Curved photonic nanojet generated by a rotating cylinder.

The curved photonic nanojet (CPNJ) produced due to the interaction between a dielectric circular cylinder rotating at a stable angular velocity and a plane wave is investigated. Based on this model, the optical Magnus effect of a dielectric circular cylinder is verified. And the analytical expression of both internal and external electric field are given based on the instantaneous rest-frame theory and the partial-wave series expansion method in cylindrical coordinates. The influence of the size parameter, the relative refractive index, and the rotating dimensionless parameter on the CPNJ are analyzed and discussed in numerical results. The "photonic nanojet curved" effect is highlighted, which can be used to generate the off-axis photonic nanojet (PNJ) controlling particles by adjusting the angular velocity of the dielectric cylinder. The results of this manuscript have promising application prospects in optical tweezers, particle manipulation, and optical trapping. Moreover, it also provides theoretical support for the particle spinning and generation of the off-axis CPNJ.

Scattering of a radially polarized Bessel beam by a PEMC sphere: photonic nanojet and bottle beam formation.

The scattering of a radially polarized (r p) Bessel vortex and nonvortex beam by a perfect electromagnetic conductor (PEMC) sphere is studied based on the generalized Lorenz-Mie theory. The electric and magnetic fields of the incident arbitrary-shaped polarized beams are constructed using vector spherical wave functions (VSWFs) and beam shape coefficients. The analytical expression of the scattered field is expanded using VSWFs and scattering coefficients, which are derived by considering PEMC boundary conditions. The expression of the normalized dimensionless far-field scattering intensity (NDFSI) is also defined and derived. The photonic nanojet (PNJ) and the "bottle beam" generated by the interaction between the PEMC sphere and the vortex and nonvortex Bessel beam under r p are emphasized in this paper. Moreover, the intensity and directivity of NDFSI are also considered. It has been found that the generation of the PNJ and the "bottle beam" is determined by the half-cone angle α 0 of the r p Bessel beam and admittance parameter M of the PEMC sphere. Furthermore, the influence of M, α 0, and integer order l of the Bessel beam on the intensity and distribution of NDFSI is also discussed. The findings are important in the research on meta-materials and promising prospects in microwave engineering, antenna engineering, imaging, subwavelength focusing, optical radiation force, and torque.

Optical Magnus radiation force and torque on a dielectric layered cylinder with a spinning absorptive dielectric core.

A dielectric cylindrical shell material with an inner stationary absorptive core (or, equivalently, a concentric layered cylinder) illuminated by an axisymmetric wave field (in 2D) with arbitrary polarization will experience a time-averaged radiation force along the direction of wave propagation, whereas the transverse component vanishes as required by symmetry. Counterintuitively, the present analysis shows that when the inner absorptive core material rotates with an initial angular velocity Ω0 around its main geometrical axis, a transverse radiation force component arises (in addition to a longitudinal force) as well as an axial radiation torque component in plane waves. This phenomenon is the analog of the classical hydrodynamic Magnus effect. In this analysis, the instantaneous rest-frame theory and the modal series expansion method in cylindrical coordinates are utilized to formulate the EM/optical scattering from a cylindrical shell with arbitrary thickness, and to compute the optical radiation force and torque vector components. Particular emphases are given on the size parameter of the cylindrical shell, the layer thickness, the angular rotation of the inner absorptive core, and the polarization (TM or TE) of the incident plane waves. Numerical computations illustrate the analysis and explicate the behaviors of the longitudinal, transverse, and axial radiation force and torque components. Related applications for the optical Magnus effect in radiation force and torque investigations can benefit from the results of the present analysis in spin-optics, rotational Doppler shift for optical waves, optical tweezers, optical manipulation of elongated spinning objects, and particle rotation.

Optical radiation force on a dielectric sphere by a polarized Airy beam.

