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.

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. Our results can find interesting applications in all fields that benefit from the use of non-diffracting 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. The present analysis is therefore fully justified.

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. Modeling the longitudinal intensity pattern at small scale can address many challenges in three-dimensional optical trapping and micromanipulation.

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.g., Gaussian beams. Expressions for the beam-shape coefficients of FWs are provided, and the GLMT is used to reconstruct their intensity profiles and to predict their optical properties for possible biomedical optics purposes.

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.