Helicoidal Wave Research Articles

Critical review of classical electrodynamics

In this paper, we will review classical electrodynamics, where our main concern will be exclusively the propagation of electromagnetic waves in the vacuum and the interaction of these waves with free charges. We will examine the reasons why the classical Maxwell's equations are not complete and consistent. We will show that there are three kinds of waves propagating in the vacuum, namely, transverse waves, longitudinal waves, and helicoidal waves. We will particularly review the theoretical and experimental aspects of longitudinal waves whose existence seems to be proven.

Doing Spin Physics with Unpolarized Particles

Twisted, or vortex, particles refer to freely propagating non-plane-wave states with helicoidal wave fronts. In this state, the particle possesses a nonzero orbital angular momentum with respect to its average propagation direction. Twisted photons and electrons have been experimentally demonstrated, and creation of other particles in twisted states can be anticipated. If brought in collisions, twisted states offer a new degree of freedom to particle physics, and it is timely to analyze what new insights may follow. Here, we theoretically investigate resonance production in twisted photon collisions and twisted e^{+}e^{-} annihilation and show that these processes emerge as a completely novel probe of spin and parity-sensitive observables in fully inclusive cross sections with unpolarized initial particles. This is possible because the initial state with a nonzero angular momentum explicitly breaks the left-right symmetry even when averaging over helicities. In particular, we show how one can produce almost 100% polarized vector mesons in unpolarized twisted e^{+}e^{-} annihilation and how to control its polarization state.

Far-field superresolution imaging using shaped acoustic vortices

The ability to overcome the limitations on resolution due to the effects of diffraction has attracted significant attention in recent years. Previously proposed methods to overcome this limit, and therefore achieve superresolution, have largely been restricted to operating within the near-field region of the aperture. In this work, we will describe how acoustic helicoidal waves can create acoustic vortices that are well below the resolution limit, and how this can enable far-field superresolution acoustic imaging. The acoustic vortices generated in this manner propagate from the near-field into the far-field through an arrangement of stable integer mode vortices, thereby enabling the generation of far-field superresolved features in the acoustic pressure field. In this paper, theoretical and numerical results will be presented for an acoustic aperture which is capable of generating superresolved far-field features in the radiated acoustic pressure, and results will be shown illustrating the superresolution capability of this novel technique. [Work supported by the Office of Naval Research.]

Electric-field-induced local rotation of molecules in nematic-cholesteric droplets

The structural dynamics of nematic-cholesteric liquid crystal (LC) droplets occurring in an isotropic environment in an alternating electric field have been studied. It is established that, above a certain threshold field strength, the conoscopic pattern of a Maltese cross becomes dynamic and begins to rotate. The threshold voltage, as well as the frequency of rotation, is almost independent of the droplet diameter. This phenomenon is related to the development of a self-consistent rotation of LC molecules in the plane perpendicular to the droplet axis. It is shown that this rotation initiates the propagation of a helicoidal wave from one pole of the droplet to another.

Three-dimensional acoustic radiation force on an arbitrarily located elastic sphere

This work aims to model the acoustic radiation forces acting on an elastic sphere placed in an inviscid fluid. An expression of the axial and transverse forces exerted on the sphere is derived. The analysis is based on the scattering of an arbitrary acoustic field expanded in the spherical coordinate system centered on the spherical scatterer. The sphere is allowed to be arbitrarily located. The special case of high order Bessel beams, acoustical vortices, are considered. These types of beams have a helicoidal wave front, i.e., a screw-type phase singularity and hence, the beam has a central dark core of zero amplitude surrounded by an intense ring. Depending on the sphere's radius, different radial equilibrium positions may exist and the sphere can be set in rotation around the beam axis by an azimuthal force. This confirms the pseudo-angular moment transfer from the beam to the sphere. Cases where the axial force is directed opposite to the direction of the beam propagation are investigated and the potential use of Bessel beams as tractor beams is demonstrated. Numerical results provide an impetus for further designing acoustical tweezers for potential applications in particle entrapment and remote controlled manipulation.

