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The remarkable properties of magnetic nanostructures have sparked considerable interest within the biomedical domain, owing to their potential for diverse applications. In targeted drug delivery systems, therapeutic molecules can be loaded onto magnetic nanocarriers and precisely guided and released within the body with the assistance of an externally applied magnetic field. However, conventional external magnetic fields generated by permanent magnets or electromagnets are limited by finite magnetic field gradients, shallow penetration depths, and low precision. The novel structured light field known as the Airy light-sheet possesses unique characteristics such as non-diffraction, self-healing, and self-acceleration, which can potentially overcome the limitations of traditional magnetic fields to some extent. While existing studies have primarily focused on the manipulation of dielectric particles by Airy light-sheet, comprehensive analyses exploring the intricate interplay between Airy light-sheet and magnetic nanostructures are currently lacking in the literature, with only preliminary theoretical discussions available. This study systematically explores the mechanical response of magnetic spherical particles under the influence of Airy light-sheet, including radiation forces and spin torques. Furthermore, we provide an in-depth analysis of the effects of particle size, permittivity, permeability, and incident light-sheet parameters on the mechanical effects. Our research findings not only offer new theoretical guidance and practical references for the application of magnetic nanoparticles in biomedicine but also provide valuable insights for the manipulation of other types of micro/nanoparticles using structured light fields.

Electromagnetic scattering is a routine tool for rapid, non-contact characterization of particle media. In previous work, the interaction targets of scattering intensity, scattering efficiency, and extinction efficiency of Bessel pincer light-sheet beams were all aimed at dielectric spheres. However, most particles in nature are charged. Considering the boundary condition on a charged sphere, the beam shape coefficients (BSCs) (pmn,qmn) of the charged spherical particle illuminated by a Bessel pincer light-sheet beam are obtained. The extinction, scattering, and absorption efficiencies are derived under the generalized Lorenz-Mie theory (GLMT) framework. This study reveals the significant differences in scattering characteristics of Bessel pincer light-sheet beams on a charged particle compared to traditional beams. The simulations show a few apparent differences in the far-field scattering intensity and efficiencies between charged and natural spheres under the influence of dimensionless size parameters. As dimensionless parameters increase, the difference between the charged and neutral spheres decreases. The effects of refractive index and beam parameters on scattering, extinction, and absorption coefficients are different but tend to converge with increasing dimensionless parameters. When applied to charged spheres with different refractive indices, the scattering, extinction, and absorption efficiencies of Bessel pincer light-sheet beams change with variations in surface charge. However, once the surface charge reaches saturation, these efficiencies become stable. This study is significant for understanding optical manipulation and super-resolution imaging in single-molecule microbiology.

Based on the optical Magnus effect, the analytical expressions of the electromagnetic field that a spinning dielectric sphere illuminated by polarized plane waves are derived according to the "instantaneous rest-frame" hypothesis and Minkowski's theory. More attention is paid to the near field. The unusual optical phenomena in mesoscale spheres without material and illumination wave asymmetry that are the photonic hook (PH) and whispering gallery mode (WGM)-like resonance caused by rotation are explored. The impact of resonance scattering on PHs is further analyzed under this framework. The influence of non-reciprocal rotating dimensionless parameter γ on PH and resonance is emphasized. The results in this paper have extensive application prospects in mesotronics, particle manipulation, resonator design, mechatronics, and planetary exploration.

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.

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.

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 ω 0 , attenuation parameter γ , and polarization of the incident Airy beam versus the size parameter k a 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 ω 0 of the Airy beams and k a 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.

In the framework of Generalized Lorenz-Mie theory (GLMT), based on the expansion results of electromagnetic field radiation components of Bessel pincer light sheets beam acting on dielectric particles of arbitrary size, the expression of radiation force components in a Cartesian coordinate system is obtained by using the Maxwell stress tensor method. On the one hand, the effects of the refractive index and the equivalent radius of spherical particles on the distribution of radiation force are discussed; On the other hand, the influence of beam scaling parameter and beam order of Bessel pincer light sheets beam on the distribution of radiation force are investigated. The results indicate that the changes of particle's refractive index and effective radius only affect the distribution of radiation force. However, the beam scaling parameter and beam order of Bessel pincer light sheets beam have a very sharp impact on the convergence position, distribution range and bending degree far away from the wave source of the radiation force. Single-beam optical tweezers using the self-focusing and self-bending Bessel pincer light-sheets beam are crucial for applications such as single molecule biophysics, optical manipulation and particle separation/clearing.

In the framework of the generalized Lorenz-Mie theory (GLMT), the optical force and torque on a graphene-coated gold nanosphere by a vector Bessel beam are investigated. The core of the particle is gold, whose dielectric function is given by the Drude-Sommerfeld model, and the coating is multilayer graphene with layer number N , whose dielectric function is described by the Lorentz-Drude model. The axial optical force Fz and torque Tz are numerically analyzed, and the effects of the layer number N , wavelength λ, and beam parameters (half-cone angle α0, polarization, and order l ) are mainly discussed. Numerical results show that the optical force and torque peaks can be adjusted by increasing the thickness of the graphene coating, and can not be adjusted by changing α0 and l . However, α0 and l can change the magnitude of the optical force and torque. The numerical results have potential applications involving the trapped graphene-coated gold nanosphere.

