Axial Radiation Research Articles

Viscous contributions to low-frequency scattering, power absorption, radiation force, and radiation torque for spheres in acoustic beams

An analysis of the dipole response of solid spheres illuminated by plane acoustic traveling waves [Settnes and Bruus, Phys. Rev. E 85, 016327 (2012)] has implications for estimating the magnitude of viscous corrections to quantities of broader interest. Their results may be recast to give the viscous correction to the dipole scattering s-function for solid spheres. For the present discussion, it may be assumed that the Stokes layer is thin relative to the sphere’s radius, giving a simple reduction in magnitude of the dipole s-function (which is unimodular in the lossless case). The power absorption for plane waves and Bessel beams follow immediately from a prior formulation [Zhang and Marston, Phys. Rev. E 84, 035601 (2011)] as does the axial radiation force. The plane-wave force agrees after correcting a minor error in Settnes and Bruus. A condition G = 0 previously noted for low-ka negative radiation forces on spheres in Bessel beams [Marston, J. Acoust. Soc. Am. 120, 3518–3524 (2006)] still gives negative forces for sufficiently large spheres. The torque caused by first-order vortex beams may also be estimated [Zhang and Marston, Phys. Rev. E 84, 065601 (2011)]. [Work supported by ONR.]

Mechanism of the quasi-zero axial acoustic radiation force experienced by elastic and viscoelastic spheres in the field of a quasi-Gaussian beam and particle tweezing

The present analysis investigates the (axial) acoustic radiation force induced by a quasi-Gaussian beam centered on an elastic and a viscoelastic (polymer-type) sphere in a nonviscous fluid. The quasi-Gaussian beam is an exact solution of the source free Helmholtz wave equation and is characterized by an arbitrary waist w0 and a diffraction convergence length known as the Rayleigh range zR. Examples are found where the radiation force unexpectedly approaches closely to zero at some of the elastic sphere’s resonance frequencies for kw0⩽1 (where this range is of particular interest in describing strongly focused or divergent beams), which may produce particle immobilization along the axial direction. Moreover, the (quasi)vanishing behavior of the radiation force is found to be correlated with conditions giving extinction of the backscattering by the quasi-Gaussian beam. Furthermore, the mechanism for the quasi-zero force is studied theoretically by analyzing the contributions of the kinetic, potential and momentum flux energy densities and their density functions. It is found that all the components vanish simultaneously at the selected ka values for the nulls. However, for a viscoelastic sphere, acoustic absorption degrades the quasi-zero radiation force.

Analysis of the radiation force and torque exerted on a chiral sphere by a Gaussian beam

Under the framework of generalized Lorenz-Mie theory, we calculate the radiation force and torque exerted on a chiral sphere by a Gaussian beam. The theory and codes for axial radiation force are verified when the chiral sphere degenerates into an isotropic sphere. We discuss the influence of a chirality parameter on the radiation force and torque. Linearly and circularly polarized incident Gaussian beams are considered, and the corresponding radiation forces and torques are compared and analyzed. The polarization of the incident beam considerably influences radiation force of a chiral sphere. In trapping a chiral sphere, therefore, the polarization of incident beams should be chosen in accordance with the chirality. Unlike polarization, variation of chirality slightly affects radiation torque, except when the imaginary part of the chirality parameter is considered.

Modified Dual-Band Stacked Circularly Polarized Microstrip Antenna

A novel high-performance circularly polarized (CP) antenna is proposed in this paper. Two separate antennas featuring the global positioning system (GPS) dual-band operation (1.575 GHz and 1.227 GHz for L1 band and L2 band, resp.) are integrated with good isolation. To enhance the gain at low angle, a new structure of patch and two parasitic metal elements are introduced. With the optimized design, good axial ratio and near-hemispherical radiation pattern are obtained.

Tri-band circularly polarized annular slot antenna for GPS and CNSS applications

A novel single-feed tri-band circularly polarized (CP) annular slot antenna is presented. The antenna structure is composed of two nonconcentric annular slots that are fed by an L-shaped series step impedance microstrip line configuration. The proposed antenna is designed to operate at the L 1 and L 2 bands of the global positioning system and the operating band of the compass navigation satellite system. Compared to the most of the previously reported tri-band CP antenna structure, the proposed antenna has low profile, compact size, and easy fabrication on the single-layer PCB. The measured results show that the impedance bandwidths are good for all bands. The axial ratio bandwidth and radiation patterns are also measured at the three resonant frequencies. The proposed compact tri-band CP antenna design is suitable for mounting onto the mobile communication devices and portable positioning systems.