The optical radiation force acting on a homogeneous and lossless dielectric spherical particle by a polarized Airy beam is analyzed in terms of the generalized Lorenz-Mie theory. The transverse and longitudinal radiation force components are theoretically evaluated and numerically simulated, emphasizing the transverse scale ω0, attenuation parameter γ, and polarization of the incident Airy beam versus the size parameter ka of the sphere. These results reveal that a polarized Airy beam can trap the dielectric sphere in its main caustic or sidelobes of the beam by the optical transverse force and be guided along the parabolic trajectory of the longitudinal optical force. Moreover, γ and ω0 of the Airy beams and ka of the dielectric sphere can affect the amplitude and distribution of the optical force components. This research may be helpful for the development of Airy optical tweezers in applications involving particle manipulation, optical levitation, particle sorting, and other emergent areas.

Optical Magnus effect in the photophoresis of a spinning absorptive dielectric circular cylinder.

When a stationary absorptive dielectric cylinder suspended in a gas (such as air) is illuminated by an axisymmetric wave field (such as plane waves), the transverse (T) photophoretic asymmetry factor (PAF) vanishes as required by geometrical symmetry [Appl. Opt.60, 7937 (2021) APOPAI0003-693510.1364/AO.435306]. Counter-intuitively, when the cylinder possesses an initial angular velocity Ω0 with a sufficiently small acceleration and spins around its main axis in the illuminating field of axisymmetric plane waves, it is shown here that the T-PAF (which is directly proportional to the T-photophoretic force vector component) is quantifiable, in analogy with the Magnus effect in hydrodynamics where a force perpendicular to the axis of the cylinder and to the propagation direction arises. Based upon the instantaneous rest-frame theory and the partial-wave series expansion method in cylindrical coordinates, the internal electric field of the spinning absorptive dielectric cylinder is determined and utilized to compute both the longitudinal (L) and T-PAFs. Particular emphases are given on the size parameter of the cylinder, its angular rotation, the light absorption inside its core material and the polarization (TM or TE) of the incident plane waves. The dimensionless intensity function (DIF) is also computed, which reveals quantitative information on the heated portions within the internal absorptive core material of the cylinder. Numerical computations illustrate the analysis and explicate the behaviors of the DIF and the L- and T-PAFs, which predict the emergence of the forward, neutral, and reverse optical/electromagnetic Magnus effect in the photophoresis of an absorptive dielectric cylinder and related applications in spin optics, optical tweezers, optical manipulation of elongated objects, and radiative transfer research.

Unconventional circularly polarized Airy light-sheet spinner tweezers.

Standard circularly polarized Airy light-sheets are synthesized by combining two dephased TE and TM wave fields, polarized in the transverse directions of wave propagation, respectively. Somewhat counterintuitively, the present analysis theoretically demonstrates the existence of unconventional circularly polarized Airy light-sheets, where one of the individual dephased wave fields is polarized along the direction of wave propagation. The vector angular spectrum decomposition method in conjunction with the Lorenz gauge condition and Maxwell's equations allow adequate determination of the Cartesian components of the incident radiated electric field components. Subsequently, the Cartesian components of the optical time-averaged radiation force and torque can be determined and computed. The example of a subwavelength light-absorptive (lossy) dielectric sphere is considered based upon the dipole approximation method. The results demonstrate the emergence of negative force components, suggesting retrograde motion and spinning reversal depending on the polarization of the Airy light-sheet and its transverse scale and attenuation parameter. The results are important in the design of light-sheet spinner tweezers and applications involving optical switching and particle manipulation and rotation.

Longitudinal and transverse PAFs for an absorptive magneto-dielectric circular cylinder in light-sheets of arbitrary wavefronts and polarization.

