Generalized Lorenz Mie Theory Research Articles

Scattering properties of dual Bessel beams on chiral layered particle

The paper investigates the scattering analytical solution of arbitrary direction double zero-order Bessel beams (ZOBBs) incident on a non-uniform layered chiral sphere. Using the generalized Lorenz-Mie theory (GLMT), the electromagnetic field expansion expression of the double ZOBBs is obtained through the vector superposition of the spherical vector wave functions (SVWFs). Analytical solutions of the scattering on chiral layered particles by dual Bessel beams are derived based on the boundary condition. The iterative coefficient equations are constructed to obtain the expansion coefficients of the SVWFs in each region of the multi-layer chiral sphere. The variation of radar cross section (RCS) with angular distribution is numerically simulated, and the scattering results of layered chiral spheres degenerated into isotropic layered spheres are compared with the literature, which verifies the correctness of the theory and program. The effects of incident angle, polarization angle, cone angle and chiral parameters on the scattering characteristics of far region and internal field of the layered chiral particle are analyzed in detail. The theory and results can offer significant assistance in studying the optical properties of non-uniform chiral particles and complex biological cells irradiated by multiple beams and may also provide important practical value in the micromanipulation of multi-layered biological structures.

Description and reconstruction of typical structured light beams with vector spherical wave functions.

It is well known that the generalized Lorenz-Mie theory (GLMT) is a rigorous analytical method for dealing with the interaction between light beams and spherical particles, which involves the description and reconstruction of the light beams with vector spherical wave functions (VSWFs). In this paper, a detailed study on the description and reconstruction of the typical structured light beams with VSWFs is reported. We first systematically derive the so-called beam shape coefficients (BSCs) of typical structured light beams, including the fundamental Gaussian beam, Hermite-Gaussian beam, Laguerre-Gaussian beam, Bessel beam, and Airy beam, with the aid of the angular spectrum decomposition method. Then based on the derived BSCs, we reconstruct these structured light beams using VSWFs and compare the results of the reconstructed beams with those of the original beams. Our results will be useful in the study of the interaction of typical structured light beams with spherical particles in the framework of GLMT.

Optical pulling force on a uniaxial anisotropic sphere by a high-order Bessel (vortex) beam.

Based on the generalized Lorenz-Mie theory (GLMT) and the scattering theory of uniaxial spheres, a theoretical approach is introduced to study the axial radiation force (AOF) exerted on a uniaxial anisotropic sphere illuminated by an on-axis high-order Bessel (vortex) beams (HOBVBs). Applying Maxwell's stress tensor, an analytical expression of the AOF on a uniaxial anisotropic sphere by the on-axis HOBVB is derived. The correctness of the theoretical and numerical results is verified by comparing the AOF on an isotropic sphere by a zero-order Bessel beam (ZOBB) with those results by a plane wave, Gaussian beam, and ZOBB. The focus of this study is to determine some conditions of the tractor beam, so as to realize the inverse motion of an anisotropic sphere through a Bessel beam. The range of optical pulling force (OPF) that can pull particles in reverse motion generated by zero-order and first-order Bessel beams is extended from isotropic spherical particles to anisotropic spherical particles. The effects of the sphere radius, conical angle, and especially electromagnetic anisotropy parameters on the OPF in water or a vacuum environment are discussed in detail. Moreover, the OPF exerted on the uniaxial anisotropic sphere illuminated by a HOBVB with l=2, 3, and 4 is also exhibited. It indicates that the HOBVB with l=2, 3 is also a good tractor beam for the uniaxial anisotropic sphere. The OPF generated by Bessel beams on uniaxial anisotropic spherical particles is not only affected by the conical angle and radius but is also significantly influenced by anisotropic parameters and topological charges. These properties of the OPF are different from those on an isotropic sphere. The theory and results are hopeful to provide an effective theoretical basis for the study of optical micromanipulation of biological and anisotropic complex particles by optical tractor (vortex) beams.

Generalized Lorenz-Mie theory and simulation software for structured light scattering by particles

Structured light refers to an optical field with modulated phase and amplitude, characterized by distinct spatial patterns. It has applications in optical manipulation, 3D imaging, remote sensing, and communications. The Generalized Lorenz-Mie Theory (GLMT) extends foundational Mie theory to accommodate complex structured lights, enabling precise characterization of structured light-particle interactions. GLMT has emerged as a central theoretical framework for analyzing interactions between spherical particles and arbitrary structured light. This paper introduces ABSphere, simulation software utilizing GLMT to model structured light-spherical particle interactions. It then comprehensively reviews representative structured lights, including Laguerre–Gaussian, Bessel, and Airy beams, elucidating their interactions with spherical particles. Understanding structured light scattering behavior is crucial for elucidating underlying interaction mechanisms with spherical particles. The paper also emphasizes the significance of modeling structured light scattering by particles and discusses future directions for ABSphere software. Through continuous theoretical refinements and advancements, deeper understanding of structured light-particle interaction mechanisms can be achieved, enabling innovations in optical applications and technologies.