Experimental investigation of a compact relativistic magnetron with axial TE11 mode radiation

As one of the relativistic electron tubes having compact configuration and high efficient output, the relativistic magnetron with direct axial radiation is very attractive in pulsed power and high power microwave fields for industrial and military applications. In this paper, the experimental investigation of a relativistic magnetron with axial TE11 mode radiation is reported. Under a total length of ∼ 0.3 m, volume of ∼ 0.014 m3, working at an applied voltage of 508 kV and a magnetic field of ∼ 0.31 T, the relativistic magnetron radiates a microwave of 540 MW with the TE11 mode at 2.35 GHz in the axial direction. The power conversion efficiency is 15.0%. After a lot of shots, the detected amplitudes of microwaves are nearly the same. The fluctuations of wave amplitudes are less than 0.3 dB.

Calculation of radiation force and torque exerted on a uniaxial anisotropic sphere by an incident Gaussian beam with arbitrary propagation and polarization directions

On the basis of spherical vector wave functions and coordinate rotation theory, the expansion of the fields of an incident Gaussian beam with arbitrary propagation and polarization directions in terms of spherical vector wave functions is investigated, and beam shape coefficients are derived. Using the results of electromagnetic scattering by a uniaxial anisotropic sphere, the analytical expressions of the radiation force and torque exerted on a homogeneous absorbing uniaxial anisotropic sphere by the arbitrary incident Gaussian beam. We numerically analyze and discuss the following: the effects of an anisotropic absorbing dielectric on the axial and transverse radiation forces exerted by an off-axis Gaussian beam on a uniaxial anisotropic sphere; the variations in the axial, transverse, and resultant radiation forces (with incident angle β and polarization angle α) imposed by an obliquely Gaussian beam on a uniaxial anisotropic sphere; and the results on the characteristics of the three components of the radiation forces versus the center-to-center distance between the sphere and beam. Selected numerically results on the radiation torque exerted on a stationary uniaxial anisotropic transparent or absorbing sphere by a linearly polarized Gaussian beam are shown, and the results are compared with those exerted an isotropic sphere. The accuracy of the theory and code is confirmed by comparing the axial radiation forces with the results obtained from references.

Attraction by sound—examples on the negative acoustic radiation forces of Bessel “tractor” beams on a sphere

Expressions for the axial (i.e. acting along the axis of wave propagation) and transverse (lateral) acoustic radiation forces on a suspended object in an ideal fluid are derived for arbitrary shaped beams. These expressions are obtained from the integration of the radiation stress tensor in the far-field. Numerical examples on non-vortex and vortex Bessel beams on a spherical target are presented. It is demonstrated the existence of both “pushing” and “tractor” behaviors for which the axial force can be oriented, respectively, along the direction of wave propagation or opposite to it. This can be adjusted by choosing specific values of the beam cone angle and the sphere size factor ka (where k is the wavenumber and a is the sphere's radius). Furthermore, by changing the topological charge m of the beam and the position of the sphere, the transverse force may be oriented radially (outward or inward) for m=0 or may exhibit a vortex pattern for m ≥ 1.

Negative acoustic radiation forces produced by Bessel beams: acoustic tractor beams and scattering

The theory for negative acoustic radiation forces on objects in various Bessel beams is reviewed [P. L. Marston, J. Acoust. Soc. Am. 120, 3518–3524 (2006); L. K. Zhang and P. L. Marston, Phys. Rev. E 84, 035601 (2011)] together with geometric insight provided by researchers in optics. When examining conditions favorable for negative radiation forces it can be helpful to consider the far field scattering for axisymmetric objects of interest because the axial radiation force can be directly related to the asymmetry in the scattering and the conic angle of the beam. The analysis also serves to clarify the way in which absorption by the object contributes to positive forces and to clarify the influence of helicity. Considering the symmetry properties of the scattering provides additional insight as does the evaluation of radiation forces and wave fields using the computational method of finite elements. In the non-absorbing case it can also be helpful to express the partial-wave amplitudes in terms of phase shifts since in acoustics there is only one phase shift for each partial-wave. [Marston and Thiessen were supported by ONR and Zhang was supported by NASA.]

