Effect of finite terms on the truncation error of Mie series

The finite sum of the squares of the Mie coefficients is very useful for addressing problems of classical light scattering. An approximate formula available in the literature, and still in use today, has been developed to determine a priori the number of the most significant terms needed to evaluate the scattering cross section. Here we obtain an improved formula, which includes the number of terms needed for determining the scattering cross section within a prescribed relative error. This is accomplished using extended precision computation, for a wide range of commonly used size parameters and indexes of refraction. The revised formula for the finite number of terms can be a promising and valuable approach for efficient modeling light scattering phenomena.Comment: 3 pages, 3 figure

Optical force in optical tweezers : theory and experiment

Orientador: Carlos Lenz CesarTese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb WataghinResumo: A pinça óptica é um instrumento capaz de manipular e aprisionar partículas dielétricas por meio da pressão de radiação. Suas aplicações nas ciências da vida e biofísica cresceram exponencialmente após a demonstração de que ela permitia manter vivos microorganismos capturados por longos tempos. Informações obtidas destes experimentos requerem um transdutor de força, para o qual se utiliza o deslocamento de uma microesfera capturada. Estamos portanto trabalhando no limite dos regimes de óptica geométrica e Rayleigh, que geralmente são utilizados para simplificar a força óptica. Até hoje não existe consenso entre as teorias das forças, para um regime de tamanho arbitrário, nas pinças ópticas nem para sistemas de alta simetria como microesferas, muito menos em geometrias mais complicadas. Uma das maiores dificuldades encontradas nesse aspecto é a ausência de boas medidas experimentais das forças ópticas, independentes de modelos. Por isso grande parte do trabalho dessa tese foi o desenvolvimento de um sistema de medidas de forças ópticas utilizando pinças duplas para obtenção de toda uma curva da força em função do deslocamento tridimensional da partícula capturada, e não apenas os valores da força em posições fixas. A segunda grande contribuição vem da descrição teórica da força óptica. A grande dificuldade nesse aspecto é a descrição de um feixe incidente de grande abertura numérica e sua decomposição em ondas parciais. É nesse contexto que se encaixa esse trabalho de tese. Acreditamos ter dado uma contribuição extremamente valiosa resolvendo de forma analítica e exata o problema da decomposição de um feixe convergente em ondas parciais relativas a qualquer origem do sistema de coordenadas em três dimensõesAbstract: The optical tweezers is an instrument capable of manipulating and trapping dielectric particles through the radiation pressure. Their applications in the life sciences and biophysics increased exponentially after it has been demonstrated that it allowed to microorganisms to be maintained alive trapped for long times. Information obtained from these experiments requires a force transducer, for which the displacement of the captured micro sphere is used. We are therefore working in the limit of the geometrical optics and Rayleigh regime, which are usually used to simplify the optical force. Until today consensus fails to exist among the theories of forces for optical tweezers, of an arbitrary size regime, neither for systems of high symmetry as micro spheres, much less in more complicated geometries. One of the greatest difficulties encountered in this aspect is the absence of good experimental measurements of optical forces, independent of models. Therefore great part of this thesis was the development of a system capable of measuring optical forces using a double tweezers setup to obtain an entire curve of the force as a function of the three-dimensional displacement of the trapped particle, and not just the values of the force for fixed positions. The next grand contribution comes from the theoretical description of the optical force. The large difficulty in this aspect is the description of incident beams of great numerical aperture and its decomposition in partial waves. It is in this context that this thesis fits in. We believed to have given an extremely valuable contribution, solving in an analytical and exact way the problem of the decomposition of a convergent beam partial waves relative the any origin of the three dimensional coordinate systemDoutoradoFísicaDoutor em Ciência

Size-dependent optical forces on dielectric microspheres in hollow core photonic crystal fibers: erratum

The beam shape coefficients for cylindrical vector modes are of great importance for other researchers to reproduce our results, however they were accidentally reported incorrectly in our recently published manuscript [Opt. Express 30(14), 24407 (2022)]. This erratum reports the correct form for the two expressions. Two typographical errors in auxiliary equations are also reported and two labels in particle time of flight probability density function plots are fixed. (c) 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreemen

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.Comment: 6 pages, 3 figure

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

Rotational dynamics of optically trapped polymeric nanofibers

The optical trapping of polymeric nanofibers and the characterization of the rotational dynamics are reported. A strategy to apply a torque to a polymer nanofiber, by tilting the trapped fibers using a symmetrical linear polarized Gaussian beam is demonstrated. Rotation frequencies up to 10 Hz are measured, depending on the trapping power, the fiber length and the tilt angle. A comparison of the experimental rotation frequencies in the different trapping configurations with calculations based on optical trapping and rotation of linear nanostructures through a T-Matrix formalism, accurately reproduce the measured data, providing a comprehensive description of the trapping and rotation dynamics.Comment: (21 pages, 5 figures