Based upon the expression of the heat source function in photophoresis, generalized mathematical expressions for the longitudinal (L) and transverse (T) photophoretic asymmetry factors (PAFs) for a light-absorptive magneto-dielectric circular cylinder of arbitrary relative permittivity and permeability, illuminated by an arbitrarily shaped polarized light-sheet, are derived and computed. The L- and T-PAFs are directly proportional to the L and T components of the photophoretic force vector, respectively, induced by light absorption inside the particle, and their sign predicts the behavior of the force (pulling/attractive or pushing/repulsive). The partial-wave series expansion method in cylindrical coordinates is used, and the obtained mathematical expressions for the L- and T-PAFs depend on the beam-shape coefficients and the internal coefficients of the cylinder. Numerical examples illustrate the theory for TE and TM polarized plane waves, and nonparaxial Airy light-sheets with particular emphasis on absorption inside the cylinder and varying the Airy light-sheet parameters. The generalized expressions presented here are applicable to any light-sheet of an arbitrary wavefront, and offer additional quantitative observables for the analysis of the photophoretic force in applications in electromagnetic scattering, optical light-sheet tweezers, particle manipulation, radiative transfer, and other research fields.

Longitudinal and transverse optical scattering asymmetry parameters for a dielectric cylinder in light-sheets of arbitrary wavefronts and polarization.

The asymmetry parameter is an important quantity used in radiative transfer modeling and scattering. This parameter specifies the amount of energy scattered by the particle along the direction of the incident illuminating field. However, a rigorous and complete analysis of the energetic scattering requires determining the energy scattered in the lateral direction as well. As such, the present work introduces generalized expressions for the scattering asymmetry parameters for a dielectric cylinder in arbitrary-shaped light-sheets, both along and perpendicular to the direction of the incident radiation. Both longitudinal and transverse scattering asymmetry parameters are defined, and their generalized expressions are obtained based on the (spatial) average cosine and sine of the scattering angle θ and the expression of the scattering cross section (or energy efficiency). The partial-wave series expansion method in cylindrical coordinates is used, and the resulting mathematical expressions depend on the beam-shaped coefficients and the scattering coefficients of the dielectric cylinder. Numerical results for arbitrary-shaped light-sheets illuminating a dielectric cylinder cross section located arbitrarily in space are presented and discussed. The longitudinal and transverse scattering asymmetry parameters defined here offer additional quantitative (quadratic) observables for the analysis of the energetic scattering in applications in electromagnetic scattering, optical light-sheet tweezers, radiative transfer computations, and remote sensing, to name a few examples.

Radiation force and torque on an elliptical cylinder illuminated by a TE-polarized non-paraxial focused Gaussian light sheet with arbitrary incidence.

Predicting and computing the optical radiation force and torque experienced by an elliptical cylinder illuminated by a structured finite light-sheet beam in two dimensions (2D) remains a challenge from the standpoint of light-matter interactions in electromagnetic (EM) optics, tweezers, laser trapping, and scattering theory. In this work, the partial-wave series expansion method in cylindrical coordinates (which utilizes standard Bessel and Hankel wave functions) is proposed, verified, and validated. Exact expressions for the longitudinal and transverse radiation force components (per length) as well as the axial radiation torque component (per length) are derived analytically without any approximations. The example of a TE-polarized non-paraxial focused Gaussian light sheet illuminating a perfect electrically conducting (PEC) elliptical cylinder is considered. The scattering coefficients of the elliptical cylinder are determined by imposing the Neumann boundary condition and numerically solving a linear system of equations by matrix inversion. The structural functions are determined using a single numerical angular integration procedure to enforce the orthogonality and thus validity of the solution, making the proposed method semi-analytical. Calculations are performed for the non-dimensional longitudinal and transverse radiation force efficiencies (or functions) as well as the axial radiation torque efficiency. Emphases are given to varying the ellipticity of the cylindrical particle, its non-dimensional size, the non-paraxial beam waist (i.e., focusing), and the angle of incidence in the polar plane. Suitable convergence plots confirm the validity of the partial-wave series method to evaluate accurately the radiation force and torque with no limitation to a particular frequency range or particle size. The results are mostly relevant in understanding the fundamentals of the optical/EM radiation force and torque theories for structured focused light sheets and related applications dealing with the interactions of EM waves with elongated tubular particles with elliptical surfaces in particle manipulation and other areas. The analogy with the acoustical counterpart is also noted, which shows the universal character of the radiation force and torque phenomena.