Generalization of helicoidal beams for short pulses

A generalization to the transient regime is developed for waves with a phase singularity of the screw type. These singular waves are commonly called vortices for all kind of waves as, for instance, optical vortex or acoustical vortex. We generalize the definition of vortices to get an azimuthal velocity invariant for all the frequency components contained in the broad spectrum of a short pulse. This generalization leads to a modification of the orbital angular momentum definition. Another generalization is introduced by considering helicoidal waves with a finite number of turns. We demonstrate that, in this last case, the topological charge is no longer an integer. This provides a physical interpretation to vortices of fractional charge that are involved here to take into account the diffraction occurring at both tips of the now finite helical wave front. We show that shortening the pulse implies an angular localization of the wave energy and, as a consequence, a spreading of the angular momentum amplitude due to the uncertainty principle.

An FE Tool for the Electromagnetic Analysis of Slow-Wave Helicoidal Structures in Traveling Wave Tubes

In this paper, the authors present a 3-D dedicated finite-element tool expressly conceived for the analysis of traveling wave tool helicoidal slow wave structures (SWSs). Accurate analysis of the SWS is a difficult task due to its complex geometry. Moreover, in order to achieve the design parameters a specific post-processing is required. Consequently, specialized 3-D numerical simulators are needed to carry out the design process. The developed tool includes a dedicated mesh generator, an eigenmode and a driven mode solver, and a post-processing module. An example of a typical SWS analysis performed by using the tool is also given

Emergent reaction-diffusion phenomena in capillary tubes

Pattern formation in the Belousov-Zhabotinsky reaction experiments carried out by filling capillary glass tubes with catalyst-immobilized gel for the reaction is reported. Under unperturbed and oscillatory conditions, helicoidal waves appear spontaneously. Quantitative structural data of those helices are obtained by devising an optical tomography technique for extracting rotationally symmetric structures from time-lapse data. Space-time representation of the catalyst oxidation reveals wave transmission phenomenon that is studied further by numerical simulations of a reduced spatial model.

Nonlinear evolution of components of an electromagnetic field of helicoidal waves in plasma

We derive model equations of the interaction between circular polarized helicon wavetrains in a two-dimensional plasma. For such quasi-one-dimensional waves a nonlinear resonance results in N-wave interactions. The corresponding system of equations is known to be integrable. A novel feature of the study, in the context of soliton theory, is the account of the wave asynchronism that seems to be essential for wavetrains with wavefronts of large steepness, observed in experiments for dense helicon plasma. To generate solutions we use recent results of the binary Darboux transformation technique, applying it to three-wave interactions. The solutions have been analysed numerically and plotted.

Ultrastructure and motility pattern of the spermatozoa of Aleochara curtula (Coleoptera, Staphylinidae)

Ultrastructure and motility pattern of spermatozoa of the rove beetle Aleochara curtula were examined using electron and light microscopic methods. The spermatozoon is about 100 μm long and filiform. The head piece comprises a 5 μm long triple layered acrosome and 10 μm long nucleus. The flagellum consists of a 9+9+2 axoneme, two accessory bodies and two mitochondrial derivatives about equal in size but of different shape in their cross sections. In both derivatives there are paracrystalline inclusions. The flagellum is attached to the head by a 2 μm long centriole adjunct which is characterized by its electron dense material that forms a three layered folded lamellar structure. When liberated in buffer solution the sperm flagella assume a coiled hook-like form with the excentric stiff head protruding in front. The spermatozoa are driven through the medium by a small helicoidal wave of high frequency superimposed to the bent flagella. The maximum speed measured was 15.2 μm/s. The sperm architecture of A. curtula is similar to that of other Aleochara species but differs in total length and dimensions of the mitochondrial derivatives. For that reason Aleochara sperm can certainly prove useful to study the effect of the mitochondrial derivatives on sperm motility.

