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

Exact Partial Wave Expansion of Optical Beams with Respect to an Arbitrary Origin

Using an analytical expression for an integral involving Bessel and Legendre functions we succeeded to obtain the partial wave decomposition of a general optical beam at an arbitrary location from the origin. We also showed that the solid angle integration will eliminate the radial dependence of the expansion coefficients. The beam shape coefficients obtained are given by an exact expression in terms of single or double integrals. These integrals can be evaluated numerically in a short time scale. We presented the results for the case of linear polarized Gaussian beam.Comment: 11 pages, 4 figure

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

Calculation of the T-matrix: general considerations and application of the point-matching method

The T-matrix method is widely used for the calculation of scattering by particles of sizes on the order of the illuminating wavelength. Although the extended boundary condition method (EBCM) is the most commonly used technique for calculating the T-matrix, a variety of methods can be used. We consider some general principles of calculating T-matrices, and apply the point-matching method to calculate the T-matrix for particles devoid of symmetry. This method avoids the time-consuming surface integrals required by the EBCM.Comment: 10 pages. 2 figures, 1 tabl

Rigorous Justification of the Localized Approximation to the Beam Shape Coefficients in Generalized Lorenz-Mie Theory .1. On-Axis Beams

Generalized Lorenz-Mie theory describes electromagnetic scattering of an arbitrary light beam by a spherical particle. The computationally most expensive feature of the theory is the evaluation of the beam-shape coefficients, which give the decomposition of the incident light beam into partial waves. The so-called localized approximation to these coefficients for a focused Gaussian beam is an analytical function whose use greatly simplifies Gaussian-beam scattering calculations. A mathematical justification and physical interpretation of the localized approximation is presented for on-axis beams

Multipole expansion of strongly focussed laser beams

Multipole expansion of an incident radiation field - that is, representation of the fields as sums of vector spherical wavefunctions - is essential for theoretical light scattering methods such as the T-matrix method and generalised Lorenz-Mie theory (GLMT). In general, it is theoretically straightforward to find a vector spherical wavefunction representation of an arbitrary radiation field. For example, a simple formula results in the useful case of an incident plane wave. Laser beams present some difficulties. These problems are not a result of any deficiency in the basic process of spherical wavefunction expansion, but are due to the fact that laser beams, in their standard representations, are not radiation fields, but only approximations of radiation fields. This results from the standard laser beam representations being solutions to the paraxial scalar wave equation. We present an efficient method for determining the multipole representation of an arbitrary focussed beam.Comment: 13 pages, 7 figure

Numerical Modelling of Optical Trapping

Optical trapping is a widely used technique, with many important applications in biology and metrology. Complete modelling of trapping requires calculation of optical forces, primarily a scattering problem, and non-optical forces. The T-matrix method is used to calculate forces acting on spheroidal and cylindrical particles.Comment: 4 pages, 4 figure

An experimental route to spatiotemporal chaos in an extended 1D oscillators array

We report experimental evidence of the route to spatiotemporal chaos in a large 1D-array of hotspots in a thermoconvective system. Increasing the driving force, a stationary cellular pattern becomes unstable towards a mixed pattern of irregular clusters which consist of time-dependent localized patterns of variable spatiotemporal coherence. These irregular clusters coexist with the basic cellular pattern. The Fourier spectra corresponding to this synchronization transition reveals the weak coupling of a resonant triad. This pattern saturates with the formation of a unique domain of great spatiotemporal coherence. As we further increase the driving force, a supercritical bifurcation to a spatiotemporal beating regime takes place. The new pattern is characterized by the presence of two stationary clusters with a characteristic zig-zag geometry. The Fourier analysis reveals a stronger coupling and enables to find out that this beating phenomena is produced by the splitting of the fundamental spatiotemporal frequencies in a narrow band. Both secondary instabilities are phase-like synchronization transitions with global and absolute character. Far beyond this threshold, a new instability takes place when the system is not able to sustain the spatial frequency splitting, although the temporal beating remains inside these domains. These experimental results may support the understanding of other systems in nature undergoing similar clustering processes.Comment: 12 pages, 13 figure

Nonlinear Generalized Schrödinger’s Equations by Lifting Hamilton-Jacobi’s Formulation of Classical Mechanics

It is well known that, by taking a limit of Schrödinger’s equation, we may recover Hamilton-Jacobi’s equation which governs one of the possible formulations of classical mechanics. Conversely, we may start from the Hamilton-Jacobi’s equation and, by using a lifting principle, we may reach a set of nonlinear generalized Schrödinger’s equations. The classical Schrödinger’s equation then occurs as the simplest equation among the set