Rigorous justification of a localized approximation to encode off-axis Gaussian acoustical beams.

With the model of generalized Lorenz-Mie theory (GLMT) and the extended boundary condition method, describing the interaction between electromagnetic (EM) waves (more specifically laser beams) and 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 EM scattering. Following a paper devoted to the evaluation of acoustical BSCs using a localized approximation in the case of on-axis Gaussian acoustical beams, the present paper deals with the evaluation of acoustical BSCs in the case of off-axis Gaussian acoustical beams.

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.

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.

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.

Theoretical prediction of photophoretic force on a dielectric sphere illuminated by a circularly symmetric high-order Bessel beam: on-axis case.

Compared to the experimental progresses made in the optical trapping of aerosol particles in gaseous media by means of photophoretic forces, the theoretical analysis of photophoretic forces is less developed, the underlying mechanisms being yet not fully understood. In this paper, theoretical derivations of photopheresis of a dielectric sphere in gaseous media illuminated by a circularly symmetric Bessel beam of arbitrary order is presented within the framework of generalized Lorenz-Mie theory. An analytic and closed-form formula for the asymmetry factor, which ultimately determines the sense of direction of photophoretic force, is provided.

Experimental optical trapping with frozen waves.

We report, to the best of our knowledge, the first optical trapping experimental demonstration of microparticles with frozen waves. Frozen waves are an efficient method to model longitudinally the intensity of nondiffracting beams obtained by superposing copropagating Bessel beams with the same frequency and order. Based on this, we investigate the optical force distribution acting on microparticles of two types of frozen waves.

Arrays of spatially structured non-diffracting optical beams.

Non-diffracting optical beams and their structured versions have been extensively studied, theoretically and experimentally, over the last two decades, rendering important applications in fields such as imaging, microscopy, remote sensing, optical manipulation, free space optics, etc. In this paper, we theoretically construct arrays of non-coaxial structured non-diffracting beams by using the so-called frozen wave method. We also develop techniques based on polarization allocations and apodizations to mitigate undesirable interferences among neighboring beams.

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.

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.

Structuring light under different polarization states within micrometer domains: exact analysis from the Maxwell equations.

We show the possibility of arbitrary longitudinal spatial modeling of non-diffracting light beams over micrometric regions. The resulting beams, which are highly non-paraxial, possess subwavelength spots and can acquire multiple intensity peaks at predefined locations over regions that are few times larger than the wavelength. The formulation we present here provides exact solutions to the Maxwell's equations where the linear, radial, and azimuthal beam polarizations are all considered.

Diffraction-resistant scalar beams generated by a parabolic reflector and a source of spherical waves.

In this work, we propose the generation of diffraction-resistant beams by using a parabolic reflector and a source of spherical waves positioned at a point slightly displaced from its focus (away from the reflector). In our analysis, considering the reflector dimensions much greater than the wavelength, we describe the main characteristics of the resulting beams, showing their properties of resistance to the diffraction effects. Due to its simplicity, this method may be an interesting alternative for the generation of long-range diffraction-resistant waves.

Analytical approach of ordinary frozen waves for optical trapping and micromanipulation.

The optical properties of frozen waves (FWs) are theoretically and numerically investigated using the generalized Lorenz-Mie theory (GLMT) together with integral localized approximation. These waves are constructed from a suitable superposition of equal-frequency ordinary Bessel beams and are capable of providing almost any desired longitudinal intensity profile along their optical axis, thus being of potential interest in applications in which intensity localization may be used advantageously, such as in optical trapping and micromanipulation systems. In addition, because FWs are composed of nondiffracting beams, they are also capable of overcoming the diffraction effects for longer distances when compared to conventional (ordinary) beams, e.

Spin angular momentum transfer from TEM(00) focused Gaussian beams to negative refractive index spherical particles.