Dynamic oscillatory powers, cross sections, and energy efficiencies in coherent optical heterodyning.

In a recent analysis [J. Quant. Spectrosc. Radiat. Transfer250, 106994 (2020)JQSRAE0022-407310.1016/j.jqsrt.2020.106994], the emergence of a dynamic oscillatory radiation force in coherent optical/electromagnetic (EM) heterodyning has been demonstrated for TM- and TE-polarized amplitude-modulated (AM) plane waves interacting with a lossless dielectric circular cylinder. A dynamic oscillatory component of the EM radiation force emerged at the beat frequency of two interfering fully correlated wave fields driven at slightly different frequencies. This work extends the scope of that analysis to examine the oscillatory behavior of energy-related physical observables from the standpoint of energy conservation applied to scattering. Partial-wave series for the oscillatory scattering, extinction and absorption powers, cross sections, and energy efficiencies are derived in cylindrical coordinates for a circular homogeneous cylinder material using the short-term time averaging (STTA) procedure and Poynting's theorem. AM plane progressive waves incident upon a lossless dielectric cylinder with arbitrary radius are considered. Numerical computations of the oscillatory scattering and extinction energy efficiencies illustrate the theory. A criterion based on computing and quantifying accurately the percentage (or relative) error between the dynamic (oscillatory) extinction and scattering efficiencies is developed and numerically evaluated. This benchmark tool provides physical validation and verification of the results from the standpoint of energy conservation. The results show that the percent (relative) error increases at the resonances of the dielectric cylinder as its refractive index increases. Far from the resonances, the oscillatory component of the STTA remains appropriate because the percent (relative) error does not exceed 0.05%, provided the beating difference frequency is much smaller than that of the primary waves. The case of an absorptive dielectric cylinder is also illustrated and discussed. The present analysis is of fundamental importance in order to validate dynamic radiation force computational results from the standpoint of energy conservation in the development, design, and optimization of oscillatory optical heterodyne tweezers and tractor beams in related applications in particle manipulation.

Optical radiation force expression for a cylinder exhibiting rotary polarization in plane quasi-standing, standing, or progressive waves.

A generalized analytical expression for the radiation force of plane quasi-standing, standing, or progressive electromagnetic (EM) waves is derived for a circular cylinder exhibiting rotary polarization in a TM-polarized incident field. Such a material, allowing rotary polarization, produces cross-polarized waves in the scattered field, which contribute to the radiation force experienced by the cylindrical object as shown here. As an example of a material exhibiting rotary polarization, a perfect electromagnetic conductor (PEMC) nonabsorptive cylinder is chosen to illustrate the analysis. In contrast with perfect electrical conductors (PECs), perfect magnetic conductors (PMCs), or conventional dielectric materials, the radiation force on a PEMC cylinder shows a direct dependency on the expansion coefficients of the cross-polarized waves, which do not exist for PECs, PMCs, or standard dielectrics. Extra new terms contribute to the generalized radiation force series expansions for plane quasi-standing, standing, or progressive waves. Numerical predictions demonstrate the possibility of trapping a circular-shaped cylinder material with rotary polarization in-plane quasi-standing or standing waves. Furthermore, the scattering, extinction, and absorption energy efficiencies for the nonabsorptive PEMC cylinder are computed, which validate the radiation force results from the standpoint of the law of energy conservation applied to EM scattering. The exact analytical radiation force expression for a PEMC cylinder of any arbitrary radius α (i.e., much smaller, comparable, or much larger than the wavelength of the illuminating incident field) in quasi-standing, standing, or progressive waves is also applicable to chiral, plasma, topological insulator, liquid crystal tubular phantom, or any other material exhibiting rotary polarization.

Induced radiation force of an optical line source on a cylinder material exhibiting circular dichroism.