Optical manipulation of anisotropic spherical shell particles in a dual-beam trap

In this paper, based on the generalized Lorenz-Mie theory (GLMT), expressions for the scattering coefficient and the shape factor of the beam are derived for a uniaxial anisotropic spherical shell (UASS) particle illuminated by standing laser beams. Through a comprehensive analysis involving the Maxwell stress tensor equations and conservation law of electromagnetic momentum, explicit expressions for both the transverse and axial radiation force (RF) acting upon UASS particles have been analytically derived. The current theories are shown to be valid by comparison with the existing reference. To achieve a more stable capture of UASS particles, the influence of the corresponding parameters of the particle and the dual laser beams on the capture and manipulation is investigated in detail. These investigations could provide an effective way to achieve improvements in optical tweezers and can become an encouraging approach to realize the high accuracy operation of UASS particles.

Analysis of Scattering characteristics of PEMC sphere by vortex Bessel beams

Generalized Lorenz-Mie theory (GLMT) is well known to analyze the scattering characteristics of spherical surfaces and metamaterials such as perfect electromagnetic conductor (PEMC) sphere. Also, metamaterials are explored very well when illuminated by electromagnetic waves/beams and their characteristics depend upon propagation and scattering response. So, in this manuscript, vortex Bessel beam (VBB) interaction from PEMC sphere has been investigated. The VBB interaction with material particles is of quite interesting due to association of orbital angular momentum (OAM) with them. By employing the Integral localized approximation (ILA) method, the beam‐shape coefficients (BSCs) regarding VBB are obtained. Computations for the scattering efficiency QSca and extinction efficiency QExt for PEMC sphere by considering the co‐polarized and cross‐polarized scattering components are presented and analyzed. Moreover, the influences of OAM mode number, electromagnetic admittance parameter, and diffraction angle are discussed. Numerical results have applications regarding transfer of OAM of VBB to PEMC sphere and associated applications in light manipulation and scattering, optical tweezers, metamaterial fields, and remote sensing.

Analysis of the scattering of chiral layered particle by dual beams

The present study investigates the interaction between a chiral multilayer dielectric sphere and dual laser beams. Using the generalized Lorenz-Mie theory (GLMT), we extend the theory of single laser beam expansion to dual laser beam expansion. Analytical solutions of the scattering on chiral layered particles by dual laser beams are derived based on the boundary continuum condition. To validate the efficiency of our theory and methodologies proposed in this paper, we conduct a comparative analysis between our findings and the simulation results reported in existing literature. The numerical outcomes presented on the scattering pattern of far region and near-surface fields are analyzed in detail with the impact of various parameters, such as the incident angle, polarization angle, waist width, beam center position, inner and outer chiral parameters. The investigations are of significant importance for the analytical understanding of the optical scattering properties of multilayered biological cells with complex shapes and possess important application values in micro-manipulation of multilayered biological structures.

An approach for a polychromatic generalized Lorenz–Mie theory

In this work a polychromatic version of the generalized Lorenz–Mie theory stricto sensu (GLMT) is derived. In this new formalism, arbitrary time-dependent fields are expanded into partial waves using Bromwich scalar potentials and, instead of the usual expansion coefficients – the beam shape coefficients (BSCs) – found in the monochromatic GLMT, now one finds field shape spectra (FSSs) which are intrinsically frequency-dependent. Expressions for the incident, scattered and internal fields are presented, and it is shown how physical quantities defined and expressed in the monochromatic GLMT in terms of the BSCs are modified and redefined in terms of the FSSs in polychromatic light scattering problems, like scattered intensities and phase angles, absorption, extinction and scattering cross-sections, and radiation pressure cross-sections.