We investigate optical torques over absorbent negative refractive index spherical scatterers under the influence of linear and circularly polarized TEM(00) focused Gaussian beams, in the framework of the generalized Lorenz-Mie theory with the integral localized approximation. The fundamental differences between optical torques due to spin angular momentum transfer in positive and negative refractive index optical trapping are outlined, revealing the effect of the Mie scattering coefficients in one of the most fundamental properties in optical trapping systems.

Radiation pressure cross sections and optical forces over negative refractive index spherical particles by ordinary Bessel beams.

When impinged by an arbitrary laser beam, lossless and homogeneous negative refractive index (NRI) spherical particles refract and reflect light in an unusual way, giving rise to different scattered and internal fields when compared to their equivalent positive refractive index particles. In the generalized Lorenz-Mie theory, the scattered fields are dependent upon the Mie scattering coefficients, whose values must reflect the metamaterial behavior of an NRI scatterer, thus leading to new optical properties such as force and torque. In this way, this work is devoted to the analysis of both radial and longitudinal optical forces exerted on lossless and simple NRI particles by zero-order Bessel beams, revealing how the force profiles are changed whenever the refractive index becomes negative.

Integral localized approximation description of ordinary Bessel beams and application to optical trapping forces.

Ordinary Bessel beams are described in terms of the generalized Lorenz-Mie theory (GLMT) by adopting, for what is to our knowledge the first time in the literature, the integral localized approximation for computing their beam shape coefficients (BSCs) in the expansion of the electromagnetic fields. Numerical results reveal that the beam shape coefficients calculated in this way can adequately describe a zero-order Bessel beam with insignificant difference when compared to other relative time-consuming methods involving numerical integration over the spherical coordinates of the GLMT coordinate system, or quadratures. We show that this fast and efficient new numerical description of zero-order Bessel beams can be used with advantage, for example, in the analysis of optical forces in optical trapping systems for arbitrary optical regimes.

Fundamentals of negative refractive index optical trapping: forces and radiation pressures exerted by focused Gaussian beams using the generalized Lorenz-Mie theory.

Based on the generalized Lorenz-Mie theory (GLMT), this paper reveals, for the first time in the literature, the principal characteristics of the optical forces and radiation pressure cross-sections exerted on homogeneous, linear, isotropic and spherical hypothetical negative refractive index (NRI) particles under the influence of focused Gaussian beams in the Mie regime. Starting with ray optics considerations, the analysis is then extended through calculating the Mie coefficients and the beam-shape coefficients for incident focused Gaussian beams. Results reveal new and interesting trapping properties which are not observed for commonly positive refractive index particles and, in this way, new potential applications in biomedical optics can be devised.

Gradient forces on double-negative particles in optical tweezers using Bessel beams in the ray optics regime.

Gradient forces on double negative (DNG) spherical dielectric particles are theoretically evaluated for v-th Bessel beams supposing geometrical optics approximations based on momentum transfer. For the first time in the literature, comparisons between these forces for double positive (DPS) and DNG particles are reported. We conclude that, contrary to the conventional case of positive refractive index, the gradient forces acting on a DNG particle may not reverse sign when the relative refractive index n goes from |n|>1 to |n|<1, thus revealing new and interesting trapping properties.

Diffraction-attenuation resistant beams: their higher-order versions and finite-aperture generations.

Recently, a method for obtaining diffraction-attenuation resistant beams in absorbing media has been developed in terms of suitable superposition of ideal zero-order Bessel beams. In this work, we show that such beams keep their resistance to diffraction and absorption even when generated by finite apertures. Moreover, we shall extend the original method to allow a higher control over the transverse intensity profile of the beams.

Trapping double negative particles in the ray optics regime using optical tweezers with focused beams.

The capabilities of optical tweezers to trap DNG (double negative) spherical particles, with both negative permittivity and permeability, are explored in detail by analyzing some interesting theoretical features not seeing in conventional DPS (double positive) particles possessing positive refractive index. The ray optics regime is adopted and, although this regime is quite simple and limited, its validity is already known and tested for DPS particles such as biological cells and molecules trapped by highly focused beams. Simulation results confirm that even for ray optics, DNG particles present unusual and interesting trapping characteristics.