Helicoidal magneto-electron waves in interstellar molecular clouds

We investigate the evolution of the magnetic flux density in a magnetically supported molecular cloud driven by Hall and Ohmic components of the electric field generated by the flows of thermal electrons. Particular attention is given to the wave transport of the magnetic field in a cloud whose gas dynamics is dominated by electron flows; the mobility of neutrals and ions is regarded as heavily suppressed. It is shown that electromagnetic waves penetrating such a cloud can be converted into helicons — weakly damped, circularly polarized waves in which the densities of the magnetic flux and the electron current undergo coherent oscillations. These waves are interesting in their own right, because for electron magnetohydrodynamics the low-frequency helicoidal waves have the same physical significance as the transverse Alfvén waves do for a single-component magnetohydrodynamics. The latter, as is known, are considered to be responsible for the widths of molecular lines detected in dark, magnetically supported clouds. From our numerical estimates for the group velocity and the rate of dissipation of helicons it follows that a possible contribution of these waves to the broadening of molecular lines is consistent with the conditions typical of dark molecular clouds.

Angular Doppler effect in the scattering of a helicoidal wave by a rotating target

The phase of an acoustic helicoidal wave advances linearly with angle around a propagation axis at a rate characterized by an angular index m. For m=1 and 2, the phase advances are 360 deg and 720 deg, respectively, for an angular advance of 360 deg. There is null in the amplitude along the beam axis. A transducer for approximating such a helicoidal beam near the axis has been demonstrated [B. T. Hefner and P. L. Marston, J. Acoust. Soc. Am. 106, 3313–3316 (1999)]. In the new work, the scattering by small objects that rotate around the helicoidal beam axis is considered. The wave scattered to a receiver on the axis will be shifted in frequency. The shift is constant and is given in magnitude by the product of the target’s rotation rate and the helicoidal wave’s angular index m. The shift is a consequence of the angular dependence of the phase of the helicoidal wave and the sign of the shift depends on the sign of m and the direction of the rotation of the target. A similar angular Doppler effect should also be present in the scattering of electromagnetic helicoidal waves. [Work supported by ONR.]

Spiral magneto-electron waves in interstellar gas dynamics

We discuss possible observational consequences resulting from the propagation of transverse magneto-electron waves in the interstellar medium. We briefly describe a magnetohydrodynamic model for the cyclotron waves with emphasis on their analogy with hydrodynamic inertial waves. It is shown that the cyclotron waves are heavily damped in the interstellar medium and, therefore, cannot affect the gas dynamics of star-forming molecular clouds. We developed an analytical model of the helicoidal magneto-electron waves based on the electromagnetic induction equation for the magnetic flux density driven by the Hall and Ohmic components of the electric field generated by flows of thermal electrons. It is established that the helicons can propagate in the interstellar medium without any noticeable attenuation. The presented numerical estimates for the group velocity of the intercloud helicons suggest that spiral circularly polarized magneto-electron waves of this type can be responsible for the broadening of molecular lines detected from dark interstellar clouds.

An acoustical helicoidal wave transducer with applications for the alignment of ultrasonic and underwater systems

A simple four-panel transducer capable of producing a beam with a screw dislocation along its axis was constructed and evaluated. A screw dislocation in a wavefront is characterized by a phase dependence about the dislocation axis that varies as exp(−imφ), where m is an integer and φ is the angle about the axis. At the axis, the phase is indeterminate and as a result there is a corresponding null in the pressure magnitude. The screw dislocation in the transducer beam is along the beam axis and is found to exist in both the far- and near-fields of the transducer. This null then clearly indicates the axis of the beam at all distances and has the potential to be used as an aid in the alignment of objects in sonar experiments or other similar applications. The helicoidal wave is also shown to possess axial angular momentum. A related transducer was summarized previously [J. Acoust. Soc. Am. 103, 2971 (1998)] and is also discussed here for the purposes of comparison.