Failures of the classical optical theorem under arbitrary-shaped beam incidence in electromagnetism, acoustics, and quantum mechanics: motivation and a review

The classical optical theorem states that for a wave propagating in a lossless medium and incident on a finite scatterer, the extinction cross section is proportional to the real part of the scattering amplitude in the forward direction. When developing a light scattering theory known as the generalized Lorenz–Mie theory, it has been a surprise to observe that in 1982, the optical theorem failed when the scatterer was illuminated by an arbitrary-shaped beam. The extremely simple reason for that failure has been understood only in 2014 and published in 2016. This represents a more than three-decade-long story, which is called a “wow” story for reasons that will be mentioned in this paper. The opportunity of this story which pertains to both the history and philosophy of sciences is considered to provide a review of the optical theorem under arbitrary-shaped beam incidence in electromagnetism, acoustics, and quantum mechanics.

Blowing-ups of beam shape coefficients of Gaussian beams using finite series in generalized Lorenz–Mie theory

Compact closed-form expressions of the beam shape coefficients (BSCs) of Gaussian beams are obtained in the generalized Lorenz–Mie theory through the finite series (FS) method. As a result, such expressions have made it possible to more deeply understand the behaviour of the BSCs and, therefore, the scattering of Gaussian beams beyond the paraxial approximation. The blowing up, in particular, of FS BSCs which has been observed for several paraxial beams is now mathematically justified as a phenomenon that is independent of numerical precision. Furthermore, numerical results demonstrate how such blow ups are related to the ratio between the beam waist radius and its wavelength.

Optical Trapping of Chiral Particles by Dual Laser Beams

In this paper, an analytical method for studying the radiation force (RF) of chiral spheres generated by dual laser beams is presented under the framework of generalized Lorenz–Mie theory (GLMT). According to the coordinate transformation relations, the arbitrarily incident laser beam is represented by vector spherical harmonic functions (VSHFs) in the sphere system. The entire induced field expression coefficients of dual laser beams can be obtained by superposition of each illuminated field. Based on the momentum conservation theory, the concrete expression of lateral and axial RF on chiral sphere is derived. The current theories are shown to be valid by comparison with the existing reference. To investigate the stable capture state of chiral sphere, the influences of the corresponding parameters of chiral particles and dual laser beams on the trapping and manipulation are investigated in detail. The analytical study on the RF of dual laser beams on chiral particles is an efficient method for improving optical tweezers technology and can become an encouraging approach to realize the high accuracy operation of chiral particles.

Rigorous justification of a localized approximation to encode on-axis Gaussian acoustical waves.

Generalized Lorenz-Mie theory (GLMT) describes the interaction between electromagnetic waves (more specifically, laser beams) and homogeneous spherical particles. An acoustical GLMT-like framework can be used to deal with acoustical wave scattering. The incident acoustical wave may then be encoded in a set of beam shape coefficients (BSCs) similar to the ones used in electromagnetic scattering. One method to evaluate the acoustical BSCs is the localized approximation which takes the form of a variant of a localized approximation used to evaluate the electromagnetic BSCs. These acoustical BSCs are discussed and rigorously justified in the case of on-axis Gaussian beams. Examples of field reconstruction and remodeling using the localized approximation are presented which reinforce the robustness of such a method for very small confinement parameters. We expect that the results presented here will encourage a wider use of localized approximation schemes in acoustic scattering problems.

A framework for the finite series method of the generalized Lorenz-Mie theory and its application to freely-propagating Laguerre-Gaussian beams

In face of a revival of interest in the finite series (FS) method due to recent developments upon generalized Lorenz-Mie theories (GLMTs), a more general, understandable, and systematic formulation is proposed. Possibly due to an apparent lack of flexibility in the FS method’s earlier statements, there has been a void in its use since the 1990s. Particularly, the method demands some degree of mathematical labor each time it is applied to a different kind of field profile. Furthermore, the algebraic complexity of its earlier occurrences might also have weighted upon the method’s historical shunning. Dissecting the later works reclaiming the FS, several possibilities for generalization, simplification, and organization were found. Accordingly, with the intent to render the method more approachable and to encourage its use, this work derives an alternative path suitable for both understanding and implementation. Applying the procedure, expressions for the beam shape coefficients of freely propagating Laguerre-Gaussian beams are obtained in closed form in a more straightforward manner when compared to previous formulations – this time not relying on recursions.