The optical radiation force experienced by a cylinder material of circular cross section exhibiting circular dichroism (known also as rotary polarization) in an electric line source illumination is considered. An exact analytical expression for the radiation force (per length) valid for any frequency range is derived assuming an electric line source radiating cylindrically diverging TM-polarized waves without any approximations. The partial-wave series expansion method in cylindrical coordinates utilizing standard Bessel and Hankel functions is used to derive the electric and magnetic field expressions and a dimensionless radiation force function (or efficiency), which depends on the scattering coefficient of the cylinder as well as the distance from the radiating source. To illustrate the analysis, numerical computations for the dimensionless radiation force function for a perfect electromagnetic conductor (PEMC) cylinder are performed with emphasis on its dimensionless size parameter and source distance, which clearly draw attention to the contribution of the cross-polarized scattered waves (resulting from the rotary polarization effect) to the total force. The numerical predictions demonstrate the possibility to pull a circular-shaped cylinder material with rotary polarization toward the illuminating electric line source with TM-polarized waves using a curved wavefront depending on the PEMC material admittance, distance to the source, and size of the cylinder.

Self-bending scalar and vector bottle sheets.

This work demonstrates the generation of auto-bending cylindrical/tubular Bessel-Gauss bottle beams in homogeneous two-dimensional (2D) space. The corresponding wave fields flow through a two-dimensional curved trajectory leaving a singularity hollow central region, exhibiting the characteristic of circumventing obstacles. Scalar and vector fields are derived based on the angular spectrum decomposition method, the Helmholtz equation, the Lorenz gauge condition, and Maxwell's equations. The profile and area of the 2D bottle beams, together with the location of the autofocusing spots, are controlled by the intrinsic parameters of the illuminating waves and polarizations of the vector potential forming the incident fields. The demonstrated auto-bending cylindrical bottle beam solutions may find potential applications in acoustical and optical cloaking, auto-bending beam tweezers, imaging around steep corners, therapeutic investigations with unconventional autofocusing beams, acoustical and light sheets (i.e., slice of beams in 2D), and other related particle manipulation, isolation, and sorting devices, to name a few examples.

Negative optical radiation force and spin torques on subwavelength prolate and oblate spheroids in fractional Bessel-Gauss pincers light-sheets.

Fractional Bessel-Gauss light-sheets [J. Opt.19, 055602 (2017)JOOPDB0150-536X10.1088/2040-8986/aa649a], which correspond to finite optical "slices" in 2D and possess asymmetric slit openings and bending characteristics, are examined from the standpoint of optical radiation force and spin torque theories for a subwavelength spheroid with arbitrary orientation in space. The vector angular spectrum decomposition method in addition to the Lorenz gauge condition and Maxwell's equations are used to determine the Cartesian components of the incident radiated electric field of the Bessel-Gauss light-sheets. In the framework of the dipole approximation, the numerical results for the Cartesian components of the optical radiation force and spin torque vectors show that negative forces (oriented in the opposite direction of wave motion) and spin torques arise depending on the beam parameters, the orientation of the subwavelength spheroid in 3D space, and its aspect ratio (i.e., prolate versus oblate). The spin torque sign reversal reveals that counter-clockwise or clockwise rotations around the center of mass of the spheroid can occur. The results find important applications in the application of auto-focusing light-sheets in particle manipulation, rotation, and optical sorting devices.

Reverse propagation and negative angular momentum density flux of an optical nondiffracting nonparaxial fractional Bessel vortex beam of progressive waves.

Energy and angular momentum flux density characteristics of an optical nondiffracting nonparaxial vector Bessel vortex beam of fractional order are examined based on the dual-field method for the generation of symmetric electric and magnetic fields. Should some conditions determined by the polarization state, the half-cone angle as well as the beam-order (or topological charge) be met, the axial energy and angular momentum flux densities vanish (representing Poynting singularities), before they become negative. These negative counterintuitive properties suggest retrograde (negative) propagation as well as a rotation reversal of the angular momentum with respect to the beam handedness. These characteristics of nondiffracting nonparaxial Bessel fractional vortex beams of progressive waves open new capabilities in optical tractor beam tweezers, optical spanners, invisibility cloaks, optically engineered metamaterials, and other applications.