Acoustical helicoidal wave transducers with applications for the alignment of ultrasonic and underwater systems

A simple four-panel transducer capable of producing a beam with a screw-dislocation along its axis was constructed and evaluated. A screw-dislocation in a wave front is characterized by a phase dependence about the dislocation axis that varies as exp(−imφ), where m is an integer and φ is the angle about the axis. At the axis the phase is indeterminate and as a result there is a corresponding null in the pressure magnitude. To generate a wave front with these characteristics, a four-panel 3-1 composite piezoelectric transducer was driven with the appropriate phasing of the panels to create dislocation along the beam axis. As a result the beam does not possess cylindrical symmetry, however, the dislocation is found to exist in both the far and near fields of the transducer. This null then clearly indicates the axis of the beam at all distances and has the potential to be used as an aid in the alignment of objects in sonar experiments or other similar applications. A related transducer was summarized previously [J. Acoust. Soc. Am. 103, 2971 (1998)] and is also discussed here for the purposes of comparison. [Work supported by the Office of Naval Research.]

Acoustical helicoidal waves and Laguerre–Gaussian beams: Applications to scattering and to angular momentum transport

Traveling waves having helicoidal wavefronts are cylindrically symmetric except for an azimuthal angular dependence of exp(imφ−iωt), where m is an integer. The amplitude vanishes at the screw-phase dislocation [J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165–190 (1974)] on the z propagation axis. Examples of paraxial helicoidal waves are the Laguerre–Gaussian beam solutions of the parabolic wave equation. Some potentially useful properties of acoustical helicoidal waves are analyzed. Just as for linearly polarized optical Laguerre–Gaussian beams [L. Allen et al., Phys. Rev. A 45, 8185–8189 (1992)], the ratio of the axial angular momentum flux to the acoustical beam power is found to be m/ω so that axial radiation torques are generated when the acoustical energy is absorbed. Helicoidal waves are predicted to backscatter in a way which reveals the axisymmetry of the scatterer when combined with a helicoidal mode-selective detector. Some strategies for acoustical helicoidal wave generation and detection will also be described. [Work supported by the Office of Naval Research.]

Double-helicoidal eigenstates in lasers

Longitudinal segmented helicoidal eigenstates in laser resonators, with different field distributions of either identical or opposite handedness, are studied theoretically and experimentally. The eigenmodes and frequencies are derived in the framework of the Jones-matrix formalism. Double helices can be applied to birefringence compensation for helicoidal waves. A novel Fabry–Perot laser cavity is realized in which both spatial hole-burning suppression and birefringence compensation are simultaneously achieved.

Measurement of small optical activities by use of helicoidal waves: erratum

Measurement of small optical activities by use of helicoidal waves: erratum

Measurement of small optical activities by use of helicoidal waves

The helicoidal eigenstates of a passive Fabry–Perot resonator that contains two quarter-wave plates allow us to propose a novel polarimetric method whose sensitivity, compared with that of single-pass devices, is demonstrated to be enhanced proportionally to the square of the cavity finesse. Good agreement between the experimental and the theoretical enhancements of sensitivity is observed, and a detectability of 10−6 deg is obtained with a cavity finesse of 150.

Front geometries of chemical waves under anisotropic conditions

An experimental study of chemical waves in the Belousov-Zhabotinsky reaction under anisotropic conditions of substrate concentrations extending over the system was carried out by use of ferroin-immobilized silica gels as reacting matrices. Unidirectionally moving wave trains (similar to the so-called “chemical pinwheels”) followed by the spontaneous fragmentation of wave fronts were observed in rectangular two-dimensional gels. A helicoidal chemical wave (or twisted scroll wave), which was predicted by numerical calculation, was detected in a micro-cylindrical gel system. A space-time representation of the chemical helix was constructed and its structural features are discussed qualitatively.