arXiv subjects

Eugenio Rodriguez

Publications and source records attributed to Eugenio Rodriguez.

5 recordsLinked to original sources

arXiv2006

Electromagnetic forces for an arbitrary optical trapping of a spherical dielectric

Analytical solution for optical trapping force on a spherical dielectric particle for an arbitrary positioned focused beam is presented in a generalized Lorenz-Mie and vectorial diffraction theory. In this case the exact electromagnetic field is considered in the focal region. A double tweezers setup was employed to perform ultra sensitive force spectroscopy and observe the forces, demonstrating the selectively couple of the transverse electric (TE), transverse magnetic (TM) modes by means of the beam polarization and positioning, and to observe correspondent morphology-dependent resonances (MDR) as a change in the optical force. The theoretical prediction of the theory agrees well with the experimental results. The algorithm presented here can be easily extended to other beam geometries and scattering particles.

physics.optics↗

arXiv2006

Holonomy orbits of the snake charmer algorithm

The snake charmer algorithm permits us to deform a piecewise smooth curve starting from the origin in R^d, so that its end follows a given path. When this path is a loop, a holonomy phenomenon occurs. We prove that the holonomy orbits are closed manifolds diffeomorphic to real Stiefel manifolds. A survey of the snake charmer algorithm is given in the paper.

math.DG↗

arXiv2006

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.

physics.optics↗

arXiv2006

Analytical results for a Bessel function times Legendre polynomials class integrals

When treating problems of vector diffraction in electromagnetic theory, the evaluation of the integral involving Bessel and associated Legendre functions is necessary. Here we present the analytical result for this integral that will make unnecessary numerical quadrature techniques or localized approximations. The solution is presented using the properties of the Bessel and associated Legendre functions.

math-ph↗

arXiv2002

The space of clouds in an Euclidean space

We study the space $\nua{m}{d}$ of clouds in $\bbr^d$ (ordered sets of $m$ points modulo the action of the group of affine isometries). We show that $\nua{m}{d}$ is a smooth space, stratified over a certain hyperplane arrangement in $\bbr^m$. We give an algorithm to list all the chambers and other strata (this is independent of $d$). With the help of a computer, we obtain the list of all the chambers for $m\leq 9$ and all the strata when $m\leq 8$. As the strata are the product of a polygon spaces with a disk, this gives a classification of $m$-gon spaces for $m\leq 9$. When $d=2,3$, $m=5,6,7$ and modulo reordering, we show that the chambers (and so the different generic polygon spaces) are distinguished by the ring structure of their ${\rm mod} 2$-cohomology.

math.DG↗