Axial radiation force exerted by general non-diffracting beams

The axial radiation force exerted by a general non-diffracting beam on an object of arbitrary shape in lossless medium is analyzed. The object may be on or off the beam's axis. The analysis is based on the plane-wave representation of the beam using an azimuthal function and conical angle. The analytical expression relates the force to axial projections of the extracted and scattered momentum. Using an extended optical theorem, the extinction is related to the scattering at the forward direction of the beam's plane wave components. The axial force is expressed using the scattering amplitude and known angular functions.

Improvement of optical trapping effect by using the focused high-order Laguerre–Gaussian beams

We investigate the optical trapping effect of high-order Laguerre–Gaussian (LG) beams acting on a dielectric sphere in Rayleigh regime. For LG beams with the azimuthal mode index l=0, it is found that under the same input power, the transverse trapping effect can be enhanced several times with increasing the radial mode index p, compared with that of the Gaussian beam; while its axial trapping effect is exactly the same as that of Gaussian beam, although the central trapping region reduces as p increases. For LG beams with l≥1, we find that the maximal transverse gradient forces increase with the increasing of p and the axial radiation forces reduces slightly, therefore an optimal choose on p and l is necessary for obtaining an optimal optical guiding. Our result is useful for analyzing the trapping efficiency of LG beams applied in micromanipulation technologies.

Axial acoustic radiation torque of a Bessel vortex beam on spherical shells

The present paper investigates the interaction of an acoustic Bessel vortex beam centered on a viscoelastic polyethylene sphere and spherical shells filled with air or water immersed in nonviscous water and mercury, and the induced axial acoustic radiation torque (ART) resulting from the transfer of angular momentum. Closed-form series expansions for the axial ART are derived for the case of progressive, standing, and quasistanding waves. The ART is shown to be the result of acoustic absorption inside the particle's material. Numerical predictions shown in the form of two-dimensional (2D) plots illustrate the theory, and reveal new properties related to the ART of Bessel vortex beams. Potential applications are in particle rotation and manipulation. Other applications, such as the characterization of fluids from induced angular accelerations (produced by the ART) and containerless processing, may benefit from the analysis developed here.

Effects of the transparent cathode on the performance of a relativistic magnetron with axial radiation

Experimental investigation of the transparent cathode used in a relativistic magnetron with axial radiation is reported in this paper. The transparent cathode is composed of six separate stalks with the diameter of 6 mm. Under the working condition of 549 kV and ∼0.38 T, the relativistic magnetron with the transparent cathode experimentally produces a 550 MW microwave. The radiation mode is TE(11) at the frequency of 2.35 GHz. The total efficiency is 16.7%. The variations of the relative positions between the separate stalks and the anode blocks can perform the maximum difference of 4 ns in microwave duration. Compared with the conventional solid cathode, the transparent cathode provides faster startup time of 12 ns, relatively wider pulse duration of 35% and relatively higher efficiency of 10.6%.

Experimental demonstration of a compact high efficient relativistic magnetron with directly axial radiation

A compact relativistic magnetron with axial microwave radiation is experimentally investigated. Under the modified magnetic field distribution, only connecting a special horn antenna in the axial direction, the relativistic magnetron can stably radiate high power and high efficiency microwaves. The total length of the device is ∼0.3 m, and the volume is ∼0.014m3. In such working condition that the applied voltage is 539 kV and the magnetic field is ∼0.38 T, the output microwave power is ∼1.24 GW. Correspondingly, the total efficiency is about 34.1%. The radiating frequency is 2.35GHz, which is in agreement with the π mode frequency of the theoretical expectation.

Angular momentum flux of nonparaxial acoustic vortex beams and torques on axisymmetric objects

An acoustic vortex in an inviscid fluid and its radiation torque on an axisymmetric absorbing object are analyzed beyond the paraxial approximation to clarify an analogy with an optical vortex. The angular momentum flux density tensor from the conservation of angular momentum is used as an efficient description of the transport of angular momentum. Analysis of a monochromatic nonparaxial acoustic vortex beam indicates that the local ratio of the axial (or radial) flux density of axial angular momentum to the axial (or radial) flux density of energy is exactly equal to the ratio of the beam's topological charge l to the acoustic frequency ω. The axial radiation torque exerted by the beam on an axisymmetric object centered on the beam's axis due to the transfer of angular momentum is proportional to the power absorbed by the object with a factor l/ω, which can be understood as a result of phonon absorption from the beam. Depending on the vortex's helicity, the torque is parallel or antiparallel to the beam's axis.

