Description of acoustical Gaussian beams from the electromagnetic Davis scheme of approximations and the on-axis localized approximation.

Electromagnetic Gaussian beams may be described by using a Davis scheme of approximations. It is demonstrated that this scheme also may be used, with minor changes, to manage the description of acoustical waves. The acoustical version of the Davis scheme afterward allows one to establish an efficient and accurate localized approximation to evaluate beam shape coefficients, which encode the structures of acoustical waves, similar to the localized approximation, which has been made famous when dealing with electromagnetic waves. The present paper is restricted to the case of on-axis beams.

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.

Longitudinal and transverse photophoretic force on a homogeneous sphere exerted by a Bessel beam with selective polarizations.

Predicting the photophoretic force exerted on an optical absorptive particle in a gaseous medium is a challenging problem because the problems of electromagnetic scattering, heat transfer, and gaseous molecule dynamics are involved and coupled with each other. Based on the calculation of the source function distribution inside a homogeneous sphere excited by a Bessel beam using the generalized Lorenz-Mie theory, analytical expressions of the asymmetry vector, which is the key quantity in the calculation of photophoretic force, are given using the adjoint boundary value method. Numerical simulations are performed to analyze the influences of polarization, the half-cone angle, and the beam order of the incident beam, particle size, and absorptivity of the particle on the asymmetry vector for both on-axis and off-axis illuminations. Longitudinal and transverse photophoretic forces on a homogeneous sphere are displayed for the slip-flow regime of gaseous media. The results offer important insights into the working mechanism underpinning the development of heat-mediated optical manipulation techniques and the measurement of the refractive index of particles.

Debye-series expansion of T-matrix for light scattering by non-spherical particles computed from Riccati-differential equations.

A new formulation of the Debye series based on the Riccati-differential equations was developed to compute electromagnetic wave scattering by non-spherical particles. In this formulation, the T-matrix was expanded in terms of the Debye series. The zeroth-order term, which corresponds to a combination of diffraction and external reflection, is given by unity minus the external reflection matrix. The higher-order terms are generated from the transmission matrix from the medium to the particle, the internal reflection matrix within the particle and the transmission matrix from the particle to the medium. We demonstrate that the aforementioned four reflection-transmission matrices satisfy the Riccati-differential equations, which can be numerically solved by the fourth-order Runge-Kutta method. The present algorithm can be applied to generalized convex non-spherical particles. The differential equations were analytically validated in the case of a homogeneous sphere. Representative results were given in the case of spheroids. The impacts of the Debye series with various orders on the optical properties of spheroids were revealed with significant details.

Discrete vector frozen waves in generalized Lorenz-Mie theory: linear, azimuthal, and radial polarizations.

This work aims to provide additional theoretical investigation of a promising class of nondiffracting vector beams-the discrete vector frozen waves (FWs)-in the generalized Lorenz-Mie theory. The exact beam shape coefficients for unsymmetrized FWs with linear, azimuth, and radial polarizations are given in analytic form, thus extending previous derivations based on circularly symmetric Davis or aplanatic Bessel beams. Owing to their unique properties, it is believed that FWs will become important wave fields in optical tweezers, optical system alignment, remote sensing, optical bistouries, atom guiding, and so on. The present analysis is therefore fully justified.

On the validity of the integral localized approximation for Bessel beams and associated radiation pressure forces.

In this paper we investigate the integral version of the localized approximation (ILA)-a powerful technique for evaluating the beam shape coefficients in the framework of the generalized Lorenz-Mie theory-as applied to ideal scalar Bessel beams (BBs). Originally conceived for arbitrary shaped beams with a propagating factor exp(±ikz), it has recently been shown that care must be taken when applying the ILA for the case of ideal scalar BBs, since they carry a propagating factor exp(±ikz cos α), with α being the axicon angle, which cannot be smoothly accommodated into its mathematical formalism. Comparisons are established between the beam shape coefficients calculated from both ILA and exact approaches, assuming paraxial approximation and both on- and off-axis beams. Particular simulations of radiation pressure forces are provided based on the existing data in the literature. This work helps us in elucidating that ILA provides adequate beam shape coefficients and descriptions of ideal scalar BBs up to certain limits and, even when it fails to do so, reliable information on the physical optical properties of interest can still be inferred, depending on specific geometric and electromagnetic aspects of the scatterer.