In this article, we study the optical force exerted on nanorods. In recent years, the capture of micro-nanoparticles has been a frontier topic in optics. A Photonic Jet (PJ) is an emerging subwavelength beam with excellent application prospects. This paper studies the optical force exerted by photonic jets generated by a plane wave illuminating a Generalized Luneburg Lens (GLLs) on nanorods. In the framework of the dipole approximation, the optical force on the nanorods is studied. The electric field of the photonic jet is calculated by the open-source software package DDSCAT developed based on the Discrete Dipole Approximation (DDA). In this paper, the effects of the nanorods' orientation and dielectric constant on the transverse force F x and longitudinal force F y are analyzed. Numerical results show that the maximum value of the positive force and the negative force are equal and appear alternately at the position of the photonic jet. Therefore, to capture anisotropic nanoscale-geometries (nanorods), it is necessary to adjust the position of GLLs continuously. It is worth emphasizing that manipulations with nanorods will make it possible to create new materials at the nanoscale.

Debye series expansion (DSE) is developed for electromagnetic (light) scattering by a charged sphere. By comparing our results with Mie theory (for a charged sphere) and with DSE (for a neutral sphere), we verify our theory numerically. DSE is employed for calculation of far-field intensity, and absorption and extinction efficiencies of charged spherical particles illuminated by a plane wave. The influences of various parameters (including surface charge, refractive index, size parameters, Debye mode, etc.) are studied. The rainbow produced by charged particles is analyzed. These results are of great significance in many fields including particle sizing, optical tweezers, etc.

The effects of the individual scattering process on the formations of both the particle hologram and its corresponding reconstructed three-dimensional particle image are investigated using the Debye series. A particle hologram model using the Debye series decomposes the object wave into different scattering modes and thus permits evaluating the effects of the individual scattering process [diffraction, reflection, transmission, refractions with (p-1) internal reflections] on the particle holography quantitatively. In the Gabor inline holography of a transparent droplet, the transmission light causes small discrepancies between the hologram fringes of an opaque particle (diffraction) and a transparent particle near the zero point of the Bessel-like modulation function, eventually giving rise to the glory spot in the center of the reconstructed dark particle image. For off-axis holography, this paper reveals the effects of reflection, particularly total reflection by bubbles, transmission, and refractions with (p-1) internal reflections of the scattered light on the formation and the reconstructed glory spot images of typical forward and backward off-axis holography.

On the basis of generalized Lorenz-Mie theory, the Debye series expansion (DSE) for radiation pressure forces (RPF) exerted on a multilayered sphere induced by focused beams is introduced. The DSE can isolate the contribution of each scattering process to RPF, and give a physical explanation of RPF. Typically, the RPF induced by a Gaussian beam is studied. The DSE is employed to the simulation of RPF corresponding to different scattering processes (diffraction, reflection, refraction, etc.) in detail, and gives the physical mechanism of RPF. The effects of various parameters, such as scattering mode p, beam position, and radius of core for coated spheres, to RPF is researched.

The Debye series expansion expresses the Mie scattering coefficients into a series of Fresnel coefficients and gives physical interpretation of different scattering modes, but when an infinite multilayered cylinder is obliquely illuminated by electromagnetic plane waves, the scattering process becomes very complicated because of cross polarization. Based on the relation of boundary conditions between global scattering process and local scattering processes, the generalized Debye series expansion of plane wave scattering by an infinite multilayered cylinder at oblique incidence is derived in this paper. The formula and the code are verified by the comparison of the results with that of Lorenz-Mie theory in special cases and those presented in the literatures.

By means of geometrical optics we present an approximation method for acceleration of the computation of the scattering intensity distribution within a forward angular range (0-60 degrees ) for gradient-index spheres illuminated by a plane wave. The incident angle of reflected light is determined by the scattering angle, thus improving the approximation accuracy. The scattering angle and the optical path length are numerically integrated by a general-purpose integrator. With some special index models, the scattering angle and the optical path length can be expressed by a unique function and the calculation is faster. This method is proved effective for transparent particles with size parameters greater than 50. It fails to give good approximation results at scattering angles whose refractive rays are in the backward direction. For different index models, the geometrical-optics approximation is effective only for forward angles, typically those less than 60 degrees or when the refractive-index difference of a particle is less than a certain value.

The Debye series has been a key tool for the understanding of light scattering features, and it is also a convenient method for understanding and improving the design of optical instruments aimed at optical particle sizing. Gouesbet has derived the Debye series formulation for generalized Lorenz-Mie theory (GLMT). However, the scattering object is a homogeneous sphere, and no numerical result is provided. The Debye series formula for plane-wave scattering by multilayered spheres has been derived before. We have devoted our work to the Debye series of Gaussian beam scattering by multilayered spheres. The integral localized approximation is employed in the calculation of beam-shape coefficients (BSCs) and allows the study of the scattering characteristics of particles illuminated by the strongly focused beams. The formula and code are verified by the comparison with the results produced by GLMT and also by the comparison with the result for the case of plane-wave incidence. The formula is also employed in the simulation of the first rainbow by illuminating the particle with one or several narrow beams.

We derive the formula of the Debye-series decomposition for normally incident plane-wave scattering by an infinite multilayered cylinder. A comparison of the scattering diagrams calculated by the Debye series and Mie theory for a graded-index polymer optical fiber is given and the agreement is found to be satisfied. This approach permits us to simulate the rainbow intensity distribution of any single order and the interference of several orders, which is of good use to the study of the scattering characteristics of an inhomogeneous cylinder and to the measurement of the refractive index profile of an inhomogeneous cylinder.

We have derived the formula for the Debye-series decomposition for light scattering by a multilayered sphere. This formulism permits the mechanism of light scattering to be studied. An efficient algorithm is introduced that permits stable calculation for a large sphere with many layers. The formation of triple first-order rainbows by a three-layered sphere and single-order rainbows and the interference of different-order rainbows by a sphere with a gradient refractive index, are then studied by use of the Debye model and Mie calculation. The possibility of taking only one single mode or several modes for each layer is shown to be useful in the study of the scattering characteristics of a multilayered sphere and in the measurement of the sizes and refractive indices of particles.