Microparticle trapping in an ultrasonic Bessel beam

This paper describes an acoustic trap consisting of a multi-foci Fresnel lens on 127 μm thick lead zirconate titanate sheet. The multi-foci Fresnel lens was designed to have similar working mechanism to an Axicon lens and generates an acoustic Bessel beam, and has negative axial radiation force capable of trapping one or more microparticle(s). The fabricated acoustic tweezers trapped lipid particles ranging in diameter from 50 to 200 μm and microspheres ranging in diameter from 70 to 90 μm at a distance of 2 to 5 mm from the tweezers without any contact between the transducer and microparticles.

Calculation of radiation forces exerted on a uniaxial anisotropic sphere by an off-axis incident Gaussian beam

Using the theory of electromagnetic scattering of a uniaxial anisotropic sphere, we derive the analytical expressions of the radiation forces exerted on a uniaxial anisotropic sphere by an off-axis incident Gaussian beam. The beam's propagation direction is parallel to the primary optical axis of the anisotropic sphere. The effects of the permittivity tensor elements ε(t) and ε(z) on the axial radiation forces are numerically analyzed in detail. The two transverse components of radiation forces exerted on a uniaxial anisotropic sphere, which is distinct from that exerted on an isotropic sphere due to the two eigen waves in the uniaxial anisotropic sphere, are numerically studied as well. The characteristics of the axial and transverse radiation forces are discussed for different radii of the sphere, beam waist width, and distances from the sphere center to the beam center of an off-axis Gaussian beam. The theoretical predictions of radiation forces exerted on a uniaxial anisotropic sphere are hoped to provide effective ways to achieve the improvement of optical tweezers as well as the capture, suspension, and high-precision delivery of anisotropic particles.

Propagation characteristics of arrayed transient electromagnetic pulses

Starting from the uniform disk current model, an analytical solution for the electromagnetic pulse axial energy radiation is derived and a physical meaning then given to the axial energy propagation characteristics of a unit antenna. From this solution, a point-source approximation model in the time domain is introduced. Parameters such as the energy propagation characteristics and beamwidth of the electromagnetic pulse beam radiating from arrayed antenna are analyzed theoretically. An arrayed transient electromagnetic pulse generator is developed incorporating a 23×16 ultra-wideband tapered slot antenna integrated with a Blumlein formation line and photoconductive semiconductor switch. Experiments performed over a 2.5 km range confirm that the arrayed transient electromagnetic pulse can propagate in free space with the specified waveform. Moreover, the field components can be superposed in phase, and the radiation beam can be focused into a single pulse. Results from calculations are in agreement with experimental results within the measurement uncertainties.

Radiation torque on solid spheres and drops centered on an acoustic helicoidal Bessel beam.

Somewhat analogous to circularly polarized electromagnetic waves carrying axial angular momentum and generating a corresponding torque, a helicoidal acoustic (vortex) beam also carries axial angular momentum and absorption of such a beam should also produce an axial radiation torque [B. T. Hefner and P. L. Marston, J. Acoust Soc. Am. 106, 3313–3316 (1999)]. Here the acoustic radiation torque on solid spheres and spherical liquid drops centered on acoustic helicoidal Bessel beams is analyzed. Using a relation between the scattering and the partial wave coefficients for a sphere in a helicoidal Bessel beam, the torque is predicted to be proportional to the ratio of the absorbed power to the acoustic frequency. Calculations suggest that beams with a low topological charge tend to be more efficient for generating torques on solid spheres for all frequencies and on liquid drops in the low frequency regime. Balanced by drag torque, a steady rotation is generated. Calculations of the steady‐state angular velocit...

Simulation investigation of the 2 mode operating tunable relativistic magnetron with axial radiation

A tunable relativistic magnetron with axial radiation operating at 2 mode is investigated by three-dimensional particle-in-cell simulation in this paper. The tuning is realized by filling solid dielectric material into the cavities of the interaction region. The effects of changing the relative permittivity and the inner radius of the dielectric material on the operating frequency, the average output power and the efficiency are analyzed. Then the principle of the tuning is demonstrated. The simulation results show that under the unchanged structure parameters and the work point, the relativistic magnetron realizes the tuning from S band to L band by varying the relative permittivity or the inner radius of the solid dielectric material. Furthermore, with inserting the dielectric material, the output capability of the relativistic magnetron is improved. When the relative permittivity is 615 and the radius is 4.184.40 cm, the increase in efficiency can reach 80%, the decreased frequency range is less than 55%.