Controllable and enhanced photonic jet generated by fiber combined with spheroid.

Dielectric microparticles are used as simple and low-cost means to achieve strong intensity confinement below the standard diffraction limit. Here we report the demonstration of enhanced light intensity in the vicinity of optical fiber combined with dielectric spheroidal particles. Specific attention is paid to the study of the influences of the spheroid's ellipticity (ratio of horizontal length to vertical length) as well as the refractive index on the intensity enhancement and focal distance. It reveals that simply varying the ellipticity, it is possible to obtain localized photon fluxes having different characteristics. This could yield a new superenhanced intensity device with excellent optical properties and low manufacturing cost for using visible light in many areas of biology, material sciences, chemistry, medicine, and tissue engineering.

Second modified localized approximation for use in generalized Lorenz-Mie theory and other theories revisited.

Arbitrary electromagnetic shaped beams may be described by using expansions over a set of basis functions, with expansion coefficients containing subcoefficients named "beam shape coefficients" (BSCs). When BSCs cannot be obtained in closed form, and/or when the beam description does not exactly satisfy Maxwell's equations, the most efficient method to evaluate the BSCs is to rely on localized approximations. One of them, named the second modified localized approximation, has been presented in a way that may be found ambiguous in some cases. The aim of the present paper is to remove any ambiguity on the use of the second modified localized approximation.

List of problems for future research in generalized Lorenz-Mie theories and related topics, review and prospectus [invited].

The expression "generalized Lorenz-Mie theories" generically denotes a class of light-scattering theories describing the interaction between an illuminating electromagnetic arbitrary-shaped beam and a particle possessing a high degree of symmetry. This allows one to use the method of separation of variables in which the illuminating beam is expressed as an expansion over a set of basis functions. Such theories have been derived and applied over the past 35 years. Although, as a whole, these theories are now well developed, there remains a list of problems to be solved, some of which are described in this paper.

Note on the use of localized beam models for light scattering theories in spherical coordinates.

Localized beam models provide the most efficient and enlightening ways to evaluate beam shape coefficients of electromagnetic arbitrary shaped beams for use in light scattering theories. At the present time, they are valid in spherical and (circular and elliptical) cylindrical coordinates. A misuse of localized beam models in spherical coordinates recently appeared several times in the literature. We therefore present a warning to avoid the propagation of an incorrect use of localized beam models.

Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam.

A rigorous theory is developed to predict the radiation pressure force (RPF) exerted on a spheroid by an arbitrarily oriented and located shaped beam. Analytical expressions of RPF are derived for a homogeneous spheroid, which can be prolate or oblate, transparent or absorbing. Exemplifying calculations are performed and RPF calculations for spheroids are compared to RPF calculations for spheres. The "Optical Stretcher" is also numerically simulated to study the RPF exerted on a red blood cell during its deformation.

Generalized Lorenz-Mie theory for an arbitrarily oriented, located, and shaped beam scattered by a homogeneous spheroid.

The theory of an arbitrarily oriented, shaped, and located beam scattered by a homogeneous spheroid is developed within the framework of the generalized Lorenz-Mie theory (GLMT). The incident beam is expanded in terms of the spheroidal vector wave functions and described by a set of beam shape coefficients (G(m)(n),(TM),G(m)(n),(TE)). Analytical expressions of the far-field scattering and extinction cross sections are derived. As two special cases, plane wave scattering by a spheroid and shaped beam scattered by a sphere can be recovered from the present theory, which is verified both theoretically and numerically. Calculations of the far-field scattering and cross sections are performed to study the shaped beam scattered by a spheroid, which can be prolate or oblate, transparent or absorbing.

Generalized Lorenz-Mie theory for a spheroidal particle with off-axis Gaussian-beam illumination.

The beam-shape coefficients of arbitrary off-axis Gaussian beams in spheroidal coordinates are evaluated with a generalized Lorenz-Mie theory. The light-scattering properties of absorbing and nonabsorbing homogeneous spheroidal particles, such as the angular distribution of scattered intensity for a wide range of particles sizes and different complex refractive indices versus the magnitude and location of the beam waist, are investigated.