Measuring static viscous permeability of porous absorbing materials.

Conventional acoustical methods for measuring the permeability or flow resistivity of a porous material require a priori estimation of the porosity. In this work, an acoustical method is presented in which a simplified expression (independent of both the frequency and porosity) for the transmitted waves at the Darcy's regime (low frequency range) is derived, and used for the inverse determination of both the viscous static permeability (or flow resistivity) and the thickness of air-saturated porous materials. The inverse problem is solved based on the least-square numerical method using experimental transmitted waves in time domain. Tests are performed using industrial plastic foams. Experimental and numerical validation results of this method are presented, which show the advantage of measuring the viscous permeability and thickness of a porous slab, without the required prior knowledge of the porosity, but by simply using the transmitted waves.

Cylindrical quasi-Gaussian beams.

Making use of the complex-source-point method in cylindrical coordinates, an exact solution representing a cylindrical quasi-Gaussian beam of arbitrary waist w(0) satisfying both the Helmholtz and Maxwell's equations is introduced. The Cartesian components of the electromagnetic field are derived stemming from different polarizations of the magnetic and electric vector potentials based on Maxwell's vectorial equations and Lorenz's gauge condition, without any approximations. Computations illustrate the theory for tightly focused and quasi-collimated cylindrical beams. The results are particularly useful in beam-forming design using high-aperture or collimated cylindrical laser beams in imaging microscopy, particle manipulation, optical tweezers, and the study of scattering, radiation forces, and torque on cylindrical structures.

Transient ultrasound propagation in porous media using Biot theory and fractional calculus: application to human cancellous bone.

A temporal model based on the Biot theory is developed to describe the transient ultrasonic propagation in porous media with elastic structure, in which the viscous exchange between fluid and structure are described by fractional derivatives. The fast and slow waves obey a fractional wave equation in the time domain. The solution of Biot's equations in time depends on the Green functions of each of the waves (fast and slow), and their fractional derivatives. The reflection and transmission operators for a slab of porous materials are derived in the time domain, using calculations in the Laplace domain. Their analytical expressions, depend on Green's function of fast and slow waves. Experimental results for slow and fast waves transmitted through human cancellous bone samples are given and compared with theoretical predictions.

Generalized equation for transient-wave propagation in continuous inhomogeneous rigid-frame porous materials at low frequencies.

This paper provides a temporal model for the propagation of transient acoustic waves in continuous inhomogeneous isotropic porous material having a rigid frame at low frequency range. A temporal equivalent fluid model, in which the acoustic wave propagates only in the fluid saturating the material, is considered. In this model, the inertial effects are described by the inhomogeneous inertial factor [A. N. Norris, J. Wave Mat. Interact. 1, 365-380 (1986)]. The viscous and thermal losses of the medium are described by two inhomogeneous susceptibility kernels which depend on the viscous and thermal permeabilities. The medium is one-dimensional and its physical parameters (porosity, inertial factor, viscous, and thermal permeabilities) are depth dependent. A generalized wave propagation equation in continuous inhomogeneous material is established and discussed.

Vector wave analysis of an electromagnetic high-order Bessel vortex beam of fractional type α.

The scalar wave theory of nondiffracting electromagnetic (EM) high-order Bessel vortex beams of fractional type α has been recently explored, and their novel features and promising applications have been revealed. However, complete characterization of the properties for this new type of beam requires a vector analysis to determine the fields' components in space because scalar wave theory is inadequate to describe such beams, especially when the central spot is comparable to the wavelength (k(r)/k≈1, where k(r) is the radial component of the wavenumber k). Stemming from Maxwell's vector equations and the Lorenz gauge condition, a full vector wave analysis for the electric and magnetic fields is presented. The results are of particular importance in the study of EM wave scattering of a high-order Bessel vortex beam of fractional type α by particles.