zero-order guided modes, the effects on confinements due to the amalgamation of birefringence (optical property of liquid crystal) and tape helix pitch (geometrical/structural property of perfect conductor) are reported. The obtained results are compared with the case of a conducting sheath helix loaded liquid crystal fiber structure, and it has been found that the conducting tape helix loadings would be more useful than the sheath helix loaded fibers.

Dispersion Features of Conducting Sheath Helix Embedded Elliptical and Circular Fibers with Chiral Nihility Core

Discussions have been made of the electromagnetic wave propagation through optical fibers of elliptical and circular cross‐sections with the loadings of conducting sheath helix at the core‐clad interface with particular orientations. In both geometrical situations, the core section of fiber is assumed to be composed of chiral nihility medium, and the clad remains linear, homogeneous, isotropic, and nonmagnetic dielectric. Dispersion relations are deduced for both fiber structures, followed by the analysis of dispersion features considering a few low‐order EH modes. Furthermore, the effects of conducting helix pitch angle on the features of wave propagation are also discussed.

Dispersion characteristics of optical fibers under PEMC twists

Electromagnetic behavior of twisted clad optical fibers is investigated under the situation of sheath helix of perfect electromagnetic (PEMC) conductor introduced at the core–clad interface. The eigenvalue equation for the structure is deduced by applying suitable boundary conditions, and the dispersion behavior of the fiber is analyzed considering the cases of non-dispersive as well as dispersive core with the sustainment of a few low-order modes. The effect on dispersion properties is observed due to alterations in the pitch angle of helical twists as well as the admittance value of the PEMC material. It has been found that the pitch angle and the admittance values can be properly adjusted to attain the degenerate properties of modes which would find many applications in optics industry.