Leonardo André Ambrosio

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.

Optical forces experienced by arbitrary-sized spherical scatterers from superpositions of equal-frequency Bessel beams

Radiation pressure cross sections over arbitrary-sized spherical scatterers are evaluated considering, as wave fields, recently developed frozen waves, which are a suitable superposition of equal-frequency Bessel beams, of arbitrary order. The so-called beam-shape coefficients are computed within the framework of the generalized Lorenz–Mie theory and with the aid of integral localized approximation. It is numerically shown that, under the paraxial regime, frozen waves could be designed to efficiently trap biological cells, viruses, bacteria, and so on, along multiple radial planes and at specific axial locations. Our results reinforce frozen waves as potential laser beams in optical trapping and manipulation.

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(±ikzu2009cosu2009α), 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.

Time-average forces over Rayleigh particles by superposition of equal-frequency arbitrary-order Bessel beams

We investigate optical forces exerted by suitable superpositions of equal-frequency Bessel beams—frozen waves—over dielectric, magnetodielectric, and negative-index Rayleigh particles. Frozen waves are capable of providing virtually any desired longitudinal intensity pattern by adequately superposing arbitrary-order Bessel beams, serving as potential beams in optical trapping, atom guiding, optical bistouries, and so on. Analytical expressions for gradient and scattering forces experienced by very small particles are deduced, and our numerical examples reveal that both low- and high-index dielectric and magnetodielectric particles can be efficiently trapped and manipulated. Our results indicate that such wave fields could actually provide three-dimensional traps in multiple transverse planes.

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.

On the accuracy of approximate descriptions of discrete superpositions of Bessel beams in the generalized Lorenz-Mie theory

This paper aims to investigate one of the most important schemes, viz. the localized approximation (LA), for describing arbitrary-shaped beams in the generalized Lorenz-Mie theory. Our focus is on a specific class of non-diffracting beams called discrete frozen waves, which are constructed from superpositions of Bessel beams and can be designed to provide virtually any longitudinal intensity pattern of interest. Recently, the LA was applied to frozen waves allowing, for the first time, for the analysis of light scattering problems from spherical scatterers and the subsequent determination of the physical/optical quantities in optical trapping. Since the LA cannot be rigorously applied to Bessel beams, it is of interest to determine whether those results and predictions previously established in the literature are reliable or not. To do so, we rely on exact descriptions of frozen waves and establish the limits to the validity of such an approximation scheme. It is revealed that, although serious doubts can be raised against its use, specially due to cumulative errors, the LA is much more robust than previously thought, and it may serve well to both paraxial and non-paraxial Frozen Waves, under certain circumstances.

On analytical descriptions of finite-energy paraxial frozen waves in generalized Lorenz-Mie theory

This paper aims to achieve analytical descriptions of specific classes of finite-energy non-diffracting beams, viz. the so-called Frozen Waves, envisioning applications in optical trapping. Such solutions to the Fresnel diffraction integral can be constructed from specific discrete superpositions of finite-energy zero-order scalar Bessel-Gauss beams. Here, we present expressions for their beam shape coefficients in the context of the generalized Lorenz-Mie theory. The paraxial regime is valid for all Bessel-Gauss beams, thus allowing the method here presented to be purely analytic. The analyticity avoids both extensive numerical computation and optimization schemes. Radiation pressure cross sections, which are proportional to optical forces, are then evaluated for Rayleigh particles as an example of application. We expect Frozen Waves to serve, in the near future, as alternative laser beams in biomedical optics and in the optical micromanipulation of biological or auxiliary particles.

Circularly symmetric frozen waves and their optical forces in optical tweezers using a ray optics approach

In this work we analyze, in the ray optics regime, the optical forces exerted on micro-sized dielectric spheres due to optical beams created as suitable discrete superpositions of scalar and vector Bessel beams — also known as frozen waves, thus envisioning applications in optical tweezers. Scalar frozen waves have been recently and theoretically introduced as auxiliary optical fields in the trapping and manipulation of neutral particles paper in both the Rayleigh (dipole) and the Mie regimes, the latter demanding a full electromagnetic treatment. Here, the extension of previous studies is twofold in the sense that we perform investigations both in the ray optics regime, which has only been previously considered in terms of simplistic models, and in terms of a vector approach which allows us to go beyond the paraxial approximation.

Longitudinal forces on a spherical dielectric particle exerted by a truncated bessel beam in the ray optics regime

A first theoretical and numerical treatment of longi-tudinal forces in an extended geometrical optics model exerted by a truncated Bessel beam (TBB) on a spherical dielectric particle is presented in this work. To describe the TBB, we use a method for spatial beam shaping to describe truncated beams with simplicity and total analyticity in the paraxial approximation, which utilizes a discrete superposition of scalar Bessel Gauss beams. We present numerical examples of longitudinal forces that a TBB exerts on a scatterer and argue about the limitations of this method. We also briefly discuss about further possible analysis that can be done with TBB and other truncated beams.

Discrete superposition of equal-frequency Bessel beams: Time-average forces exerted on dielectric and magnetodielectric Rayleigh particles

We demonstrate the ability of scalar frozen waves - wave fields constructed from suitable superpositions of equal-frequency and arbitrary-order Bessel beams - to trap and manipulate both low- and high-index dielectric and magnetodielectric Rayleigh particles. Explicit analytical expressions are derived for the optical forces based on a dipole approximation and taking into account magnetic polarizabilities. Two examples of frozen waves are numerically investigated, revealing that it is indeed possible to optically trap such particles at multiple transverse planes and at specific radial positions. Our results suggest that such optical wave fields may serve as laser beams in optical trapping, atom guiding, optical bistouries and so on.