Optical Manipulation of Nanoparticles: A Selective Excitation Approach Using Highly Focused Orbital Angular Momentum Beams

Orbital angular momentum and polarization states of highly focused vector vortex beams can be engineered to selectively excite the desired multipoles in nanoparticles, making them ideal candidates for complex optical applications. A platform based on the generalized Lorenz–Mie theory integrated with the complex source point method is developed to model the interaction of such beams with particles analytically. The existing platform is extended for obtaining the full‐vector electromagnetic fields, outlining the observed effects that adding a substrate brings to the problem space. Despite the cross‐coupling between different multipoles induced by the substrate, it is concluded that the proper choice of beam parameters enables the selective excitation of multipoles even in the critical case of a plasmonic substrate. The proposed formalism is general and allows a multipole study of the optical forces. Selective excitation is exploited to control the imparted optical forces on particles placed on a plasmonic substrate. 3D trapping regions are achievable for highly absorptive and high‐refractive‐index particles. Motion trajectory analyses are performed to demonstrate the trapping stability, concluding that highly focused optical beams, owing to the exceptional selective excitation ability, are suitable candidates for novel optical manipulation applications.

Radiation force and torque on an absorptive electromagnetic conductor sphere by an arbitrary-shaped optical polarized beam

The optical radiation force (ORF) and optical spin torque (OST) on an absorptive electromagnetic conductor (AEMC) sphere by an arbitrary-shaped optical polarized beam are investigated in the framework of the generalized Lorenz–Mie theory (GLMT). The analytical expressions of ORF and OST are derived, and both of them are decomposed into three components (co-polarized, cross-polarized, and interference components) due to the unique “optical rotation” effect of the AEMC. The ORF and OST exerted on both a PEMC and an AEMC sphere by an Airy beam are discussed, and the impact of the losses Mi of AEMC is focused on. Besides, the influence of particle size parameter ka and admittance parameter M on the ORF and OST are also mainly analyzed. The optical pulling force built on this system is paid attention to and discussed. And the impact of the polarization states of the incident beam on the ORF and OST is also discussed. Furthermore, the comparison of ORF that the Airy beam interacts with a dielectric sphere and an AEMC sphere is studied emphatically. The findings in this manuscript will take effect on particle manipulation, optical spanners, optical tweezers, and metamaterial field.

Scattering properties of Bessel beams on metal particles

Based on Generalized Lorenz-Mie Theory (GLMT), the scattering phenomenon caused by Bessel beam irradiation on metal particles is studied. The order and polarization mode of Bessel beam, as well as the influence of the size of metal particles on the total intensity distribution of the light field around metal particles are investigated by using the software simulation calculation. The results show that for spherical metal particles of the same size, the higher order Bessel beam is more likely to bypass the metal particles in the forward propagation, while the lower order Bessel beam bypassed the particles in the propagation is related to the beam polarization mode. The results have potential applications in microscopy super-resolution imaging and detection of tiny particles.

Optical Torque Exerted on a Charged Sphere by a Polarized Bessel Beam

In the framework of generalized Lorenz–Mie theory, we report here the results of our comprehensive study for analyzing and computing the optical torque (OT) caused by AGVBB on a charged sphere of arbitrary size. The effects of polarization, order, half-cone angle, the position of particle, and the surface charge are carefully considered. The axial and transverse components or OTs are numerically calculated, and the sign reversal of the axial OTs and vortex-like character of the total transverse OTs are mainly discussed. The results reported here are expected to have significant impact on improving the ability of optical manipulation and 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 Force of Bessel Pincer Light-Sheets Beam on a Dielectric Sphere of Arbitrary Size.

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.

Analysis of radiation force on a uniaxial anisotropic sphere by dual zero-order Bessel beams

Based on the generalized Lorenz–Mie theory (GLMT), a theoretical approach is introduced to study the radiation force exerted on a uniaxial anisotropic sphere illuminated by dual zero-order Bessel beams (ZOBBs). The beams propagate with arbitrary direction, and are expanded in terms of the spherical vector wave functions (SVWFs) in the particle coordinate system using the coordinate rotation theorem. The total expansion coefficients of the incident fields are derived by superposition of the vector fields. Applying the Maxwell’s stress tensor, the analytical expressions of the radiation forces on a homogeneous absorbing uniaxial anisotropic sphere are derived. Comparing the radiation forces of dual ZOBBs with those results of dual ZOBBs simplified into single ZOBBs and dual plane waves, the accuracy and correctness of the theory are verified. In order to study the equilibrium state, the effects of beam parameters, particle size parameters, and anisotropy parameters on the radiation forces are discussed in detail. Comparing with the isotropic particle, the equilibrium status is sensitive to the anisotropic parameters. Moreover, the properties of optical force on a uniaxial anisotropic sphere in single ZOBB trap and zero-order Bessel standing wave trap are compared. The theory and results of this paper are hopeful to provide an effective theoretical basis for the study of optical micromanipulation of biological and anisotropic complex particles by multi-beams.